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General Chemistry

A Free Online Textbook

Cover Graphic: A three-dimensional representation of an atomic 4f orbital

A three-dimensional representation of an atomic 4f orbital.

About General Chemistry

General Chemistry is an introduction to the basic concepts of chemistry, including atomic structure and bonding, chemical reactions, and solutions. Other topics covered include gases, thermodynamics, kinetics and equilibrium, redox, and chemistry of the elements.

It is assumed that the reader has basic scientific understanding. Otherwise, minimal knowledge of chemistry is needed prior to reading this book.

Beyond General Chemistry

  • Organic Chemistry - Chemistry studies focusing on the carbon atom and compounds.
  • Inorganic Chemistry - Chemistry studies focusing on salts, metals, and other compounds not based on carbon.
  • Biochemistry - Chemistry studies of or relating to living organisms.

About Wikibooks

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Authors and Significant Contributors


Chemistry is Everywhere

Chemistry: the study of the properties, composition, and transformation of matter.

The modern human experience places a large emphasis upon the material world. From the day of our birth to the day we die, we are frequently preoccupied with the world around us. Whether struggling to feed ourselves, occupying ourselves with modern inventions, interacting with other people or animals, or simply meditating on the air we breathe, our attention is focused on different aspects of the material world. In fact only a handful of disciplines—certain subsets of religion, philosophy, and abstract math—can be considered completely unrelated to the material world. Everything else is somehow related to chemistry, the scientific discipline which studies the properties, composition, and transformation of matter.

Branches of Chemistry

Chemistry itself has a number of branches:

  • Analytical chemistry seeks to determine the composition of substances.
  • Biochemistry is the study of chemicals found in living things (such as DNA and proteins).
  • Inorganic Chemistry studies substances that do not contain carbon.
  • Organic chemistry studies carbon-based substances. Carbon, as described in more detail in this book, has unique properties that allow it to make complex chemicals, including those of living organisms. An entire field of chemistry is devoted to substances with this element.
  • Physical chemistry is the study of the physical properties of chemicals, which are characteristics that can be measured without changing the composition of the substance.
This is the structure of table salt, or sodium chloride.

Chemistry as a discipline is based on a number of other fields. Because it is a measurement-based science, math plays an important role in its study and usage. A proficiency in high-school level algebra should be all that is needed in this text, and can be obtained from a number of sources. Chemistry itself is determined by the rules and principles of physics. Basic principles from physics may be introduced in this text when necessary.

Why Study Chemistry?

There are many reasons to study chemistry. It is one pillar of the natural sciences necessary for detailed studies in the physical sciences or engineering. The principles of biology and psychology are rooted in the biochemistry of the animal world, in ways that are only now beginning to be understood. Modern medicine is firmly rooted in the chemical nature of the human body. Even students without long-term aspirations in science find beauty in the infinite possibilities that originate from the small set of rules found in chemistry.

Chemistry has the power to explain everything in this world, from the ordinary to the bizarre. Why does iron rust? What makes propane such an efficient, clean burning fuel? How can soot and diamond be so different in appearance, yet so similar chemically? Chemistry has the answer to these questions, and so many more. Understanding chemistry is the key to understanding the world as we know it.

This Book: General Chemistry

An introduction to the chemical world is set forth in this text. The units of study are organized as follows.

  1. Properties of Matter: An explanation of the most fundamental concept in chemistry: matter.
  2. Atomic Structure: While technically in the domain of physics, atoms determine the behavior of matter, making them a necessary starting point for any discussion of chemistry.
  3. Compounds and Bonding: Chemical bonding is introduced, which explains how less than one hundred naturally-occurring elements can combine to form all the different compounds that fill our world.
  4. Chemical Reactions: Things get interesting once chemical reactions start making and breaking bonds.
  5. Aqueous Solutions: Substances dissolved in water have special properties. This is when acids and bases are introduced.
  6. Phases of Matter: A detailed look at the organization of substances, with particular focus on gases.
  7. Chemical Equilibria: Chemical reactions don't go on forever. Equilibrium is the balance that reactions seek to achieve.
  8. Chemical Kinetics: Kinetics explain why it takes years for an iron nail to rust, but only a split second for a hydrogen-filled hot air balloon to explode.
  9. Thermodynamics: Two things decide which reactions can occur and which reactions cannot: heat and chaos. Or enthalpy and entropy, as they are called in thermodynamics
  10. Chemistries of Various Elements: An exploration of the elements that make up all substance. Includes an introduction to nuclear chemistry and carbon, the essence of organic chemistry.

<< Begin Your Study of General Chemistry! >>


Basic Properties of Matter

What is Matter?

Matter has mass and volume, as exemplified by this concrete block.

Matter is defined as anything that occupies space and has mass. Anything that has mass must be 3-dimensional, which is why, however small atoms (the stuff that makes up matter) are, they are 3-dimensional.

Mass is a measure of an object's inertia. It is proportional to weight: the more mass an object has, the more weight it has. However, mass is not the same as weight. Weight is a force created by the action of gravity on a substance while mass is a measure of an object's resistance to change in motion. For example, your weight on the moon would be one-sixth your weight on the earth, as the moons gravitational field is one-sixth that of earth's. Mass is measured by comparing the substance of interest to a standard kilogram called the International Prototype Kilogram (IPK). The IPK is a metal cylinder for which the height and diameter both equal 39.17 millimeters and is made of an alloy of 90% platinum and 10% iridium. Thus, the standard kilogram is defined and all other masses are a comparison to this kilogram. When atom masses are measured in a mass spectrometer, a different internal standard is used. Your take home lesson with regard to mass is that mass is a relative term judged by a comparison.

Volume is a measure of the amount of space occupied by an object. Volume can be measured directly with equipment designed using graduations marks or indirectly using length measurements depending on the state (gas, liquid, or solid) of the material. A graduated cylinder, for example, is a tube that can hold a liquid which is marked and labeled at regular intervals, usually every 1 or 10 mL. Once a liquid is placed in the cylinder, one can read the graduation marks and record the volume measurement. Since volume changes with temperature, graduated equipment has limits to the precision with which one can read the measurement. Solid objects that have regular shape can have their volume calculated by measuring their dimensions. In the case of a box, its volume equals length times width times height.

It is particularly interesting to note that measuring is different from calculating a specific value. While mass and volume can both be determined directly relative to either a defined standard or line marks on glass, calculating other values from measurements is not considered measuring. For example, once you have measured the mass and volume of a liquid directly, one can then calculate the density of a substance by dividing the mass by the volume. This is considered indirectly determining density. Interestingly enough, one can also measure density directly if an experiment which allows the comparison of density to a standard is set up.

Another quantity of matter directly or indirectly determined is the amount of substance. This can either represent a counted quantity of objects (e.g. three mice or a dozen bagels) or the indirectly determined number of particles of a substance being dealt with such as how many atoms are contained in a sample of a pure substance. The latter quantity is described in terms of moles. One mole is specifically defined as the number of particles in 12 grams of the isotope Carbon-12. This number is 6.02214078(18)x 1023 particles.

Units of Measure
  • Mass: the kilogram (kg). Also, the gram (g) and milligram (mg).
    • 1 kg = 1000 g
    • 1000 mg = 1 g.
  • Volume: the liter (L), milliliter (mL). Also, cubic centimeters (cc) and cubic meters (m3).
    • 1 cc = 1 mL
    • 1000 mL = 1 L
    • 1000 L = 1 m3
  • Amount: the mole (mol).
    • 1 mol = 6.02214078(18)x 1023 particles

Atoms, Elements, and Compounds

The fundamental building block of matter is the atom.

The red dots are protons, the black dots are neutrons, and the blue dots are electrons.

Any atom is composed of a little nucleus surrounded by a "cloud" of electrons. In the nucleus there are protons and neutrons.

However, the term "atom" just refers to a building block of matter; it doesn't specify the identity of the atom. It could be an atom of carbon, or an atom of hydrogen, or any other kind of atom.

This is where the term "element" comes into play. When an atom is defined by the number of protons contained in its nucleus, chemists refer to it as an element. All elements have a very specific identity that makes them unique from other elements. For example, an atom with 6 protons in its nucleus is known as the element carbon. When speaking of the element fluorine, chemists mean an atom that contains 9 protons in its nucleus.

  • Atom: A fundamental building block of matter composed of protons, neutrons, and electrons.
  • Element: A uniquely identifiable atom recognized by the number of protons in the nucleus.

Despite the fact that we define an element as a unique identifiable atom, when we speak, for example, 5 elements, we don't usually mean those 5 atoms are of the same type (having the same number of protons in their nucleus). We mean 5 'types' of atoms. It is not necessary there are only 5 atoms. There may be 10, or 100, etc. atoms, but those atoms belong to one of 5 types of atoms. I'd rather define 'element' as 'type of atom'. I think it is more precise. If we'd like to refer to 5 atoms having the same 6 protons in their nucleus, I'd say '5 carbon atoms' or '5 atoms of carbon'.

It is important to note that if the number of protons in the nucleus of an atom changes, so does the identity of that element. If we could remove a proton from nitrogen (7 protons), it is no longer nitrogen. We would, in fact, have to identify the atom as carbon (6 protons). Remember, elements are unique and are always defined by the number of protons in the nucleus. The Periodic Table of the Elements shows all known elements organized by the number of protons they have.

An element is composed of the same type of atom; elemental carbon contains any number of atoms, all having 6 protons in their nuclei. In contrast, compounds are composed of different type of atoms. More precisely, a compound is a chemical substance that consists of two or more elements. A carbon compound contains some carbon atoms (with 6 protons each) and some other atoms with different numbers of protons.

Compounds have properties different from the elements that created them. Water, for example, is composed of hydrogen and oxygen. Hydrogen is an explosive gas and oxygen is a gas that fuels fire. Water has completely different properties, being a liquid that is used to extinguish fires.

The smallest representative for a compound (which means it retains characteristics of the compound) is called a molecule. Molecules are composed of atoms that have "bonded" together. As an example, the formula of a water molecule is "H2O": two hydrogen atoms and one oxygen atom.

Properties of Matter

Properties of matter can be divided in two ways: extensive/intensive, or physical/chemical.

  • Intensive properties do not depend on the amount of matter. These include boiling point and color.
  • Extensive properties depend on the amount of matter that is being measured. These include mass and volume.
  • Physical properties can be measured without changing the chemical's identity. The freezing point of a substance is physical. When water freezes, it's still H2O.
  • Chemical properties deal with how one chemical reacts with another. We know that wood is flammable because it becomes heat, ash, and carbon dioxide when heated in the presence of oxygen.

States of Matter

One important physical property is the state of matter. Three are common in everyday life: solid, liquid, and gas. The fourth, plasma, is observed in special conditions such as the ones found in the sun and fluorescent lamps. Substances can exist in any of the states. Water is a compound that can be liquid, solid (ice), or gas (steam).

The ice in this picture is a solid. The water in the picture is a liquid. In the air there is water vapor, which is a gas.
The states of matter depend on the bonding between molecules.


Solids have a definite shape and a definite volume. Most everyday objects are solids: rocks, chairs, ice, and anything with a specific shape and size. The molecules in a solid are close together and connected by intermolecular bonds. Solids can be amorphous, meaning that they have no particular structure, or they can be arranged into crystalline structures or networks. For instance, soot, graphite, and diamond are all made of elemental carbon, and they are all solids. What makes them so different? Soot is amorphous, so the atoms are randomly stuck together. Graphite forms parallel layers that can slip past each other. Diamond, however, forms a crystal structure that makes it very strong.


Liquids have a definite volume, but they do not have a definite shape. Instead, they take the shape of their container to the extent they are indeed "contained" by something such as beaker or a cupped hand or even a puddle. If not "contained" by a formal or informal vessel, the shape is determined by other internal (e.g. intermolecular) and external (e.g. gravity, wind, inertial) forces. The molecules are close, but not as close as a solid. The intermolecular bonds are weak, so the molecules are free to slip past each other, flowing smoothly. A property of liquids is viscosity, the measure of "thickness" when flowing. Water is not nearly as viscous as molasses, for example.


Gases have no definite volume and no definite shape. They expand to fill the size and shape of their container. The oxygen that we breathe and steam from a pot are both examples of gases. The molecules are very far apart in a gas, and there are minimal intermolecular forces. Each atom is free to move in any direction. Gases undergo effusion and diffusion. Effusion occurs when a gas seeps through a small hole, and diffusion occurs when a gas spreads out across a room. If someone leaves a bottle of ammonia on a desk, and there is a hole in it, eventually the entire room will reek of ammonia gas. That is due to the diffusion and effusion. These properties of gas occur because the molecules are not bonded to each other. The molecules in gas, are free and they can move around unlike solid molecules.

  • In gases, intermolecular forces are very weak, hence molecules move randomly colliding with themselves, and with the wall of their container, thus exerting pressure on their container. When heat is given out by gases, the internal molecular energy decreases; eventually, the point is reached when the gas liquifies.

Changes in Matter

There are two types of change in matter: physical change and chemical change. As the names suggest, physical changes never change the identity of the matter, only its size, shape or state. In a physical change, atoms are not rearranged and the matter's physical and chemical properties are unchanged. Chemical changes, on the other hand, rearrange the atoms of matter in new combinations, resulting in matter with new physical and chemical properties.

Chemical changes are also known as chemical reactions. The "ingredients" of a reaction are the reactants, and the end results are called the "products". The change from reactants to products can be signified by an arrow.Chemical changes are mostly irreversible

A Chemical Reaction

Reactants → Products

Note that the number of reactants and products don't necessarily have to be the same. However, the number of each type of atom must remain constant. This is called the Law of Conservation of Matter. It states that matter can never be created or destroyed, only changed and rearranged. If a chemical reaction begins with 17 moles of carbon atoms, it must end with 17 moles of carbon atoms. They may be bonded into different molecules, or in a different state of matter, but they cannot disappear.

When changes occur, energy is often transformed. However, like atoms, energy cannot disappear. This is called the Law of Conservation of Energy. A simple example would be putting ice cubes into a soft drink. The ice cubes get warmer as the drink gets colder, because energy cannot be created or destroyed, only transferred. Note that energy can be "released" or "stored" by making and breaking bonds. When a plant converts the energy from sunlight into food, that energy is stored in the chemical bonds within the sugar molecules.

Chemical change or Physical change?

Is blending together a smoothie a physical or chemical change?

Physical changes do not cause a substance to become a fundamentally different substance. Chemical changes, on the other hand, cause a substance to change into something entirely new. Chemical changes are typically irreversible, but that is not always the case. It is easier to understand the difference between physical and chemical changes with examples.

State changes are physical. Phase changes are when you melt, freeze, boil, condense, sublimate, or deposit a substance. They do not change the nature of the substance unless a chemical change occurs along with the physical change.
Cutting, tearing, shattering, and grinding are physical. These may be irreversible, but the result is still composed of the same molecules. When you cut your hair, that is a physical change, even though you can't put the hair back on your head again.
Mixing together substances is physical. For example, you could mix salt and pepper, dissolve salt in water, or mix molten metals together to produce an alloy.
Gas bubbles forming is chemical. Not to be confused with bubbles from boiling, which would be physical (a phase change). Gas bubbles indicate that a chemical reaction has occurred.
Precipitates forming is chemical. When dissolved substances are mixed, and a cloudy precipitate appears, there has been a chemical change.
Rotting, burning, cooking, and rusting (for example) are chemical. The resulting substances are entirely new chemical compounds. For instance, wood becomes ash and heat; iron becomes rust; sugar ferments into alcohol.
Changes of color or release of odors (i.e. release of a gas) might be chemical. As an example, the element chromium shows different colors when it is in different compounds, but a single chromium compound will not change color on its own without some sort of reaction.
Release/absorption of energy (heat, light, sound) is generally not easily categorized. Hot/cold packs involve dissolving a salt in water to change its temperature (more on that in later chapters); popping popcorn is mostly physical (but not completely).

Classification of Matter

Matter can be classified by its state.

  • Solids have a set volume and shape.The inter molecular force of attraction for solid matter is very strong.
  • Liquids have a set volume, but change shape. The inter molecular force of attraction for liquid matter is weaker than solid matter.
  • Gases have neither definite volume nor shape. The inter molecular force of attraction for gaseous matter is negligible.
  • Plasma which are usually gaseous state of matter in which a part or all of the atoms or molecules are dissociated to form ions.
  • Einstein Bose Condensate (EBC) is a theoretical state of matter. The inter molecular force of attraction for EBC is so strong that the molecules cannot move whatsoever.

Matter can also be classified by its chemical composition.

  • An element is a pure substance made up of atoms with the same number of protons. As of 2011, 118 elements have been observed, 92 of which occur naturally. Carbon (C), Oxygen (O), Hydrogen (H) are examples of elements. The periodic table is a tabular representation of the known elements.
  • A compound consists of two or more chemical elements that are chemically bonded together. Water (H2O) and table sugar (C12H22O11) are examples of chemical compounds. The ratio of the elements in a compound is always the same. For example in water, the number of H atoms is always twice the number of O atoms.
  • A mixture consists of two or more substances (element or compound) mixed together without any chemical bond. Salad is a good example. A mixture can be separated into its individual components by mechanical means.

Types of Mixtures

There are many kinds of mixtures. They are classified by the behavior of the phases, or substances that have been mixed.

Homogeneous Mixtures

Soda water is a homogeneous mixture. (The straw looks broken because of refraction.)

A homogeneous mixture is uniform, which means that any given sample of the mixture will have the same composition. Air, sea water, and carbonation dissolved in soda are all examples of homogeneous mixtures, or solutions. No matter what sample you take from the mixture, it will always be composed of the same combination of phases. Chocolate chip ice cream is not homogeneous—one spoonful taken might have two chips, and then another spoonful might have several chips.

An example for a homogeneous mixture is a solution. The substance that gets dissolved is the solute. The substance that does the dissolving is the solvent. Together they make a solution. If you stir a spoonful of salt into a glass of water, salt is the solute that gets dissolved. Water is the solvent. The salty water is now a solution, or homogeneous mixture, of salt and water.

When different gases are mixed, they always form a solution. The gas molecules quickly spread out into a uniform composition.

Heterogeneous Mixtures

A heterogeneous mixture is not uniform. Different samples may have different compositions, like the example of chocolate chip ice cream. Concrete, soil, blood, and salad are all examples of heterogeneous mixtures.

This dust is a suspension because it settles after the work is done.


When sand gets kicked up in a pond, it clouds the water. It has a greater mass than water hence it sinks to the bottom and settles down, and is no longer mixed into the water. This is an example of a suspension. Suspensions are heterogeneous mixtures that will eventually settle. They are usually, but not necessarily, composed of phases in different states of matter. Italian salad dressing has three phases: the water, the oil, and the small pieces of seasoning. The seasonings are solids that will sink to the bottom, and the oil and water are liquids that will separate.


Toothpaste is a colloid, because it's part solid and part liquid.

What exactly is toothpaste? We can't exactly classify it by its state of matter. It has a definite shape and volume, like a solid. But then you squeeze the tube, and it flows almost like a liquid. And then there's jelly, shaving cream, smoke, dough, and Silly Putty...

These are examples of colloids. A colloid is a heterogeneous mixture of two substances of different phases. Shaving cream and other foams are gas dispersed in liquid. Jello, toothpaste, and other gels are liquid dispersed in solid. Dough is a solid dispersed in a liquid. Smoke is a solid dispersed in a gas.

Colloids consist of two phases: a dispersed phase inside of a continuous medium.

The Tyndall Effect

The Tyndall effect distinguishes colloids from solutions. In a solution, the particles are so fine that they will not scatter light. This is not true for a colloid. If you shine light through a solution, the beam of light will not be visible. It will be visible in a colloid. For instance, if you have ever played with a laser pointer, you have seen the Tyndall effect. You cannot see the laser beam in air (a solution), but if you shine it into a mist, the beam is visible. Clouds look white (or gray), as opposed to blue, because of the Tyndall effect - the light is scattered by the small droplets of suspended water.

Methods for Separating Mixtures

Filtration is one way to separate a mixture.

Because there is no chemical bonding in a mixture, the phases can be separated by mechanical means. In a heterogeneous mixture like a salad, the pieces can easily be picked out and separated. It is as simple as sifting through the salad and picking out all the tomatoes and radishes, for example. However, many mixtures contain particles that are too small, liquids, or too many particles to be separated manually. We must use more sophisticated methods to separate the mixture.


Imagine you have a sandbox, but there are bits of broken glass in it. All you would need is some sort of filter. The sand particles are much smaller than the glass chips, so a mesh filter would let sand pass but stop the glass. Filtration is used in all sorts of purification methods. Some filters, like dialysis tubing, are such fine filters that water can pass, but dissolved glucose cannot.


A distillation apparatus has a boiling flask, a place to cool the vapor down, and a collecting flask.

If you were given a glass of saltwater, could you drink it? Sure, if you distill it first. Distillation is the boiling of a mixture to separate its phases. Salt is a solid at room temperature, and water is a liquid. Water will boil far before salt even begins to melt. So separating the two is as simple as boiling the water until all that remains is the solid salt. If desired, the water vapor can be collected, condensed, and used as a source of pure water.

Distillation can also be used if two liquids are mixed but have different boiling points. Separation of several liquids with similar boiling points can be achieved using fractionation.

Centrifugation and Sedimentation

Sedimentation is used to purify waste water, by letting it settle and removing the settled material (sludge, in this case).

These processes rely on differences in density. In a medical lab, blood often goes into a centrifuge. A centrifuge is a machine that spins a sample at fairly high rates of speed. Red blood cells are much denser than the watery substance (called plasma, but it's not the plasma state of matter) that makes up blood. As a result of the spinning, the denser phases move outward and the less dense phases move inward, towards the axis of rotation. Then, the red blood cells can be separated from the plasma.

Sedimentation is similar, but it happens when particles of different densities have settled within a liquid. If a jar of muddy water is left to settle, the heaviest particles sink to the bottom first. The lightest particles sink last and form a layer on top the heavier particles. You may have seen this effect in a bottle of salad dressing. The seasonings sink to the bottom, the water forms a lower layer, and the oil forms an upper layer. The separate phases can be skimmed out. To return it to a mixture, simply shake it up to disturb the layers.

Unique Properties

Chromatography separates things dissolved in liquid.

The differences in substances' properties can be exploited to allow separation. Consider these examples:

  • A mixture of sand and iron filings can be separated by magnet.
  • Salt and sand can be separated by solution (sand will not dissolve in water, salt will)
  • Helium can be separated from a mixture with hydrogen by combustion (this is a very dangerous operation, since hydrogen in the presence of oxygen is highly explosive). Hydrogen is flammable, but helium is not.

Other methods

There are countless other ways to separate mixtures. For instance, gel electrophoresis is used to separate different sized pieces of DNA. They are placed into gel, and an electric current is applied. The smaller pieces move faster and separate from the larger pieces.

Chromatography separates phases dissolved in liquid. If you want to see an example, take a strip of paper and draw a dot on it with a colored marker. Dip the strip into water, and wait a while. You should see the ink separate into different colors as they spread out from the dot.

Numbers Used to Describe Atoms


If the red parts are protons and the green parts are neutrons, what's the atomic, neutron, and mass number of this atom? (lithium)

The Atomic number is the number of protons in the nucleus of an atom. This number determines the element type of the atom. For instance, all neon atoms have exactly ten protons. If an atom has ten protons, then it must be neon. If an atom is neon, then it must have ten protons.

The atomic number is sometimes denoted Z. Continuing with the example of neon, .

The Neutron number is the number of neutrons in the nucleus of an atom. Remember that neutrons have no electric charge, so they do not affect the chemistry of an element. However, they do affect the nuclear properties of the element. For instance, Carbon-12 has six neutrons, and it is stable. Carbon-14 has eight neutrons, and it happens to be radioactive. Despite these differences, both forms of carbon behave the same way when forming chemical compounds.

The neutron number is sometimes denoted N.

The Mass number is the sum of protons and neutrons in an atom. It is denoted A. To find the mass number of an atom, remember that A = Z + N. The mass number of an atom is always an integer. Because the number of neutrons can vary among different atoms of the same element, there can be different mass numbers of a given element. Look back to the example of carbon. Carbon-14 has a mass number of 14, and Carbon-12 has a mass number of 12. Every carbon atom must have six protons, so Carbon-14 has eight neutrons and Carbon-12 has six neutrons.

Isotopes of the same element have nearly identical chemical properties (because they have the same number of protons and electrons). Their only difference is the number of neutrons, which changes their nuclear properties like radioactivity.


There is a convenient way of writing the numbers that describe atoms. It is easiest to learn by examples.

Helpful Hint!
Keep in mind that any of the three numbers written around the element symbol are optional, but they should be written if it is important to the given situation. The charge number is left off if the atom has zero charge (equal number of protons and electrons). The mass number and atomic number are usually left off.
This is how we write fluorine-19. The atomic number is below and the mass number is above, followed by its symbol on the periodic table of the elements.
This example shows carbon-12. Notice how the atomic number is missing. You know which element it is because of the C, so there is no need to write the number of protons. The atomic number is rarely written because the element symbol implies how many protons there are.
The last example shows both the atomic number and mass number, along with a charge. The charge is the difference in the number of protons compared to the number of electrons. You can read more about charge, protons, and electrons later on. From the example, you can see that this magnesium atom would have 12 protons, 13 neutrons, and 10 electrons. Its mass is 25 (12 p + 13 n) and its charge is +2 (12 p - 10 e).
Exercise for the reader!

Try writing the symbol for an atom with seven protons, seven neutrons, and eight electrons. You will need to look up its symbol on the periodic table.

Atomic Mass

The mass of an atom is measured in atomic mass units (amu). An atom's mass can be found by summing the number of protons and neutrons. By definition, 12 amu equals the atomic mass of carbon-12. Protons and neutrons have an approximate mass of 1 amu, and electrons have a negligible mass.

Usually, a pure element is made up of a number of isotopes in specific ratios. Because of this, the measured atomic mass of carbon is not exactly 12. It is an average of all the masses of all the isotopes, with the more common ones contributing more to the measured atomic mass. By convention atomic masses are given no units.


Pretend that the element Wikibookium has two isotopes. The first has a mass number of 104, and the second has a mass number of 107. Considering that 75% of the naturally occurring atoms are of the first isotope, and the rest are of the second. The average atomic mass is calculated as

0.75 × 104 + 0.25 × 107 = 104.75

In this case, a bunch of Wikibookium atoms would have an average mass of 104.75 amu, but each individual atom might have a mass number of 104 or 107. Keep in mind that all of the atoms would have the same number of protons. Their masses are different because of the number of neutrons.

== Moles == mole is defined as the amount of an element whose number of particles are equal to that in 12g of C-12 carbon, also known as Avogadro's number. Avogadro's number equals 6.022 × 1023. Moles are not very confusing: if you have a dozen atoms, you would have 12. If you have a mole of atoms, you would have 6.022 × 1023. Why is this ridiculously large number important? It can be used to convert between atomic mass units and grams. One mole of carbon-12 is exactly 12 grams, by definition. Similarly, one mole of any element is the atomic mass of that element expressed as a weight in grams. The atomic mass is equal to the number of grams per mole of that element.


There are 128.2 g of rubidium (atomic mass = 85.47 amu). How many atoms are there?

(128.2 g) / (85.47 g/mol) = 1.5 mol
(1.5 mol) × (6.022 × 1023) = 9.03 × 1023 atoms of rubidium

These one-liter containers each hold 0.045 moles of nitrogen-based gas. (1 L) / (22.4 L/mol) = 0.045 mol

Moles are also important because every 22.4 liters of gas contain 1 mole of gas molecules at standard temperature and pressure (STP, 0 °C and 1 atmosphere of pressure). Avogadro discovered this. (That's why it's his number.) A container filled with fluorine gas would have to be 22.4 L large to hold one mole of F2 molecules. Knowing this fact allows you to determine the mass of a gas molecule if you know the volume of the container. This holds true for every gas.

Why every single gas? Atoms and molecules are tiny. The volume of a gas is mostly empty space, so the molecules have an insignificantly small volume. As you will eventually learn, this ensures that there is always one mole of gas atoms for every 22.4 liters at STP.

Atomic Structure

History of Atomic Structure

Why Is The History Of The Atom So Important?

It is fundamental to the understanding of science that science is understood to be a process of trial and improvement and represents the best known at the time, not an unerring oracle of truth. Development of an idea and refinement through testing is shown more in the understanding of atomic structure.

The Greek Theorists

A bust of Democritus (or Democrites), who came up with the idea of indivisible atoms.

The earliest known proponent of anything resembling modern atomic theory was the ancient Greek thinker Democritus. He proposed the existence of indivisible atoms as a response to the arguments of Parmenides and the paradoxes of Zeno.

Parmenides argued against the possibility of movement, change, and plurality on the premise that something cannot come from nothing. Zeno attempted to prove Parmenides' point by a series of paradoxes based on difficulties with infinite divisibility.

In response to these ideas, Democritus posited the existence of indestructible atoms that exist in a void. Their indestructibility provided a retort to Zeno, and the void allowed him to account for plurality, change, and movement. It remained for him to account for the properties of atoms, and how they related to our experiences of objects in the world.

Democritus proposed that atoms possessed few actual properties, with size, shape, and mass being the most important. All other properties, he argued, could be explained in terms of the three primary properties. A smooth substance, for instance, might be composed of primarily smooth atoms, while a rough substance is composed of sharp ones. Solid substances might be composed of atoms with numerous hooks, by which they connect to each other, while the atoms of liquid substances possess far fewer points of connection.

Democritus proposed 5 points to his theory of atoms. [1] These are:

  1. All matter is composed of atoms, which are bits of matter too small to be seen. These atoms CANNOT be further split into smaller portions.
  2. There is a void, which is empty space between atoms.
  3. Atoms are completely solid.
  4. Atoms are homogeneous, with no internal structure.
  5. Atoms are different in their size, their shape, and their weight.


Although alchemy was futile, the alchemists did come up with several useful methods, including distillation (shown here).
A fire, shown by Lavoisier to be a chemical reaction and not an element.

Empedocles proposed that there were four elements, air, earth, water, and fire and that everything else was a mixture of these. This belief was very popular in the medieval ages and introduced the science of alchemy. Alchemy was based on the belief that since everything was made of only four elements, you could transmute a mixture into another mixture of the same type. For example, it was believed that lead could be made into gold.

Alchemy's problem was exposed by Antoine Lavoisier when he heated metallic tin in a sealed flask. A grayish ash appeared on the surface of the melting tin, which Lavoisier heated until no more ash formed. After the flask cooled, he inverted it and opened it underwater. He discovered the water rose one-fifth of the way into the glass, leading Lavoisier to conclude that air itself is a mixture, with one-fifth of it having combined with the tin, yet the other four-fifths did not, showing that air was not an element.

Lavoisier repeated the experiment again, substituting mercury for tin, and found that the same happened. Yet after heating gently, he found that the ash released the air, showing that the experiment could be reversed. He concluded that the ash was a compound of the metal and oxygen, which he proved by weighing the metal and the ash, and showing that their combined weight was greater than that of the original metal.

Lavoisier then stated that combustion was not an element, but instead was a chemical reaction of a fuel and oxygen.

John Dalton

Modern atomic theory was born with Dalton when he published his theories in 1803. His theory consists of five important points, which are considered to be mostly true today: (from Wikipedia)

  • Elements are composed of tiny particles called atoms.
  • All atoms of a given element are identical.
  • The atoms of a given element are different from those of any other element; the atoms of different elements can be distinguished from one another by their respective relative weights.
  • Atoms of one element can combine with atoms of other elements to form chemical compounds; a given compound always has the same relative numbers of types of atoms.
  • Atoms cannot be created, divided into smaller particles, nor destroyed in the chemical process; a chemical reaction simply changes the way atoms are grouped together.

We now know that elements have different isotopes, which have slightly different weights. Also, nuclear reactions can divide atoms into smaller parts (but nuclear reactions aren't really considered chemical reactions). Otherwise, his theory still stands today.

Dmitri Mendeleev

In the late 1800's, Russian scientist Dmitri Mendeleev was credited with creating one of the first organized periodic tables. Organizing each element by atomic weight, he cataloged each of the 56 elements discovered at the time. Aside from atomic weight, he also organized his table to group the elements according to known properties.

While writing a series of textbooks, Mendeleev realized he was running out of space to treat each element individually. He began to regularly "linewrap" the elements onto the next line, and create what is now called the periodic table of the elements. Using his table, he predicted the existence of later-discovered elements, such as "eka-aluminum" and "eka-silicon" (gallium and germanium) according to patterns found earlier. His predictions were a success, proving his table to be exceptionally accurate. Later theories, those of the electrons around the atom, explain why elements in the same period, or group, have similar chemical properties. Chemists would later organise each element by atomic number, not atomic weight, giving rise to the modern Periodic Table of Elements.

J.J. Thomson

Discovery of the Electron

Cathode rays are actually made of electrons.

In the year 1889 the British physicist J.J. Thomson discovered the electron. Thomson conducted a number of experiments using cathode ray tube. Cathode rays are constructed by sealing two electrodes in a glass tube connected to a voltage supplier and a vacuum pump removing the air from it. When the electrodes are attached to high voltage of about 15000v and low pressure, a beam of radiation is emitted from the negative electrode(cathode)moving towards the positive electrode(anode). These beams are said to be green rays called cathode rays. (1) The ray is said to be taken towards Faraday's tube(gold leaf electroscope) and was charged by induction and deflect positively charged gold leaf electroscope (2) a freely moving paddle wheel was placed on the path of the rays and it was able to move it suggesting that it has momentum (3) The ray was placed in a magnetic and electric field moving towards the north and positive pole respectively Thomson discovered that cathode rays travel in straight lines except, when they are bent by electric or magnetic fields. The cathode rays bent away from a negatively charged plate, Thomson concluded that these rays are made of negatively charged particles; today we call them electrons. Thomson found that he could produce cathode rays using electrodes of various materials. He then concluded that electrons were found in all atoms and are over a thousand times smaller than protons. Thompson used an apparatus to determine the charge to mass ratio(e/m)after the ray emerge he placed a magnetic field of a known magnetic influence and the rays bent towards the north to a particular position then he added an electric field to return the ray back to it original position and recorded the charges used by the electric field so he divided them to get the ratio of about -1.7*10^8kg

The "Plum Pudding" Atomic Model

Soon after the discovery of the electron, Thomson began speculating on the nature of the atom. He suggested a "plum pudding" model. In this model the bits of "plum" were the electrons which were floating around in a "pudding" of positive charge to match that of the electrons and make an electrically neutral atom. A modern illustration of this idea would be a chocolate chip cookie, with the chips representing negatively charged electrons and the dough representing positive charge.


The results of the gold foil experiment disproved the "plum pudding" model: the alpha particles should have passed through (top), but a few of them deflected at large angles (bottom).

Ernest Rutherford is known for his famous gold foil experiment in 1911. Alpha particles, which are heavy and positively charged (actually, helium nuclei, but that's beside the point), were fired at a very thin layer of gold. Most of the alpha particles passed straight through, as expected. According to the plum pudding model all of the particles should have slowed as they passed through the "pudding", but none should have been deflected. Surprisingly, a few alpha particles were deflected back the way they came. He stated that it was "as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

The result of the experiment allowed Rutherford to conclude that the plum pudding model is wrong.

  • Atoms have a nucleus, very small and dense, containing the positive charge and most of the atom's mass.
  • The atom consists of mostly empty space.
  • The electrons are attracted to the nucleus, but remain far outside it.

Niels Bohr

The Bohr model of the atom has shells with numbered spherical energy levels - the larger numbers mean larger spheres and higher energy levels. The wave exiting the picture on the left has come from an electron jump, resulting in a photon. (Level sizes not to scale.)

Bohr created his own model of the atom, improving on Rutherford's. Bohr used an equation developed by Rydberg that provided a mathematical relationship between the visible spectral lines of the hydrogen atom. The equation requires that the wavelengths emitted from the hydrogen atom be related to the difference of two integers. Bohr theorized that these integers represent "shells" or "orbits" in which electrons travel around the nucleus, each with a certain energy level. The energy of an orbit is proportional to its distance from the nucleus. An atom will absorb and release photons that have a specific amount of energy. The energy is the result of an electron jumping to a different shell. Starting with Rydberg's equation, along with Planck and Einstein's work on the relationship between light and energy, Bohr was able to derive an equation to calculate the energy of each orbit in the hydrogen atom. The Bohr model depicts the atom as a nucleus with electrons orbiting around it at specific distances. This model is also referred to as the Planetary Model.

Robert Millikan

Robert Millikan is credited for the "Oil Drop Experiment", in which the value of the electron charge was determined. He created a mechanism where he could spray oil drops that would settle into a beam of X rays. The beam of X rays caused the oil drops to become charged with electrons. The oil droplets were in between a positively charged plate and a negatively charged plate which, when proper electric voltage was applied, caused the oil droplet to remain still. Robert Millikan measured the diameter of each individual oil drop using a microscope.

Millikan was able to calculate the mass of each oil droplet because he knew the density of the oil (). Using the mass of each oil droplet and the equation for the force of gravitational attraction (which he rearranged from to , where is the mass of each individual oil droplet, is the acceleration due to gravity, and is the electrical force which equals force in the first equation), Millikan was able to find the value of the charge of the electron, .

The X rays, however, did not always produce an oil drop with only one negative charge. Thus, the values Millikan obtained may have looked like this:

  • coulomb
  • coulomb
  • coulomb
  • coulomb

Millikan found that these values all had a common divisor: coulomb. He concluded that different values occurred because the droplets acquired charges of -5, -4, -3, and -2, as in this example. Thus, he stated that the common divisor, coulomb, was the charge of the electron.



Subatomic Particles

Particle Properties

Before learning about subatomic particles, some basic properties should be understood.


Particles may be electrically charged. Charge is a property which defines the force that a particle will exert on other charged particles. There is a well known saying that applies perfectly: "Opposites attract." (Likewise, like charges repel.) Positive charges and negative charges will attract each other and come together. Two positive or two negative charges will push each other away.

Helpful Hint!
Not all particles have charge.

The amount of charge a particle has is measured in coulombs, but it is more conveniently expressed in terms of an integer. For instance, a helium ion that has 2 less electrons than usual has a charge of +2, and a bromide ion with one more electron than usual has a charge of -1. (This may seem backwards, but remember that an electron has a negative charge.) Notice that charge not only applies to subatomic particles, but also ions and other things as well. Always remember to specify if a charge is positive or negative. Unlike ordinary numbers, we always write the plus sign for positive charges to avoid confusion with a negative charge.


Mass is the measure of inertia. From a subatomic point of view, mass can also be understood in terms of energy, but that does not concern us when dealing with chemistry. Mass for particles, atoms, and molecules is not measured in grams, as with ordinary substances. Instead, it is measured in atomic mass units, or amu. For more information about mass and amu, read the previous chapters on properties of matter.

The Nucleus

An atom (not to scale!)

At the center of each atom lies the nucleus. It is incredibly small: if you were to take the average atom (itself miniscule in size) and expand it to the size of a football stadium, then the nucleus would be about the size of a marble. It is, however, astoundingly dense: despite the tiny percentage of the atom's volume it contains nearly all of the atom's mass. The nucleus almost never changes under normal conditions, remaining constant throughout chemical reactions. Nuclei are themselves made up of a pair of smaller and more dense particles, the proton and the neutron. These particles are collectively dubbed nucleons.


Protons have a charge of +1 and a mass of 1 amu. They are often represented by a .

Protons will be important when learning about acids and bases—they are the essence of acid. Remember that the number of protons in an atom is its atomic number, and defines what element it will be. The number of protons in a nucleus ranges from one to over a hundred.

Consider the element hydrogen. Its atomic number is 1, so it has one proton and one electron. If it is made into an ion (an atom with missing or extra electrons), it will simply be a lone proton. Thus, a proton is the nucleus of a hydrogen atom, and a proton is a hydrogen ion. Therefore, a proton can be written as or , both symbols for a hydrogen ion.


Neutrons have no charge and a mass of 1 amu. A neutron is slightly heavier than a proton, but the difference is insignificant. Neutrons are often written .

Our friends the physicists say that neutrons and protons are made of even smaller particles called quarks. Fortunately, we don't need to know about that because quarks do not affect chemistry. Instead, quarks fall in the field of Quantum Mechanics.

Unlike the protons, neutrons cannot exist outside the nucleus indefinitely as they become unstable and break down. Within one nucleus there can be many protons and neutrons all in close proximity to one another. The number of neutrons in a nucleus ranges from zero to over a hundred.

You may wonder why neutrons exist. They have no charge, so can they do anything? The answer is yes—neutrons are very important. Remember that opposites attract and likes repel. If so, then how can several protons stay clumped together in the dense nucleus of an atom? It would seem as if the protons would repel and scatter the nucleus. However, there is a strong nuclear force that holds the nucleus together. This incredible force causes nucleons to attract each other with much greater strength than the electric force can repel them, but only over extremely short distances.

A delicate balance exists between the number of protons and neutrons. Protons, which are attracted to one another via the strong force but simultaneously repelled by their electromagnetic charges, cannot exist in great numbers within the nucleus without the stabilizing action of neutrons, which are attracted via the strong force but are not charged. Conversely, neutrons lend their inherent instability to the nucleus and too many will destabilize it.

Lastly, neutrons are very important in nuclear reactions, such as those used in power plants. Neutrons act like a bullet that can split an atom's nucleus. Because they have no charge, neutrons are neither attracted nor repelled by atoms and ions.

The Electron Cloud

Surrounding the dense nucleus is a cloud of electrons. Electrons have a charge of -1 and a mass of 0 amu. That does not mean they are massless. Electrons do have mass, but it is so small that it has no effect on the overall mass of an atom. An electron has approximately 1/1800 the mass of a proton or neutron. Electrons are written .

Electrons orbit the outside of a nucleus, unaffected by the strong nuclear force. They define the chemical properties of an atom because virtually every chemical reaction deals with the interaction or exchange of the outer electrons of atoms and molecules.

Electrons are attracted to the nucleus of an atom because they are negative and the nucleus (being made of protons and neutrons) is positive. Opposites attract. However, electrons don't fall into the nucleus. They orbit around it at specific distances because the electrons have a certain amount of energy. That energy prevents them from getting too close, as they must maintain a specific speed and distance. Changes in the energy levels of electrons cause different phenomena such as spectral lines, the color of substances, and the creation of ions (atoms with missing or extra electrons).

Electron Interactions

Atoms will always have equal numbers of protons and electrons, so their overall charge is zero. Atoms are neutral. Ions, on the other hand, are atoms that have gained or lost electrons and now have an unequal number of protons and electrons. If there are extra electrons, the ion will be negatively charged. If there are missing electrons, the ion will be positively charged, due to the majority of positive protons.

Valence electrons (the outermost electrons) are responsible for an atom's behavior in chemical bonds. The core electrons are all of the electrons not in the outermost shell, and they rarely get involved. An atom will attempt to fill its valence shell. This occurs when an atom has eight valence electrons (as explained in the next chapter), so atoms will undergo chemical bonds to either share, give, or take the electrons it needs. Sodium, for example, is very likely to give up its one valence electron, so that its outer shell is empty (the shell underneath it is full). Chlorine is very likely to take an electron because it has seven and wants eight. When sodium and chlorine are mixed, they exchange electrons and create sodium chloride (table salt). As a result, both elements have full valence shells, and a very stable compound is formed.

Introduction to Quantum Theory

Introduction to Quantum Mechanics

In the late 19th century, many physicists believed that they had made great progress in physics, and there wasn't much more that needed to be discovered. The classical physics at the time was widely accepted in the scientific community. However, by the early 20th century, physicists discovered that the laws of classical mechanics break down in the atomic world, and experiments such as the photoelectric effect completely contradict the laws of classical physics. As a result of these crises, physicists began to construct new laws of physics which would apply to the atomic world; these theories would be collectively known as quantum mechanics. Quantum mechanics, in some ways, completely changed the way physicists view the universe, and it also marked the end of the idea of a clockwork universe (the idea that the universe was predictable).

Electromagnetic Radiation

Electromagnetic radiation (ER) is a form of energy that sometimes acts like a wave, and other times acts like a particle. Visible light is a well-known example. All forms of ER have two inversely proportional properties: wavelength and frequency. Wavelength is the distance from one wave peak to the next, which can be measured in meters. Frequency is the number of wave peaks observed in a given point during a second. The unit for frequency is hertz.

Since wavelength and frequency are inversely related, their product (multiplication) always equals a constant — specifically, 3.0 x 108 m/sec represented by the letter c, which is better known as the speed of light. This relationship is written mathematically as , with the greek letter λ (lambda) representing wavelength and the letter representing frequency.

The wavelength and frequency of any specific occurrence of ER determine its position on the electromagnetic spectrum.

As you can see, visible light is only a tiny fraction of the spectrum.

The energy of a single particle of an electromagnetic wave (called a photon) is given by , where is Plank's constant and is the frequency. Energy is directly proportional to frequency — doubling the frequency will double the energy.

The Discovery of the Quantum

As photons strike a metal, electrons are freed. The photoelectric effect depends only on the light's frequency, not intensity, which defies wave behavior.

So far we have only discussed the wave characteristics of energy. However, the wave model cannot account for something known as the photoelectric effect. This effect is observed when light focused on certain metals apparently causes electrons to be emitted. (Photoelectric or solar panels work on this principle.)

For each metal it was found that there is a minimum frequency of electromagnetic radiation that is needed to be shone on it in order for it to emit electrons. This conflicted with the earlier thought that the energy of light was linked only to its intensity. Under that theory, the effect of light should be cumulative - dim light should add up, little by little, until it causes electrons to be emitted. Instead, there is a clear-cut minimum of the frequency of light that triggers the electron emissions.

The implication of this is that the energy of light is tied to frequency, and furthermore that it is quantized, meaning that it carries "packets" of energy in discrete amounts. These packets are more commonly referred to as photons. This observation led to the discovery of the minimum amount of energy that could be gained or lost by an atom. Max Planck named this minimum amount the quantum, plural "quanta", meaning "how much". One photon of light carries exactly one quantum of energy.

The Quantum Model


Werner Heisenberg (1927)

It turns out that photons are not the only thing that act like waves and particles. Electrons, too, have this characteristic, known as wave-particle duality. Electrons can be thought of as waves of a certain length, thus they would only be able to form a circle around the nucleus at certain distances that are multiples of the wavelength. Of course, this brings up a problem: are electrons particles in a specific location, or waves in a general area? Werner Heisenberg tried using photons to locate electrons. Of course, when photons reach electrons, the electrons change velocity, and move to an excited state. As a result, it is impossible to precisely measure the velocity and location of an electron at the same time. This is known as the observer effect. This is frequently confused with the Heisenberg Uncertainty Principle, which goes even further, saying that there are limits to the degree to which both the position and momentum of a particle can even be known. This is due to the fact that electrons cannot exhibit both their wave and particle properties at the same time when being observed to interact with their surroundings. The momentum of an electron is proportional to its velocity, but based on its wave properties; its position is based on its particle position in space. The Heisenberg uncertainty principle is a kind of scientific dilemma: the more you know about something's velocity, the less you know about its position; and the more you know about its position, the less you know about its velocity. The significance of this uncertainty is that you can never know exactly where an atom's electrons are, only where they are most likely to be.

A wave forming a circle

On the tiny scale of an atom, the particle model of an electron does not accurately describe its properties. An electron tends to act more like a water wave than a billiard ball. At any one moment in time the ball is in some definite place; it is also moving in some definite direction at a definite speed. This is certainly not true for waves or electrons in general. The Heisenberg uncertainty principle states that the exact position and momentum of an electron cannot be simultaneously determined. This is because electrons simply don't have a definite position, and direction of motion, at the same time!

One way to try to understand this is to think of an electron not as a particle but as a wave. Think of dropping a stone into a pond. The ripples start to spread out from that point. We can answer the question "Where is the wave?" with "It's where you plonked the stone in". But we can't answer the question "What direction is the wave moving?" because it's moving in all directions. It's spreading out. Now think of a wave at the seaside. We know the direction of motion. It's straight in towards the beach. But where is the wave? We can't pinpoint an exact location. It's all along the water.

The Wave Function

Think of the wave equation like a sprinkler—you cannot predict the exact path of a particular water droplet, but you do know (based on the range and shape of the sprinkler) where it is most likely to go.

If we can never know exactly where an electron is, then how do we know about the way they orbit atoms? Erwin Schrödinger developed the Quantum Mechanical model, which describes the electron's behavior in a given system. It can be used to calculate the probability of an electron being found at a given position. You don't know exactly where the electron is, but you know where it is most likely and least likely to be found. In an atom, the wave function can be used to model a shape, called an orbital, which contains the area an electron is almost certain to be found inside.


In the following sections, we will learn about the shells, subshells, and orbitals that the electrons are in. Try not to get confused; it can be difficult. Understanding this information will help you to learn about bonding, which is very important.

Each electron orbiting in an atom has a set of four numbers that describe it. Those four numbers, called quantum numbers, describe the electron's orbit around the nucleus. Each electron in an atom has a unique set of numbers, and the numbers will change if the electron's orbit is altered. Examples are if bonding occurs, or an electron is energized into a higher-energy orbit. In the next chapter, we will learn the meaning of those four values.

The Quantum Atom

The Quantum Numbers

These four numbers are used to describe the location of an electron in an atom.

Number Symbol Possible Values
Principal Quantum Number
Angular Momentum Quantum Number
Magnetic Quantum Number
Spin Quantum Number

Principal Quantum Number (n)

Determines the shell the electron is in. The shell is the main component that determines the energy of the electron (higher n corresponds to higher energy), as well as size of the orbital, corresponding to maximum nuclear distance (higher n means further possible distance from the nucleus). The row that an element is placed on the periodic table tells how many shells there will be. Helium (n = 1), neon (n = 2), argon (n = 3), etc. Note that the shells will have different numbers, as described by the table above; for example, argon will contain the , , and subshells, for that total of 3.

Angular Momentum Quantum Number (l)

Also known as azimuthal quantum number. Determines the subshell the electron is in. Each subshell has a unique shape and a letter name. The s orbital is shaped like a sphere and occurs when l = 0. The p orbitals (there are three) are shaped like teardrops and occur when l = 1. The d orbitals (there are five) occur when l = 2. The f orbitals (there are seven) occur when l = 3. (By the way, when l = 4, the orbitals are "g orbitals", but they (and the l = 5 "h orbitals") can safely be ignored in general chemistry.). The numbers of the subshells in each shell can be calculated using the principal quantum number like so. For example, in the shell, the subshells are an subshell, and 3 subshells. You will learn how to determine the number of orbitals for each subshells in the next section.

This number also gives information as to what the angular node of an orbital is. A node is defined as a point on a standing wave where the wave has minimal amplitude. When applied to chemistry this is the point of zero-displacement and thus where no electrons are found. In turn angular node means the planar or conical surface in which no electrons are found or where there is no electron density. The models shown on this page show the most simple representations of these orbitals and their nodes. More accurate, but more complex depictions are not necessary for the scope of this book.

Here are pictures of the orbitals. Keep in mind that they do not show the actual path of the electrons, due to the Heisenberg Uncertainty Principle. Instead, they show the volume where the electron is most likely to occur, i.e. the probability amplitude is largest. The two colors represent two signs (phases) of the wave function (the choice is arbitrary). Each of the depicted orbitals is a superposition of two opposite m quantum numbers (see below).

ml 0 -1 and 1 -2 and 2 -3 and 3
S orbital →
P orbitals →
D orbitals →
F orbitals →

Magnetic Quantum Number (ml)

ml -3 -2 -1 0 1 2 3
S orbital →
P orbitals →
D orbitals →
F orbitals →

Magnetic quantum number determines the orbital in which the electron lies. The number of orbitals in each subshell can be calculated like so: . ml determines how rapidly the complex phase increases around the z-axis. Without magnetic field, these orbitals all have the same energy, they are degenerate and can be combined into different shapes and spatial orientations. The orbitals in a subshell with degeneracy are called degenerate orbitals. This simply means that the orbitals in each p subshell all have the same energy level. The difference in shapes as well as orientation of higher subshells is not important during general chemistry, and the orbitals in the same higher subshells are still degenerate regardless of shape differences.

Spin Quantum Number (ms)

Does not determines the spin on the electron. +½ corresponds to the up arrow in an electron configuration box. If there is only one electron in an orbital (one arrow in one box), then it is always considered +½. The second arrow, or down arrow, is considered -½. Every orbital can contain one "spin up" electron, and one "spin down" electron.

Some Examples

Let's examine the quantum numbers of electrons from a magnesium atom, 12Mg. Remember that each list of numbers corresponds to (n, l, ml, ms).

Two s electrons: (1, 0, 0, +½) (1, 0, 0, -½)
Two s electrons: (2, 0, 0, +½) (2, 0, 0, -½)
Six p electrons: (2, 1, -1, +½) (2, 1, -1, -½) (2, 1, 0, +½) (2, 1, 0, -½) (2, 1, 1, +½) (2, 1, 1, -½)
Two s electrons: (3, 0, 0, +½) (3, 0, 0, -½)

The Periodic Table

Notice a pattern on the periodic table. Different areas, or blocks, have different types of electrons. The two columns on the left make the s-block. The six columns on the right make the p-block. The large area in the middle (transition metals) makes the d-block. The bottom portion makes the f-block (Lanthanides and Actinides). Each row introduces a new shell (aka energy level). Basically, the row tells you how many shells of electrons there will be, and the column tells you which subshells will occur (and which shells they occur in). The value of ml can be determined by some of the rules we will learn in the next chapter. The value of ms doesn't really matter as long as there are no repeating values in the same orbital.

Shells and Orbitals

Electron shells

Each shell is subdivided into subshells, which are made up of orbitals, each of which has electrons with different angular momentum. Each orbital in a subshell has a characteristic shape, and is named by a letter. They are: s, p, d, and f. In a one-electron atom (e.g. H, He+, Li+2, etc.) the energy of each orbital within a particular shell is identical. However, when there are multiple electrons, they interact and split the orbitals into slightly different energies. The letters s, p, d and f specify the subshells (angular quantum number l) and the orbital is specified by the magnetic quantum number m. The angular and magnetic quantum numbers relate to the magnitude and direction of the electron's angular momentum, respectively. Within any particular subshell, the energy of the orbitals depends on the angular momentum of orbitals s, p, d, and f in order of lowest to highest energy.

This image shows the orbitals (along with hybrid orbitals for bonding and a sample electron configuration, explained later).

The s subshell

The simplest subshell in the atom is the 1s subshell. It has no radial or angular nodes: the 1s subshell is simply a sphere of electron density. A node is a point where the electron positional probability is zero. As with all subshell the number of radial nodes increases with the principle quantum number (i.e. the 2s orbital has one radial node, the 3s has two etc.). Because the angular momentum quantum number is 0, there is only one choice for the magnetic quantum number - there is only one s orbital per shell. The s orbital can hold two electrons, as long as they have different spin quantum numbers. S orbitals are involved in bonding.

The p subshell

Starting from the 2nd shell, there is a set of p subshell. The angular momentum quantum number of the electrons confined to p subshell is 1, so each orbital has one angular node. There are 3 choices for the magnetic quantum number, which indicates 3 differently oriented p subshell. Finally, each orbital can accommodate two electrons (with opposite spins), giving the p orbitals a total capacity of 6 electrons.

The orbital of p subshell all have two lobes of electron density pointing along each of the axes. Each one is symmetrical along its axis. The notation for the orbitals of p subshell indicate which axis it points down, i.e. px points along the x axis, py on the y axis and pz up and down the z axis. Note that although pz corresponds to the ml = 0 orbital, px and py are actually mixtures of ml = -1 and ml = 1 orbitals. The p orbitals are degenerate — they all have the same energy. P orbitals are very often involved in bonding.

2px 2py 2pz

The d subshell

The first set of d orbitals is the 3d set. The angular momentum quantum number is 2, so each orbital has two angular nodes. There are 5 choices for the magnetic quantum number, which gives rise to 5 different d orbitals. Each orbital can hold two electrons (with opposite spins), giving the d orbitals a total capacity of 10 electrons.

Note that all the d orbitals have four lobes of electron density, except for the dz2 orbital, which has two opposing lobes and a doughnut of electron density around the middle. The d orbitals can be further subdivided into two smaller sets. The dx2-y2 and dz2 all point directly along the x, y, and z axes. They form an eg set. On the other hand, the lobes of the dxy, dxz and dyz all line up in the quadrants, with no electron density on the axes. These three orbitals form the t2g set. In most cases, the d orbitals are degenerate, but sometimes they can split, with the eg and t2g subsets having different energy. Crystal Field Theory predicts and accounts for this. D orbitals are sometimes involved in bonding, especially in inorganic chemistry.

The f subshell

The first set of f orbitals is the 4f subshell. There are 7 possible magnetic quantum numbers, so there are 7 f orbitals. Their shapes are fairly complicated, and they rarely come up when studying chemistry. There are 14 f electrons because each orbital can hold two electrons (with opposite spins).

Filling Electron Shells

Filling Electron Shells

When an atom or ion receives electrons into its orbitals, the orbitals and shells fill up in a particular manner.

Aufbau principle

You may consider an atom as being "built up" from a naked nucleus by gradually adding to it one electron after another, until all the electrons it will hold have been added. Much as one fills up a container with liquid from the bottom up, the orbitals of an atom are filled from the lowest energy orbitals to the highest energy orbitals.

Orbitals with the lowest principal quantum number () have the lowest energy and will fill up first, in smaller atoms. Larger atoms with more subshells will seem to fill "out of order", as the other factors influencing orbital energy become important. Within a shell, there may be several orbitals with the same principal quantum number. In that case, more specific rules must be applied. For example, the three p orbitals of a given shell all occur at the same energy level. So, how are they filled up? Answer: all the three p orbitals have same energy so while filling the p orbitals we can fill any one of the Px, Py or Pz first. It is a convention that we chose to fill Px first, then Py and then Pz for our simplicity. Hence you can opt for filling these three orbitals from right to left also. Aufbau principle state that “atomic orbitals are filled with electrons in order of increasing energy level”.

Hund's Rule

According to Hund's rule, orbitals of the same energy are each filled with one electron before filling any with a second. Also, these first electrons have the same spin.

This rule is sometimes called the "bus seating rule". As people load onto a bus, each person takes his or her own seat, sitting alone. Only after all the seats have been filled will people start doubling up.

Pauli Exclusion principle

No two electrons can have all four quantum numbers the same. What this translates to in terms of our picture of orbitals is that each orbital can only hold two electrons, one "spin up" (+½) and one "spin down" (-½).

This animation demonstrates the Aufbau principle, Hund's Rule, and the Pauli Exclusion principle.

Orbital Order

1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, 8s.

Although this looks confusing, there is an easy way to remember. Go in order of the lines from top to bottom, top right end to bottom left of each line.

Understanding the above rules and diagrams will allow you to determine the electron configuration of almost any atom or ion.

How to Write the Electron Configuration of an Isolated Atom

Electron-configuration notation is relatively straightforward. An isolated Calcium atom 20Ca, for example, would have configuration of 1s22s22p63s23p64s2 in its ground state. Other configurations like 1s22s22p63s23p64s14p1 are possible, but these excited states have a higher energy. They are not stable and generally only exist for a brief moment.

The ground state configuration for Ca could be abbreviated by using the preceding noble gas (the elements found all the way on the right of the periodic table) as [Ar]4s2, where Ar is argon.

Noble gases have very stable configurations, and are extremely reluctant to lose or gain electrons. Noble gas atoms are also the only ones regularly found as isolated atoms in the ground state. Atoms of other elements all undergo bonding under the conditions that we live under and this affects the orbitals that the outermost electrons are in. In that sense the electron configurations for the other elements are somewhat hypothetical: to encounter an isolated atom of, say, tungsten (W), we would have to first vaporize a metal that boils at 5800K. However, knowing atomic configurations is useful because it does help us to understand how and why they bond, i.e. why and how they change the configuration of their outer valence electrons.

Rule of Stability

A subshell is particularly stable if it is half full or full. Given two configurations, the atom would "choose" the more stable one.

Example: In the following configuration, Cu: [Ar]4s23d9, copper's d shell is just one away from stability, and therefore, one electron from the s shell jumps into the d shell: [Ar]4s13d10. This way, the d shell is full, and is therefore stable, and the s shell is half full, and is also stable.

Another example: Chromium has a configuration of [Ar]4s13d5, although you would expect to see four d electrons instead of five. This is because an s electron has jumped into the d orbital, giving the atom two half-full shells—much more stable than a d orbital with only four electrons.

The stability rule applies to atoms in the same group as chromium and copper.

If one of these atoms has been ionized, that is, it loses an electron, it will come from the s orbital rather than the d orbital. For instance, the configuration of Cu+ is [Ar]4s03d10. If more electrons are removed, they will come from the d orbital.


The spin of an electron creates a magnetic field (albeit ridiculously weak), so unpaired electrons create a small magnetic field. Paired electrons have opposite spin, so the magnetic fields cancel each other out, leading to diamagnetism.

Magnetism is a well-known effect. Chances are, you have magnets on your refrigerator. As you already know, only certain elements are magnetic. Electron configurations help to explain why.

Diamagnetism is actually a very weak repulsion to magnetic fields. All elements have diamagnetism to some degree. It occurs when there are paired electrons.

Paramagnetism is an attraction to external magnetic fields. It is also very weak. It occurs whenever there is an unpaired electron in an orbital.

Both diamagnetism and paramagnetism are responses of spins acting independently from each other. This leads to rather weak repulsion and attraction respectively. However, when they are located in a solid they may also interact with each other and respond collectively and that can lead to rather different properties:

Ferromagnetism is the permanent magnetism that we encounter in our daily lives. It occurs when all the unpaired spins in a solid couple and tend to align themselves in the same direction, leading to a strong attraction when exposed to a magnetic field. This only occurs at room temperature with three elements: iron (Fe), nickel (Ni), and cobalt (Co). Gadolinium (Gd) is a borderline case. It loses its ferromagnetism at 20oC; above that temperature the spins start to act alone. However, there are many alloys and compounds that exhibit strong ferromagnetic coupling. The strongest one is Nd2Fe14B

Antiferromagnetism is also a permanent magnetism in which unpaired spins align, but they do so in opposite directions. The result that the material does not react very strongly to a magnetic field at all. Chromium (Cr) is an example.

'Ferrimagnetism is a combination of ferro- and antiferromagetism. Unpaired spins align partly in opposite directions, but the compensation is not complete. This is why the material is still attracted strongly to a magnetic field. Magnetite Fe3O4 is such a substance. It was the first material studied for its magnetic properties and may, well, be the one sitting on your fridge.

Periodicity and Electron Configurations

Blocks of the Periodic Table

The Periodic Table does more than just list the elements. The word periodic means that in each row, or period, there is a pattern of characteristics in the elements. This is because the elements are listed in part by their electron configuration. The Alkali metals and Alkaline earth metals have one and two valence electrons (electrons in the outer shell) respectively. These elements lose electrons to form bonds easily, and are thus very reactive. These elements are the s-block of the periodic table. The p-block, on the right, contains common non-metals such as chlorine and helium. The noble gases, in the column on the right, almost never react, since they have eight valence electrons, which makes it very stable. The halogens, directly to the left of the noble gases, readily gain electrons and react with metals. The s and p blocks make up the main-group elements, also known as representative elements. The d-block, which is the largest, consists of transition metals such as copper, iron, and gold. The f-block, on the bottom, contains rarer metals including uranium. Elements in the same Group or Family have the same configuration of valence electrons, making them behave in chemically similar ways.

Organization of Subshells

Causes for Trends

Potassium has many core electrons; the lone outer electron can easily be peeled off due to the "shielding" effect.

There are certain phenomena that cause the periodic trends to occur. You must understand them before learning the trends.

Effective Nuclear Charge

The effective nuclear charge is the amount of positive charge acting on an electron. It is the number of protons in the nucleus minus the number of electrons in between the nucleus and the electron in question. The nucleus attracts the electron, but other electrons in lower shells repel it (opposites attract, likes repel).

Shielding Effect

The shielding (or screening) effect is similar to effective nuclear charge. The core electrons repel the valence electrons to some degree. The more electron shells there are (a new shell for each row in the periodic table), the greater the shielding effect is. Essentially, the core electrons shield the valence electrons from the positive charge of the nucleus.

Electron-Electron Repulsions

When two electrons are in the same shell, they will repel each other slightly. This effect is mostly canceled out due to the strong attraction to the nucleus, but it does cause electrons in the same shell to spread out a little bit. Lower shells experience this effect more because they are smaller and allow the electrons to interact more.

Coulomb's Law

Coulomb's law is an equation that determines the amount of force with which two charged particles attract or repel each other. It is , where is the amount of charge, is the distance between charges, and is a constant. For atoms, the charges are typically described as integer multiples (positive for protons, negative for electrons) of the elementary charge , which is 1.6022 x 10-19 coulombs. You can see that doubling the distance would quarter the force.

Trends in the Periodic table

Most of the elements occur naturally on Earth. However, all elements beyond uranium (number 92) are called trans-uranium elements and never occur outside of a laboratory. Most of the elements occur as solids or gases at STP. STP is standard temperature and pressure, which is 0° C and 1 atmosphere of pressure. There are only two elements that occur as liquids at STP: mercury (Hg) and bromine (Br).

Bismuth (Bi) is the last stable element on the chart. All elements after bismuth are radioactive and decay into more stable elements. Some elements before bismuth are radioactive, however.

Atomic Radius

Leaving out the noble gases, atomic radii are larger on the left side of the periodic chart and are progressively smaller as you move to the right across the period. As you move down the group, radii increase.

Atomic radii decrease along a period due to greater effective nuclear charge. Atomic radii increase down a group due to the shielding effect of the additional core electrons, and the presence of another electron shell.

Ionic Radius

For nonmetals, ions are bigger than atoms, as the ions have extra electrons. For metals, it is the opposite.

Extra electrons (negative ions, called anions) cause additional electron-electron repulsions, making them spread out farther. Fewer electrons (positive ions, called cations) cause fewer repulsions, allowing them to be closer.

Ionization Energy

Ionization energy is also a periodic trend within the periodic table organization. Moving left to right within a period or upward within a group, the first ionization energy generally increases. As the atomic radius decreases, it becomes harder to remove an electron that is closer to a more positively charged nucleus.

Ionization energy decreases going left across a period because there is a lower effective nuclear charge keeping the electrons attracted to the nucleus, so less energy is needed to pull one out. It decreases going down a group due to the shielding effect. Remember Coulomb's Law: as the distance between the nucleus and electrons increases, the force decreases at a quadratic rate.

Periodic trend for ionization energy. Each period begins at a minimum for the alkali metals, and ends at a maximum for the noble gases.

It is considered a measure of the tendency of an atom or ion to surrender an electron, or the strength of the electron binding; the greater the ionization energy, the more difficult it is to remove an electron. The ionization energy may be an indicator of the reactivity of an element. Elements with a low ionization energy tend to be reducing agents and form cations, which in turn combine with anions to form salts.

Electron Affinity

Electron affinity is the energy released when an electron is added to an atom, producing a negative ion.

Electron affinity is highest in the upper left, lowest on the bottom right. However, electron affinity is actually negative for the noble gasses. They already have a complete valence shell, so there is no room in their orbitals for another electron. Adding an electron would require creating a whole new shell, which takes energy instead of releasing it. Several other elements have extremely low electron affinities because they are already in a stable configuration, and adding an electron would decrease stability.

Electron affinity occurs due to the same reasons as ionization energy.


Electronegativity is how much an atom attracts electrons within a bond. It is measured on a scale with fluorine at 4.0 and francium at 0.7. Electronegativity decreases from upper right to lower left.

Electronegativity decreases because of atomic radius, shielding effect, and effective nuclear charge in the same manner that ionization energy decreases.

Metallic Character

Metallic elements are shiny, usually gray or silver colored, and good conductors of heat and electricity. They are malleable (can be hammered into thin sheets), and ductile (can be stretched into wires). Some metals, like sodium, are soft and can be cut with a knife. Others, like iron, are very hard. Non-metallic atoms are dull, usually colorful or colorless, and poor conductors. They are brittle when solid, and many are gases at STP. Metals give away their valence electrons when bonding, whereas non-metals take electrons.

The metals are towards the left and center of the periodic table—in the s-block, d-block, and f-block . Poor metals and metalloids (somewhat metal, somewhat non-metal) are in the lower left of the p-block. Non-metals are on the right of the table.

Metallic character increases from right to left and top to bottom. Non-metallic character is just the opposite. This is because of the other trends: ionization energy, electron affinity, and electronegativity.

Octet Rule and Exceptions

The octet rule refers to the tendency of atoms to prefer to have eight electrons in the valence shell (outer orbital). When atoms have fewer than eight electrons, they tend to react and form more stable compounds. When discussing the octet rule, we do not consider d or f electrons. Only the s and p electrons are involved in the octet rule, making it useful for the representative elements (elements not in the transition metal or inner-transition metal blocks). An octet corresponds to an electron configuration ending with s2p6.


Atoms will react to get in the most stable state possible. A complete octet is very stable because all orbitals will be full. Atoms with greater stability have less energy, so a reaction that increases the stability of the atoms will release energy in the form of heat or light. Reactions that decrease stability must absorb energy, getting hotter.

The other tendency of atoms is to maintain a neutral charge. Only the noble gases (the elements on the right-most column of the periodic table) have zero charge with filled valence octets. All of the other elements have a charge when they have eight electrons all to themselves. The result of these two guiding principles is the explanation for much of the reactivity and bonding that is observed within atoms: atoms seek to share electrons in a way that minimizes charge while fulfilling an octet in the valence shell.


The formula for table salt is NaCl. It is the result of Na+ ions and Cl- ions bonding together. If sodium metal and chlorine gas mix under the right conditions, they will form salt. The sodium loses an electron, and the chlorine gains that electron. In the process, a great amount of light and heat is released. The resulting salt is mostly unreactive — it is stable. It won't undergo any explosive reactions, unlike the sodium and chlorine that it is made of.

Why? Referring to the octet rule, atoms attempt to get a noble gas electron configuration, which is eight valence electrons. Sodium has one valence electron, so giving it up would result in the same electron configuration as neon. Chlorine has seven valence electrons, so if it takes one it will have eight (an octet). Chlorine has the electron configuration of argon when it gains an electron.

The octet rule could have been satisfied if chlorine gave up all seven of its valence electrons and sodium took them. In that case, both would have the electron configurations of noble gasses, with a full valence shell. However, their charges would be much higher. It would be Na7- and Cl7+, which is much less stable than Na+ and Cl-. Atoms are more stable when they have no charge, or a small charge.


There are few exceptions to the octet rule.

Two Electrons

The main exception to the rule is hydrogen, which is at its lowest energy when it has two electrons in its valence shell. Helium (He) is similar in that it, too, only has room for two electrons in its only valence shell.

Hydrogen and helium have only one electron shell. The first shell has only one s orbital and no p orbital, so it holds only two electrons. Therefore, these elements are most stable when they have two electrons. You will occasionally see hydrogen with no electrons, but H+ is much less stable than hydrogen with one or two electrons.

Lithium, with three protons and electrons, is most stable when it gives up an electron.

Less Than an Octet

Other notable exceptions are aluminum and boron, which can function well with six valence electrons. Consider BF3. The boron shares its three electrons with three fluorine atoms. The fluorine atoms follow the octet rule, but boron has only six electrons. Although atoms with less than an octet may be stable, they will usually attempt to form a fourth bond to get eight electrons. BF3 is stable, but it will form BF4- when possible. Most elements to the left of the carbon group have so few valence electrons that they are in the same situation as boron: they are electron deficient. Electron deficient elements often show metallic rather than covalent bonding.

More Than an Octet

In Period 3, the elements on the right side of the periodic table have empty d orbitals. The d orbitals may accept electrons, allowing elements like sulfur, chlorine, silicon and phosphorus to have more than an octet. Compounds such as PCl5 and SF6 can form. These compounds have 10 and 12 electrons around their central atoms, respectively.

Xenon hexafluoride uses d-electrons to form more than an octet. This compound shows another exception: a noble gas compound.

Even palladium has 18 electrons in its valence shell

Odd Numbers

Some elements, notably nitrogen, have an odd number of electrons and will form somewhat stable compounds. Nitric oxide has the formula NO. No matter how electrons are shared between the nitrogen and oxygen atoms, there is no way for nitrogen to have an octet. It will have seven electrons instead. A molecule with an unpaired electron is called a free radical and radicals are highly reactive, so reactive that many of them only exist for a fraction of a second. As radicals go, NO and NO2 are actually remarkably stable. At low temperatures NO2 does react with itself to form N2O4, its dimer, that is not a radical.

Nitrogen dioxide has an unpaired electron. (Note the positive charge above the N).

Compounds and Bonding

Overview of Bonding

Introduction to Bonding

Put simply, chemical bonding join atoms together to form more complex structures (like molecules or crystals). Bonds can form between atoms of the same element, or between atoms of different elements. There are several types of chemical bonding which have different properties and give rise to different structures.

In many cases, atoms try to react to form valence shells containing eight electrons. The octet rule describes this, but it also has many exceptions

  • Ionic bonding occurs between positive ions (cations) and negative ions (anions). In an ionic solid, the ions arrange themselves into a rigid crystal lattice. NaCl (common salt) is an example of an ionic substance. In ionic bonding there is an attractive force established between large numbers of positive cations and negative anions, such that a neutral lattice is formed. This attraction between oppositely-charged ions is collective in nature and called ionic bonding.
  • Covalent bonds are formed when the orbitals of two non-metal atoms physically overlap and share electrons with each other. There are two types of structures to which this can give rise: molecules and covalent network solids. Methane (CH4) and water (H2O) are examples of covalently bonded molecules, and glass is a covalent network solid.
  • Metallic bonding occur between atoms that have few electrons compared to the number of accessible orbitals. This is true for the vast majority of chemical elements. In a metallically bonded substance, the atoms' outer electrons are able to freely move around - they are delocalised to form an 'electron pool'. Iron is a metallically bonded substance.

Chemical bonding is one of the most crucial concepts in the study of chemistry. In fact, the properties of materials are basically defined by the type and number of atoms they contain and how they are bonded together.

So far, you have seen examples of intramolecular bonds. These bonds connect atoms into molecules or whole crystals. There are also intermolecular bonds that connect molecules into large substances. These are also called intermolecular forces, or IMF. IMF are weaker than intramolecular bonds, and as they do not permanently join two molecules or ions, it is generally considered incorrect to refer to them as bonds. Sometimes, a substance will not have both IMF and intramolecular bonds. In the case of ionic crystals (like salt) or covalent networks (like diamond), the solid is made out of a network of intramolecular bonds connecting all the component atoms or ions in a repeating pattern, with no separate units to be attracted to each other by IMF. In the case of metallic bonding, the atoms are all interconnected into one large piece of metal, but the electrons move freely rather than being confined to the static bonds of a crystal lattice or covalent network.


What determines the type of bond formed between two elements? There are two ways of classifying elements to determine the bond formed: by electronegativity, or by metallic/non-metallic character.


Electronegativity is a property of atoms that is reflected in the layout of the periodic table of the elements. Electronegativity is greatest in the elements in the upper right of the table (e.g., fluorine), and lowest in the lower left (e.g., francium).

Electronegativity is a relative measure of how strongly an atom will attract the electrons in a bond. Although bonds are the result of atoms sharing their electrons, the electrons can be shared unequally. The more electronegative atom in a bond will have a slight negative charge, and the less electronegative atom will have a slight positive charge. Overall, the molecule may have no charge, but the individual atoms will. This is a result of the electronegativity—by attracting the electrons in a bond, an atom gains a slight negative charge. Of course, if two elements have equal electronegativity, they will share the electrons equally.

Linus Pauling created a commonly-used measure of electronegativity.

Metallic elements have low electronegativity, and non-metallic elements have high electronegativity. If two elements are close to each other on the periodic table, they will have similar electronegativities.

Electronegativity is measured on a variety of scales, the most common being the Pauling scale. Created by chemist Linus Pauling, it assigns 4.0 to fluorine (the highest) and 0.7 to francium (the lowest).


When drawing diagrams of bonds, we indicate covalent bonds with a line. We may write the electronegativity using the symbols and . Look at this example.

Hydrogen fluoride (HF):

The plus goes over the less electronegative atom. From the above diagram, we can see that the fluorine attracts the electrons in the covalent bond more than the hydrogen does. Fluorine will have a slight negative charge because of this, and hydrogen will have a slight positive charge. Overall, hydrogen fluoride is neutral.

Ionic Bonding

What are ions?

Ions are atoms or molecules which are electrically charged. Cations are positively charged and anions carry a negative charge. Ions form when atoms gain or lose electrons. Since electrons are negatively charged, an atom that loses one or more electrons will become positively charged; an atom that gains one or more electrons becomes negatively charged.

Description of Ionic Bonding

Ionic bonding is the attraction between positively- and negatively-charged ions. These oppositely charged ions attract each other to form ionic networks (or lattices). Electrostatics explains why this happens: opposite charges attract and like charges repel. When many ions attract each other, they form large, ordered, crystal lattices in which each ion is surrounded by ions of the opposite charge. Generally, when metals react with non-metals, electrons are transferred from the metals to the non-metals (this is because metals tend to have relatively low ionization energy and non-metals tend to have high electron affinity). The metals form positively-charged ions and the non-metals form negatively-charged ions. The smallest unit of an ionic compound is the formula unit, but this unit merely reflects that ratio of ions that leads to neutrality of the whole crystal, e.g. NaCl or MgCl2. One cannot distinguish individual NaCl or MgCl2 molecules in the structure.

It is however possible that the stacking consists of molecular ions like NH4+ and NO3- in ammonium nitrate. In such structures, the ions are charged molecules rather than charged atoms.

The ions arrange themselves into a lattice where each ion is surrounded by ions of the opposite type.
An example of both atomic (Li+) and molecular (NO3-) ions

Ionic bonding may also be referred to as electrovalent bonding.


Example ionic compounds: Sodium chloride (), potassium nitrate ().

Ionically bonded substances typically have the following characteristics.

  • High melting point (solid at room temperature)
  • Hard but brittle (can shatter)
  • Many dissolve in water
  • Conductors of electricity when dissolved or melted

In general the forces keeping the lattice together depend on the product of the charges of the ions it consists of. A comparison e.g. of NaCl (+1)*(-1) to MgO (+2)*(-2) shows that magnesium oxide is kept together much more strongly -roughly 4 times- than sodium chloride. This is why sodium chloride has a much lower melting point and also dissolves much more easily in a solvent like water than magnesium oxide does.


Ionic compound dissolved in a polar solvent, in this case water. (not to scale)

Most ionic compounds are soluble in polar solvents. Polar solvents are simply solvents that have molecules with positive and negative poles. The most common example of a polar solvent is water (H2O).

The reason that they are soluble in polar solvents is because the positive ions are attracted to the negative pole of the solvent and the negative ions are attracted to the positive pole of the solvent. Due to this, the ionic compound dissociates or splits in the solvent into its constituent ions.

For example, H2O is composed of relatively more positive hydrogen atoms and relatively more negative oxygen atoms. When an ionic compound like NaCl is added to the water, the positive ions will be attracted to the more negative oxygen atoms and negative ions will be attracted to the more positive hydrogen atoms.

This is a very useful property of many ionic compounds, but not all, as there are exceptions where certain compounds cannot be dissolved in certain polar solvents.


For a substance to conduct electricity, there must be some carrier of charge. For example, in metals, what transports the charge is the mobile electrons surrounding the positive ions.

However, in the solid state, ionic compounds lack any mobile particle capable of carrying charge as the ions cannot move within the lattice because the electrostatic force holding them in place is extremely strong. This changes when the compound is dissolved or molten. When dissolved, the ions dissociate and are capable of moving around. The same is true for molten ionic compounds. Which is why molten and dissolved ionic compounds can conduct electricity, while solid ionic compounds cannot.


The electron transfer between Na and Cl.

Ionic bonding occurs when metals and non-metals chemically react. As a result of its low ionization energy, a metal atom is not destabilized very much if it loses electrons to form a complete valence shell and becomes positively charged. As its affinity is rather large, a non-metal is stabilized rather strongly by gaining electrons to complete its valence shell and become negatively charged. When metals and non-metals react, the metals lose electrons by transferring them to the non-metals, which gain them. The total process -a small loss plus a large gain- leads to a net lowering of the energy. Consequently, ions are formed, which instantly attract each other leading to ionic bonding.

For instance, in the reaction of Na (sodium) and Cl (chlorine), each Cl atom takes one electron from a Na atom. Therefore each Na becomes a Na+ cation and each Cl atom becomes a Cl- anion. Due to their opposite charges, they attract each other and are joined by millions and millions of other ions to form an ionic lattice. The lattice energy that results from this massive collective stacking further stabilizes the new compound. The formula (ratio of positive to negative ions) in the lattice is NaCl, i.e. there are equal numbers of positive and negative charges ensuring neutrality.

The charges must balance because otherwise the repulsion between the majority charges would become prohibitive. In the case of magnesium chloride, the magnesium atom gives up two electrons to become stable. Note that it is in the second group, so it has two valence electrons. The chlorine atom can only accept one electron, so there must be two chlorine ions for each magnesium ion. Therefore, the formula for magnesium chloride is MgCl2. If magnesium oxide were forming, the formula would be MgO because oxygen can accept both of magnesium's electrons.

Exercise for the reader

Try figuring out what the formula for magnesium nitride would be. Use the periodic table to help.

It should also be noted that some atoms can form more than one ion. This usually happens with the transition metals. For instance Fe (iron) can become Fe2+ (called iron(II) or -by an older name- ferrous). Fe can also become Fe3+ (called iron(III) or -sometimes still- ferric).

Common Ions

Ionic bonding typically occurs in reactions between a metal and non-metal, but there are also certain molecules called polyatomic ions that undergo ionic bonding. Within these polyatomic ions, there can be covalent (or polar) bonding, but as a unit it undergoes ionic bonding. There are countless polyatomic ions, but you should be familiar with the most common ones. You would be well advised to memorize these ions.

Name Formula Name Formula
Ammonium NH4+ Hydronium H3O+
Peroxide O22- Hydroxide OH-
Nitrite NO2- Nitrate NO3-
Sulfite SO32- Sulfate SO42-
Hydrogen sulfite HSO3- Phosphate PO43-
Hypochlorite ClO- Chlorite ClO2-
Chlorate ClO3- Perchlorate ClO4-
Carbonate CO32- Hydrogen carbonate HCO3-

Covalent Bonds

Covalent bonds create molecules, which can be represented by a molecular formula. For chemicals such as a basic sugar (C6H12O6), the ratios of atoms have a common multiple, and thus the empirical formula is CH2O. Note that a molecule with a certain empirical formula is not necessarily the same as one with the same molecular formula.

Formation of Covalent Bonds

Covalent bonds form between two atoms which have incomplete octets — that is, their outermost shells have fewer than eight electrons. They can share their electrons in a covalent bond. The simplest example is water (H2O). Oxygen has six valence electrons (and needs eight) and the hydrogens have one electron each (and need two). The oxygen shares two of its electrons with the hydrogens, and the hydrogens share their electrons with the oxygen. The result is a covalent bond between the oxygen and each hydrogen. The oxygen has a complete octet and the hydrogens have the two electrons they each need.

When atoms move closer, their orbitals change shape, letting off energy. However, there is a limit to how close the atoms get to each other—too close, and the nuclei repel each other.

One way to think of this is a ball rolling down into a valley. It will settle at the lowest point. As a result of this potential energy "valley", there is a specific bond length for each type of bond. Also, there is a specific amount of energy, measured in kilojoules per mole (kJ/mol) that is required to break the bonds in one mole of the substance. Stronger bonds have a shorter bond length and a greater bond energy.

The Valence Bond Model

One useful model of covalent bonding is called the Valence Bond model. It states that covalent bonds form when atoms share electrons with each other in order to complete their valence (outer) electron shells. They are mainly formed between non-metals.

An example of a covalently bonded substance is hydrogen gas (H2). A hydrogen atom on its own has one electron—it needs two to complete its valence shell. When two hydrogen atoms bond, each one shares its electron with the other so that the electrons move about both atoms instead of just one. Both atoms now have access to two electrons: they become a stable H2 molecule joined by a single covalent bond.

Diagram of a covalent bond between hydrogen atoms

Double and Triple Bonds

Covalent bonds can also form between other non-metals, for example chlorine. A chlorine atom has 7 electrons in its valence shell—it needs 8 to complete it. Two chlorine atoms can share 1 electron each to form a single covalent bond. They become a Cl2 molecule.

Oxygen can also form covalent bonds, however, it needs a further 2 electrons to complete its valence shell (it has 6). Two oxygen atoms must share 2 electrons each to complete each other's shells, making a total of 4 shared electrons. Because twice as many electrons are shared, this is called a 'double covalent bond'. Double bonds are much stronger than single bonds, so the bond length is shorter and the bond energy is higher.

Furthermore,, nitrogen has 5 valence electrons (it needs a further 3). Two nitrogen atoms can share 3 electrons each to make a N2 molecule joined by a 'triple covalent bond'. Triple bonds are stronger than double bonds. They have the shortest bond lengths and highest bond energies.

Electron Sharing and Orbitals

Carbon, contrary to the trend, does not share four electrons to make a quadruple bond. The reason for this is that the fourth pair of electrons in carbon cannot physically move close enough to be shared. The valence bond model explains this by considering the orbitals involved.

Recall that electrons orbit the nucleus within a cloud of electron density (orbitals). The valence bond model works on the principle that orbitals on different atoms must overlap to form a bond. There are several different ways that the orbitals can overlap, forming several distinct kinds of covalent bonds.

The Sigma Bond

The first and simplest kind of overlap is when two s orbitals come together. It is called a sigma bond (sigma, or σ, is the Greek equivalent of 's'). Sigma bonds can also form between two p orbitals that lie pointing towards each other. Whenever you see a single covalent bond, it exists as a sigma bond. When two atoms are joined by a sigma bond, they are held close to each other, but they are free to rotate like beads on a string.

The electron density is in between the two atoms in an σ bond.

The Pi Bond

The second, and equally important kind of overlap is between two parallel p orbitals. Instead of overlapping head-to-head (as in the sigma bond), they join side-to-side, forming two areas of electron density above and below the molecule. This type of overlap is referred to as a pi (π, from the Greek equivalent of p) bond. Whenever you see a double or triple covalent bond, it exists as one sigma bond and one or two pi bonds. Due to the side-by-side overlap of a pi bond, there is no way the atoms can twist around each other as in a sigma bond. Pi bonds give the molecule a rigid shape.

Pi bonds are weaker than sigma bonds since there is less overlap. Thus, two single bonds are stronger than a double bond, and more energy is needed to break two single bonds than a single double bond.

The electron density lies above and below the atoms in a π bond.


Consider a molecule of methane: a carbon atom attached to four hydrogen atoms. Each atom is satisfying the octet rule, and each bond is a single covalent bond.

Now look at the electron configuration of carbon: 1s22s22p2. In its valence shell, it has two s electrons and two p electrons. It would not be possible for the four electrons to make equal bonds with the four hydrogen atoms (each of which has one s electron). We know, by measuring bond length and bond energy, that the four bonds in methane are equal, yet carbon has electrons in two different orbitals, which should overlap with the hydrogen 1s orbital in different ways.

To solve the problem, hybridization occurs. Instead of a s orbital and three p orbital, the orbitals mix, to form four orbitals, each with 25% s character and 75% p character. These hybrid orbitals are called sp3 orbitals, and they are identical. Observe:

Now these orbitals can overlap with hydrogen 1s orbitals to form four equal bonds. Hybridization may involve d orbitals in the atoms that have them, allowing up to a sp3d2 hybridization.

Exercise for the reader

Predict the hybridized electron configuration of carbon in ethene. How many sigma bonds are there? How many pi bonds?

Hint: Hybridized electrons form only sigma bonds. Pi bonds form only between p electrons.

Metallic Bonds

Review on structure

Atoms are particles composed of 3 subatomic particles. The protons, neutrons, and electrons. The protons and neutrons are in the nucleus and the electrons orbit this nucleus. These electrons can leave the atom and this is important to note especially for metals. The energy required to remove an electron is referred to as ionization energy and is very low for metals and so metals tend to lose their outermost (valence) electrons whenever possible. The attractive force between electrons and the nucleus is referred to as the electrostatic force of attraction. This electrostatic force is very strong and is capable of holding large structures together.


Metallic bonds occur among metal atoms. Whereas ionic bonds join metals to non-metals, metallic bonding joins a bulk of metal atoms. A sheet of aluminium foil and a copper wire are both places where you can see metallic bonding in action.

The "sea of electrons" is free to flow about the crystal of positive metal ions.

When metallic bonds form, the s and p electrons delocalize. Instead of orbiting their atoms, they form a "sea of electrons" surrounding the positive metal ions. The electrons are free to move throughout the resulting network. The electrostatic force of attraction between this "sea of electrons" and the positive ions acts as a form of "glue" holding together the metallic structure.


The delocalized nature of the electrons explains a number of unique characteristics of metals:

Metals are good conductors of electricity The sea of electrons is free to flow, allowing electrical currents.
Metals are good conductors of heat As heat energy is defined by the motion of particles, the sea of electrons provides an excellent medium for this kinetic energy to be transferred.
Metals are ductile (able to draw into wires)
and malleable (able to be hammered into thin sheets)
As the metal is deformed, local bonds are broken but quickly reformed in a new position.
Metals are gray and shiny Photons (particles of light) cannot penetrate the metal, so they bounce off the sea of electrons.
Gold is yellow and copper is reddish-brown There is actually an upper limit to the frequency that is reflected. It is too high to be visible in most metals, but not gold and copper.
Metals have very high melting and boiling points Metallic bonding is very strong, so the atoms are reluctant to break apart into a liquid or gas.

Reactivity and solubility

Nearly all metals are near completely insoluble in most solvents whether organic or inorganic. This is because the bonds between metals are exceedingly strong and solvents cannot dissolve the metal. However, if the metal undergoes a reaction and forms an ionic compound it can dissolve. Metals react when an electronegative substance attracts the electrons in the sea of electrons and the structure collapses without the force holding it together. Metals almost always form ionic compounds however on occasion they can participate in a form of covalent bonding. These compounds however, do not share any of the properties of metallic bonding. Furthermore, it is important to distinguish between a compound of a metal and an alloy.


Metallic bonds can occur between different elements. A mixture of two or more metals is called an alloy. This is what differentiates alloys and compounds containing metals, as alloys are only mixtures. Depending on the size of the atoms being mixed, there are two different kinds of alloys that can form:

It is also worth note that substitutional/interstitial alloys can exist when there are more than 2 metals are involved in the formation of an alloy.

The resulting mixture will have a combination of the properties of both metals involved. Interstitial alloys tend to be (with exceptions) stronger than their component metals. This is because the particles of varying size tend to prevent the various layers in a metal from sliding over each other smoothly. An example of this would be the difference between bronze and its components copper and tin. Copper on its own is a softer metal unfit for use as a weapon, while bronze was widely used during the Bronze Age for swords and armour. Alloys can also have various other benefits such as corrosion resistance, torsional strength, and much more.

Molecular Shape

Covalent molecules are bonded to other atoms by electron pairs. Being mutually negatively charged, the electron pairs repel the other electron pairs and attempt to move as far apart as possible in order to stabilize the molecule. This repulsion causes covalent molecules to have distinctive shapes, known as the molecule's molecular geometry. There are several different methods of determining molecular geometry. A scientific model, called the VSEPR (valence shell electron pair repulsion) model can be used to qualitatively predict the shapes of molecules. Within this model, the AXE method is used in determining molecular geometry by counting the numbers of electrons and bonds related to the center atom(s) of the molecule.

The VSEPR model is by no means a perfect model of molecular shape! It is simply a system which explains the known shapes of molecular geometry as discovered by experiment. This can allow us to predict the geometry of similar molecules, making it a fairly useful model. Modern methods of quantitatively calculating the most stable (lowest energy) shapes of molecules can take several hours of supercomputer time, and is the domain of computational chemistry.

Table of Geometries

Orbital Hybridization
sp2 sp3 sp3d sp3d2
2 Groups Linear Bent Bent Linear
3 Groups Trigonal Planar Trigonal Pyramidal T-Shaped
4 Groups Tetrahedral See-saw Square Planar
5 Groups Trigonal Bipyramidal Square Pyramidal
6 Groups Octahedral

The hybridization is determined by how many "things" are attached to the central atom. Those "things" can be other atoms or non-bonding pairs of electrons. The number of groups is how many atoms or electron pairs are bonded to the central atom. For example, methane (CH4) is tetrahedral-shaped because the carbon is attached to four hydrogens. Ammonia (NH3) is not trigonal planar, however. It is trigonal pyramidal because it is attached to four "things": the three hydrogens and a non-bonding pair of electrons (to fulfill nitrogen's octet).

Tetrahedral Shape

Consider a simple covalent molecule, methane (CH4). Four hydrogen atoms surround a carbon atom in three-dimensional space. Each CH bond consists of one pair of electrons, and these pairs try to move as far away from each other as possible (due to electrostatic repulsion). You might think this would lead to a flat shape, with each hydrogen atom 90° apart. However, in three dimensions, there is a more efficient arrangement of the hydrogen atoms. If each hydrogen atom is at a corner of a tetrahedron centered around the carbon atom, they are separated by about cos-1(-1/3) ≈ 109.5°—the maximum possible.


To align four orbitals in this tetrahedral shape requires the reformation of one s and three p orbitals into an sp3 orbital.

CH4 is a tetrahedral molecule.

Lone Electron Pairs

The VSEPR model treats lone electron pairs in a similar way to bonding electrons. In ammonia (NH3) for example, there are three hydrogen atoms and one lone pair of electrons surrounding the central nitrogen atom. Because there are four groups, ammonia has a tetrahedral shape but unlike methane, the angle between the hydrogen atoms is slightly smaller, 107.3°. This can be explained by theorizing that lone electron pairs take up more space physically than bonding pairs. This is a reasonable theory: in a bond, the electron pair is distributed over two atoms whereas a lone pair is only located on one. Because it is bigger, the lone pair forces the other electron pairs together.

The lone pair occupies more space than a bonding pair, decreasing the angles.

Testing this assumption with water provides further evidence. In water (H2O) there are two hydrogen atoms and two lone pairs, again making four groups in total. The electron pairs repel each other into a tetrahedral shape. The angle between the hydrogen atoms is 104.5°, which is what we expect from our model. The two lone pairs both push the bonds closer together, giving a smaller angle than in ammonia.

Linear and Planar Shapes

Electron-Poor Atoms

In some molecules, there are less than four pairs of valence electrons. This occurs in electron deficient atoms such as boron and beryllium, which don't conform to the octet rule (they can have 6 and 4 valence electrons respectively). In boron trifluoride (BF3), there are only three electron pairs which repel each other to form a flat plane. Each fluorine atom is separated by cos-1(-1/2) = 120°. A different set of hybrid orbitals is formed in this molecule: the 2s and two 2p orbitals combine to form three sp2 hybrid orbitals. The remaining p orbital is empty and sits above and below the plane of the molecule.

Beryllium, on the other hand, forms only two pairs of valence electrons. These repel each other at cos-1(-1) = 180°, forming a linear molecule. An example is beryllium chloride, which has two chlorine atoms situated on opposite sides of a beryllium atom. This time, one 2s and one 2p orbital combine to form two sp hybrid orbitals. The two remaining p orbitals sit above and to the side of the beryllium atom (they are empty).

Bent vs. Linear

The non-bonding pair causes sp2 hybridization, leading to a bent shape.
No non-bonding pairs causes sp hybridization, leading to a linear shape.

Some elements will have a bent shape, others have a linear shape. Both are attached to two groups, so it depends on how many non-bonding pairs the central atom has.

Take a look at sulfur dioxide (SO2) and carbon dioxide (CO2). Both have two oxygen atoms attached with double covalent bonds. Carbon dioxide is linear, and sulfur dioxide is bent. The difference is in their valence shells. Carbon has four valence electrons, sulfur has six. When they bond, carbon has no non-bonding pairs, but sulfur has one.

Five and Six Groups

Recall that some elements, especially sulfur and phosphorus, can bond with five or six groups. The hybridization is sp3d or sp3d2, with a trigonal bipyramidal or octahedral shape respectively. When there are non bonding pairs, other shape can arise (see the above chart).

How The Shapes Look

The yellow groups are non-bonding electron pairs. The white groups are bonded atoms, and the pink is the central atom. This is referred to as the AXE method; A is the central atom, X's are bonded atoms, and E's are non-bonding electron pairs.

Molecules are not static; their bonds are continually twisting, stretching and bending. According to quantum theory, the energies of these bond movements are quantized, and this fact forms the basis of infrared spectroscopy, an important chemical tool in analyzing organic molecules.

Intermolecular Bonds


The polar bonds are symmetric, but they don't point in opposite directions. The result is a dipole (positive pointing down).

Covalent bonds can be polar or non-polar, and so can the overall compound depending on its shape. When a bond is polar, it creates a dipole, a pair of charges (one positive and one negative). If they are arranged in a symmetrical shape, so that they point in opposite directions, they will cancel each other. For example, since the four hydrogens in methane (CH4) are facing away from each other, there is no overall dipole and the molecule is non-polar. In ammonia (NH3), however, there is a negative dipole at the nitrogen, due to the asymmetry caused by the non-bonding electron pair. The polarity of a compound determines its intermolecular bonding abilities.

Polar and Non-Polar Shapes

When a molecule has a linear, trigonal planar, tetrahedral, trigonal bipyramidal, or octahedral shape, it will be non-polar. These are the shapes that do not have non-bonding lone pairs. (e.g. Methane, CH4) But if some bonds are polar while others are not, there will be an overall dipole, and the molecule will be polar (e.g. Chloroform, CHCl3).

The other shapes (with non-bonding pairs) will be polar. (e.g. Water, H2O) Unless, of course, all the covalent bonds are non-polar, in which case there would be no dipoles to begin with.

Dipole-Dipole Bonds

When two polar molecules are near each other, they will arrange themselves so that the negative and positive sides line up. There will be an attractive force holding the two molecules together, but it is not nearly as strong a force as the intramolecular bonds. This is how many types of molecules bond together to form large solids or liquids.

Dipole-dipole forces hold these two HCl molecules together.

Hydrogen Bonding

Certain chemicals with hydrogen in their chemical formula have a special type of intermolecular bond, called hydrogen bonds. Hydrogen bonds will occur when a hydrogen atom is attached to an oxygen, nitrogen, or fluorine atom. This is because there is a large electronegativity difference between hydrogen and fluorine, oxygen, and nitrogen. Thus, molecules such as , , are extremely polar molecules with very strong dipole-dipole forces. As a result of the high electronegativities of fluorine, oxygen, and nitrogen, these elements will pull the electrons almost completely away from the hydrogen. The hydrogen becomes a bare proton sticking out from the molecule, and it will be strongly attracted to the negative side of any other polar molecules. Hydrogen bonding is an extreme type of dipole-dipole bonding. These forces are weaker than intramolecular bonds, but are much stronger than other intermolecular forces, causing these compounds to have high boiling points.

The dotted line represents a hydrogen bond.

Covalent Networks

A covalent network

Silicon dioxide forms a covalent network. Unlike carbon dioxide (with double bonds), silicon dioxide forms only single covalent bonds. As a result, the individual molecules covalently bond into a large network. These bonds are very strong (being covalent) and there is no distinction between individual molecules and the overall network. Covalent networks hold diamonds together. Diamonds are made of nothing but carbon, and so is soot. Unlike soot, diamonds have covalent networks, making them very hard and crystalline.

Van der Waals forces

Van der Waals, or London dispersion forces are caused by temporary dipoles created when electron locations are lopsided. The electrons are constantly orbiting the nucleus, and by chance they could end up close together. The uneven concentration of electrons could make one side of the atom more negatively-charged than the other, creating a temporary dipole. As there are more electrons in an atom, and the shells are farther away from the nucleus, these forces become stronger.

Van der Waals forces explain how nitrogen can be liquified. Nitrogen gas is diatomic; its equation is N2. Since both atoms have the same electronegativity, there is no dipole and the molecule is non-polar. If there are no dipoles, what would make the nitrogen atoms stick together to form a liquid? Van der Waals forces are the answer. They allow otherwise non-polar molecules to have attractive forces. These are by far the weakest forces that hold molecules together.

Melting and Boiling Points

When comparing two substances, their melting and boiling points may be questioned. To determine which substance has the higher melting or boiling point, you must decide which one has the strongest intermolecular force. Metallic bonds, ionic bonds, and covalent networks are very strong, as they are actually intramolecular forces. These substances have the highest melting and boiling points because they only separate into individual molecules when the powerful bonds have been broken. Breaking these intramolecular forces requires great amounts of heat energy.

Substances with hydrogen bonding, an intermolecular force, will have much higher melting and boiling points than those that have ordinary dipole-dipole intramolecular forces. Non-polar molecules have the lowest melting and boiling points, because they are held together by the weak van der Waals forces.

If you need to compare the boiling points of two metals, the metal with the larger atomic radius will have weaker bonding, due to the lower concentration of charge. When comparing boiling points of the non-polar gases, like the noble gases, the gas with the largest radius will have the highest points because it has the most potential for van der Waals forces.

Ionic compounds can be compared using Coulomb's Law. Look for substances with high ionic charges and low ionic radii.

Chemical Reactions

Naming Substances

Substances with carbon and hydrogen are organic compounds. They have special names that are beyond the scope of this book. For more information, see the Organic Chemistry Wikibook.

Some compounds have common names, like water for H2O. However, there are thousands of other compounds that are uncommon or have multiple names. Also, the common name is usually not recognized internationally. What looks like water to you might look like agua or vatten to someone else. To allow chemists to communicate without confusion, there are naming conventions to determine the systematic name of a chemical.

Naming Ions and Ionic Compounds

Ions are atoms that have lost or gained electrons. Note that in a polyatomic ion, the ion itself is held together by covalent bonds. Monoatomic cations (positive) are named the same way as their element, and they come first when naming a compound. Monoatomic anions (negative) have the suffix -ide and come at the end of the compound's name.

Examples of ionic compounds
  • NaCl - Sodium chloride
  • MgCl2 - Magnesium chloride
  • Ca3N2 - Calcium nitride

Notice that there is no need to write how many ions there are. Between the periodic table and our knowledge of ionic bonding, we can determine the number of ions, based on which elements are used.

Polyatomic Ions

Polyatomic ions have special names. Many of them contain oxygen and are called oxyanions. When different oxyanions are made of the same element, but have a different number of oxygen atoms, then prefixes and suffixes are used to tell them apart. The chlorine family of ions is an excellent example.

Name Formula
Chloride Cl-
Hypochlorite ClO-
Chlorite ClO2-
Chlorate ClO3-
Perchlorate ClO4-

The -ate suffix is used on the most common oxyanion (like sulfate SO42- or nitrate NO3-). The -ite suffix is used on the oxyanion with one oxygen atom fewer (like sulfite SO32- or nitrite NO2-). Sometimes there can be a hypo- prefix, meaning one oxygen atom fewer than for -ite. There is also a per- prefix, meaning one more oxygen atom than an -ate molecule has.

One last prefix you may find is thio-. It means an oxygen has been replaced with a sulfur within the oxyanion. Cyanate is OCN-, and thiocyanate is SCN-.

Examples of polyatomic ions
  • NH4Cl - Ammonium chloride
  • K(HCO3) - Potassium hydrogen carbonate
  • AgNO3 - Silver nitrate
  • CuSO3 - Copper (II) sulfite

In the last example, copper had a roman numeral 2 after its name because most of the transition metals can have more than one charge. The charge on the ion must be known, so it is written out for ions that have more than one common charge. Silver always has a charge of 1+, so it isn't necessary (but not wrong) to name its charge. Zinc always has a charge of 2+, so you don't have to name its charge either. Aluminum will always have a charge of +3. All other metals (except the Group 1 and 2 elements) must have roman numerals to show their charge.

Common polyatomic ions that you should know are listed in the following table

Name Formula
Acetate C2H3O2-
Ammonium NH4+
Carbonate CO32-
Cyanide CN-
Cyanate CNO-
Thiocyanate CNS-
Hypochlorite ClO-
Chlorite ClO2-
Chlorate ClO3-
Perchlorate ClO4-
Hypobromite BrO-
Bromite BrO2-
Bromate BrO3-
Perbromate BrO4-
Hypoiodite IO-
Iodite IO2-
Iodate IO3-
Periodate IO4-
Nitrite NO2-
Nitrate NO3-
Peroxide O22-
Permanganate MnO4-
Sulfite SO32-
Sulfate SO42-
In older texts, ions were assigned names based on their Latin root and a suffix. Common ions with this naming system include "plumbous/plumbic" for lead(II)/lead(IV) and "ferrous/ferric" for iron(II)/iron(III). These Latin-based names are outdated, so it's not important to learn them. We now use the Stock system instead.

Further explanation of the roman numerals is in order. Many atoms (especially the transition metals) are capable of ionizing in more than one way. The name of an ionic compound must make it very clear what the exact chemical formula is. If you wrote "copper chloride", it could be CuCl or CuCl2 because copper can lose one or two electrons when it forms an ion. The charge must be balanced, so there would be one or two chloride ions to accept the electrons. To be correct, you must write "copper(II) chloride" if you want CuCl2 and "copper (I) chloride" if you want CuCl. Keep in mind that the roman numerals refer to the charge of the cation, not how many anions are attached.

Common metal ions are listed below and should be learned:

Name Formula
Iron(II)/Ferrous Fe2+
Iron(III)/Ferric Fe3+
Copper(I)/Cuprous Cu+
Copper(II)/Cupric Cu2+
Tin (II)/Stannous Sn2+
Tin (IV)/Stannic Sn4+
Lead (II)/Plumbous (most common) Pb2+
Lead (IV)/Plumbic Pb4+
Mercury (I) (Note: Mercury (I) is a polyatomic ion) Hg22+
Mercury (II) Hg2+

Naming molecules in chemistry

There are two systems of naming molecular compounds. The first uses prefixes to indicate the number of atoms of an element that are in the compound. If the substance is binary (containing only two elements), the suffix -ide is added to the second element. Thus water is dihydrogen monoxide. A prefix is not necessary for the first element if there is only one, so SF6 is 'sulfur hexafluoride'. The prefix system is used when both elements are non-metallic.

Number Prefix
1 Mono-
2 Di-
3 Tri-
4 Tetra-
5 Penta-
6 Hexa-
7 Hepta-
8 Octa-
9 Nona-
10 Deca-
11 Undeca-
12 Dodeca-

The second system, the stock system, uses oxidation numbers to represent how the electrons are distributed through the compound. This is essentially the roman numeral system that has already been explained, but it applies to non-ionic compounds as well. The most electronegative component of the molecule has a negative oxidation number that depends on the number of pairs of electrons it shares. The less electronegative part is assigned a positive number. In the stock system, only the cation's number is written, and in Roman numerals. The stock system is used when there is a metallic element in the compound. In the case of V2O5, it could also be called vanadium(V) oxide. Knowing that oxygen's charge is always -2, we could determine that there were five oxygens and two vanadiums, if we were given the name without the formula.

Naming acids

If an acid is a binary compound, it is named as hydro[element]ic acid. If it contains a polyatomic ion, then it is named [ion name]ic acid if the ion ends in -ate. If the ion ends in -ite then the acid will end in -ous. These examples should help.

Examples of acid names
  • HCl - Hydrochloric acid
  • HClO - Hypochlorous acid
  • HClO2 - Chlorous acid
  • HClO3 - Chloric acid
  • HClO4 - Perchloric acid

Formulas and Numbers

Calculating Formula Masses

In molecules but not ionic compounds, the formula mass is also known as the molecular mass.

The calculation of a compound's formula mass (the mass of its molecule or formula unit) is straightforward. Simply add the individual mass of each atom in the compound (found on the periodic table). For example, the formula mass of glucose (C6H12O6) is 180 amu.

Molar masses are just as easy to calculate. The molar mass is equal to the formula mass, except that the unit is grams per mole instead of amu.

Calculating Percentage Composition

Percentage composition is the relative mass of one substance in a compound compared to the whole. For example, in methane (CH4), the percentage mass of hydrogen is 25% because hydrogen makes up a total of 4 amu out of 16 amu overall.

Using Percentage Composition

Percentage composition can be used to find the empirical formula of a compound, which shows the ratios of elements in the compound. However, this is not the same as the molecular formula. For example, many sugars have the empirical formula CH2O, which could correspond to a molecular formula of CH2O, C2H4O2, C6H12O6, etc.

To find the empirical formula from percentage composition, follow these procedures for each element.
  1. Convert from percentage to grams (for simplicity, assume a 100 g sample).
  2. Divide by the element's molar mass to find moles.
  3. Simplify to lowest whole-number ratio.

For example, a compound is composed of 75% carbon and 25% hydrogen by mass. Find the empirical formula.

  • 75g C / (12 g/mol C) = 6.25 mol C
  • 25g H / (1 g/mol H) = 25 mol H
  • 6.25 mol C / 6.25 = 1 mol C
  • 25 mol H / 6.25 = 4 mol H

Thus the empirical formula is CH4.

Calculating Molecular Formula

If you find the empirical formula of a compound and its molar/molecular mass, then you can find its exact molecular formula. Remember that the molecular formula is always a whole-number multiple of the empirical formula. For example, a compound with the empirical formula HO has a molecular mass of 34.0 amu. Since HO would only be 17.0 amu, which is half of 34.0, the molecular formula must be H2O2.

Exercise for the reader

An unknown substance must be identified. Lab analysis has found that the substance is composed of 80% Fluorine and 20% Nitrogen with a molecular mass of 71 amu. What is the empirical formula? What is the molecular formula?


The word stoichiometry derives from two Greek words: stoicheion (meaning "element") and metron (meaning "measure"). Stoichiometry deals with calculations about the masses (sometimes volumes) of reactants and products involved in a chemical reaction. It is a very mathematical part of chemistry, so be prepared for lots of calculator use.

Jeremias Benjaim Richter (1762-1807) was the first to lay down the principles of stoichiometry. In 1792 he wrote: "Die stöchyometrie (Stöchyometria) ist die Wissenschaft die quantitativen oder Massenverhältnisse zu messen, in welchen die chymischen Elemente gegen einander stehen." [Stoichiometry is the science of measuring the quantitative proportions or mass ratios in which chemical elements stand to one another.]

Molar Calculations

Your Tool: Dimensional Analysis

Luckily, almost all of stoichiometry can be solved relatively easily using dimensional analysis. Dimensional analysis is just using units, instead of numbers or variables, to do math, usually to see how they cancel out. For instance, it is easy to see that:

It is this principle that will guide you through solving most of the stoichiometry problems (chemical reaction problems) you will see in General Chemistry. Before you attempt to solve a problem, ask yourself: what do I have now? where am I going? As long as you know how many (units) per (other units), this will make stoichiometry significantly easier.

Moles to Mass

Where can you find the molar mass of these elements? The periodic table. You should always have one on hand—don't expect to get very far without one!

How heavy is 1.5 mol of lead? How many moles in 22.34g of water? Calculating the mass of a sample from the number of moles it contains is quite simple. We use the molar mass (mass of one mole) of the substance to convert between mass and moles. When writing calculations, we denote the molar mass of a substance by an upper case "M" (e.g. M(Ne) means "the molar mass of neon"). As always, "n" stands for the number of moles and "m" indicates the mass of a substance. To find the solutions to the two questions we just asked, let's apply some dimensional analysis:

Can you see how the units cancel to give you the answer you want? All you needed to know was that you had 1.5 mol Pb (lead), and that 1 mol Pb weighs 207.2 grams. Thus, multiplying 1.5 mol Pb by 207.2 g Pb and dividing by 1 mol Pb gives you 310.8 g Pb, your answer.

Mass to Moles

But we had one more question: "How many moles in 22.34g of water?" This is just as easy:

Where did the 18 g H2O come from? We looked at the periodic table and simply added up the atomic masses of two hydrogens and an oxygen to get the molecular weight of water. This turned out to be 18, and since all the masses on the periodic table are given with respect to 1 mole, we knew that 1 mol of water weighed 18 grams. This gave us the relationship above, which is really just (again) watching units cancel out!

Calculating Molar Masses

Before we can do these types of calculations, we first have to know the molar mass. Fortunately, this is not difficult, as the molar mass is exactly the same as the atomic weight of an element. A table of atomic weights can be used to find the molar mass of elements (this information is often included in the periodic table). For example, the atomic weight of oxygen is 16.00 amu, so its molar mass is 16.00 g/mol.

For species with more than one element, we simply add up the atomic weights of each element to obtain the molar mass of the compound. For example, sulfur trioxide gas is made up of sulfur and oxygen, whose atomic weights are 32.06 and 16.00 respectively.

The procedure for more complex compounds is essentially the same. Aluminium carbonate, for example, contains aluminium, carbon, and oxygen. To find the molar mass, we have to be careful to find the total number of atoms of each element. Three carbonate ions each containing three oxygen atoms gives a total of nine oxygens. The atomic weights of aluminium and carbon are 26.98 and 12.01 respectively.

Empirical Formulae

The empirical formula of a substance is the simplest ratio of the number of moles of each element in a compound. The empirical formula is ambiguous, e.g. the formula CH could represent CH, C2H2, C3H3 etc. These latter formulae are called molecular formulae. It follows that the molecular formula is always a whole number multiple of the empirical formula for a compound.

Calculating the empirical formula is easy if the relative amounts of each element in the compound are known. For example, if a sample contains 1.37 mol oxygen and 2.74 mol hydrogen, we can calculate the empirical formula. A good strategy to use is to divide all amounts given by the smallest non-integer amount, then multiply by whole numbers until the simplest ratio is found. We can make a table showing the successive ratios.

Hydrogen Oxygen
2.74 1.37 divide by 1.37

The empirical formula of the compound is H2O.

Here's another example. A sample of piperonal contains 1.384 mol carbon, 1.033 mol hydrogen and 0.519 mol oxygen.

Carbon Hydrogen Oxygen
1.384 1.033 0.519 divide by 0.519
2.666 2 1 multiply by 3
8 6 3 ANSWER

The empirical formula of piperonal is C8H6O3.

Converting from Masses

Often, we are given the relative composition by mass of a substance and asked to find the empirical formula. These masses must first be converted to moles using the techniques outlined above. For example, a sample of ethanol contains 52.1% carbon, 13.2% hydrogen, and 34.7% oxygen by mass. Hypothetically, 100g of this substance will contain 52.1 g carbon, 13.2 g hydrogen and 34.7 g oxygen. Dividing these by their respective molar masses gives the amount in moles of each element (as we learned above). These are 4.34 mol, 13.1 mol, and 2.17 mol respectively.

Carbon Hydrogen Oxygen
4.34 13.1 2.17 divide by 2.17
2 6 1 ANSWER

The empirical formula of ethanol is C2H6O.

Molecular Formula

Beware: In the case of H2O, the whole number multiple is 1, so its empirical formula is the same as its molecular formula. This is not always the case!

As mentioned above, the molecular formula for a substance equals the count of atoms of each type in a molecule. This is always a whole number multiple of the empirical formula. To calculate the molecular formula from the empirical formula, we need to know the molar mass of the substance. For example, the empirical formula for benzene is CH, and its molar mass is 78.12 g/mol. Divide the actual molar mass by the mass of the empirical formula, 13.02 g/mol, to determine the multiple of the empirical formula, "n". The molecular formula equals the empirical formula multiplied by "n".

This shows that the molecular formula for benzene is 6 times the empirical formula of CH. The molecular formula for benzene is C6H6.

Solving Mass-Mass Equations

A typical mass-mass equation will give you an amount in grams and ask for another answer in grams.

To solve a mass-mass equation, follow these rules
  1. Balance the equation if it is not already.
  2. Convert the given quantity to moles.
  3. Multiply by the molar ratio of the demanded substance over the given substance.
  4. Convert the demanded substance into grams.

For example, given the equation , find out how many grams of silver (Ag) will result from 43.0 grams of copper (Cu) reacting.

  • Convert the given quantity to moles.
  • Multiply by the molar ratio of the demanded substance and the given substance.
  • Convert the demanded substance to grams.


To solve a stoichiometric problem, you need to know what you already have and what you want to find. Everything in between is basic algebra.

Key Terms
  • Molar mass: mass (in grams) of one mole of a substance.
  • Empirical formula: the simplest ratio of the number of moles of each element in a compound
  • Molecular formula: the actual ratio of the number of moles of each element in a compound

In general, all you have to do is keep track of the units and how they cancel, and you will be on your way!

Chemical Equations

Chemical equations are a convenient, standardized system for describing chemical reactions. They contain the following information.

  • The type of reactants consumed and products formed
  • The relative amounts of reactants and products
  • The electrical charges on ions
  • The physical state of each species (e.g. solid, liquid)
  • The reaction conditions (e.g. temperature, catalysts)

The final two points are optional and sometimes omitted.

Anatomy of an Equation

Hydrogen gas and chlorine gas will react vigorously to produce hydrogen chloride gas. The equation above illustrates this reaction. The reactants, hydrogen and chlorine, are written on the left and the products (hydrogen chloride) on the right. The large number 2 in front of HCl indicates that two molecules of HCl are produced for each 1 molecule of hydrogen and chlorine gas consumed. The 2 in subscript below H indicates that there are two hydrogen atoms in each molecule of hydrogen gas. Finally, the (g) symbols subscript to each species indicates that they are gases.

Reacting Species

Species in a chemical reaction is a general term used to mean atoms, molecules or ions. A species can contain more than one chemical element (HCl, for example, contains hydrogen and chlorine). Each species in a chemical equation is written:

E is the chemical symbol for the element, x is the number of atoms of that element in the species, y is the charge (if it is an ion) and (s) is the physical state.

The symbols in parentheses (in subscript below each species) indicate the physical state of each reactant or product. For ACS Style[1] the state is typeset at the baseline without size change.

  • (s) means solid
  • (l) means liquid
  • (g) means gas
  • (aq) means aqueous solution (i.e. dissolved in water)

For example, ethyl alcohol would be written because each molecule contains 2 carbon, 6 hydrogen and 1 oxygen atom. A magnesium ion would be written because it has a double positive ("two plus") charge. Finally, an ammonium ion would be written because each molecule contains 1 nitrogen and 4 hydrogen atoms and has a charge of 1+.


The numbers in front of each species have a very important meaning—they indicate the relative amounts of the atoms that react. The number in front of each species is called a coefficient. In the above equation, for example, one H2 molecule reacts with one Cl2 molecule to produce two molecules of HCl. This can also be interpreted as moles (i.e. 1 mol H2 and 1 mol Cl2 produces 2 mol HCl).

It is important that the Law of Conservation of Mass is not violated. There must be the same number of each type of atoms on either side of the equation. Coefficients are useful for keeping the same number of atoms on both sides:

If you count the atoms, there are four hydrogens and two oxygens on each side. The coefficients allow us to balance the equation; without them the equation would have the wrong number of atoms. Balancing equations is the topic of the next chapter.

Other Information

Occasionally, other information about a chemical reaction will be supplied in an equation (such as temperature or other reaction conditions). This information is often written to the right of the equation or above the reaction arrow. A simple example would be the melting of ice.

, which could be written as

Reactions commonly involve catalysts, which are substances that speed up a reaction without being consumed. Catalysts are often written over the arrow. A perfect example of a catalyzed reaction is photosynthesis. Inside plant cells, a substance called chlorophyll converts sunlight into food. The reaction is written:


This is the equation for burning methane gas (CH4) in the presence of oxygen (O2) to form carbon dioxide and water: CO2 and H2O respectively. Notice the use of coefficients to obey the Law of Conservation of Matter.
This is a precipitation reaction in which dissolved lead cations and iodide anions combine to form a solid yellow precipitate of lead iodide (an ionic solid).

These two equations involve a catalyst. They occur one after another, using divanadium pentoxide to convert sulfur dioxide into sulfur trioxide. If you look closely, you can see that the vanadium catalyst is involved in the reaction, but it does not get consumed. It is both a reactant and a product, but it is necessary for the reaction to occur, making it a catalyst.
If we add both equations together, we can cancel out terms that appear on both sides. The resulting equation is much simpler and self-explanatory (although the original pair of equations is more accurate in describing how the reaction proceeds).

Balancing Equations

Balancing Equations

Chemical equations are useful because they give the relative amounts of the substances that react in a chemical equation.

In some cases, however, we may not know the relative amounts of each substance that reacts. Fortunately, we can always find the correct coefficients of an equation (the relative amounts of each reactant and product). The process of finding the coefficients is known as balancing the equation.

During a chemical reaction, atoms are neither created or destroyed. The same atoms are present before and after a reaction takes place; they are just rearranged. This is called the Law of Conservation of Matter, and we can use this law to help us find the right coefficients to balance an equation.

For example, assume in the above equation that we do not know how many moles of ammonia gas will be produced:

From the left side of this equation, we see that there are 2 atoms of nitrogen gas in the molecule N2 (2 atoms per molecule x 1 molecule), and 6 atoms of hydrogen gas in the 3 H2 molecules (2 atoms per molecule x 3 molecules). Because of the Law of Conservation of Matter, there must also be 2 atoms nitrogen gas and 6 atoms of hydrogen gas on the right side. Since each molecule of the resultant ammonia gas (NH3) contains 1 atom of nitrogen and 3 atoms of hydrogen, 2 molecules are needed to obtain 2 atoms of nitrogen and 6 atoms of hydrogen.

An Example

This chemical equation shows the compounds being consumed and produced; however, it does not appropriately deal with the quantities of the compounds. There appear to be two oxygen atoms on the left and only one on the right. But we know that there should be the same number of atoms on both sides. This equation is said to be unbalanced, because the number of atoms are different.
To make the equation balanced, add coefficients in front of each molecule as needed. The 2 in front of hydrogen on the left indicates that twice as many atoms of hydrogen are needed to react with a certain number of oxygen atoms. The coefficient 1 is not written, since it assumed in the absence of any coefficient.
Now, let's consider a similar reaction between hydrogen and nitrogen.
Typically, it is easiest to balance all pure elements last, especially hydrogen. First, by placing a two in front of ammonia, the nitrogens are balanced.
This leaves 6 moles of atomic hydrogen in the products and only two moles in the reactants. A coefficient of 3 is then placed in front of the hydrogen to give a fully balanced reaction.

Tricks in balancing certain reactions


A combustion reaction is a reaction between a carbon chain (basically, a molecule consisting of carbons, hydrogen, and perhaps oxygen) with oxygen to form carbon dioxide and water, plus heat. Combustion reactions could get very complex:

Fortunately, there is an easy way to balance these reactions.

First, note that the carbon in C6H6 can only appear on the product side in CO2. Thus, we can write a coefficient of 6 in front of CO2.

Next, note that the hydrogen in C6H6 can only go to H2O. Thus, we put a 3 in front of H2O.

We have 15 oxygen atoms on the product side, so there are O2 molecules on the reactant side. To make this an integer, we multiply all coefficients by 2.

Another Example

Helpful Hint!
Note: Fractions are technically allowed as coefficients, but they are generally avoided. Multiply all coefficients by the denominator to remove a fraction.
As reactions become more complex, they become more difficult to balance. For example, the combustion of butane (lighter fluid).
Once again, it is better to leave pure elements until the end, so first we'll balance carbon and hydrogen. Oxygen can then be balanced after. It is easy to see that one mole of butane will produce four moles of carbon dioxide and five moles of water.
Now there are 13 oxygen atoms on the right and two on the left. The odd number of oxygens prevents balancing with elemental oxygen. Because elemental oxygen is diatomic, this problem comes up in nearly every combustion reaction. Simply double every species except for oxygen to get an even number of oxygen atoms in the product.
The carbon and hydrogens are still balanced, and now there are an even number of oxygens in the product. Finally, the reaction can be balanced.

Limiting Reactants and Percent Yield

Limiting Reactants

When chemical reactions occur, the reactants undergo change to create the products. The coefficients of the chemical equation show the relative amounts of substance needed for the reaction to occur. Consider the combustion of propane:

For every one mole of propane, there must be five moles of oxygen. For every one mole of propane combusted, there will be three moles of carbon dioxide and four moles of water produced (along with much heat). If a propane grill is burning, there will be a very large amount of oxygen available to react with the propane gas. In this case, oxygen is the excess reactant. There is so much oxygen that the exact amount doesn't matter—it will not run out.

On the other hand, there is not an unlimited amount of propane. It will run out far before the oxygen runs out, making it a limiting reactant. The amount of propane available will decide how far the reaction will go.

2H2 + O2 → 2H2O

If there are three moles of hydrogen, and one mole of oxygen, which is the limiting reactant? How much product is created?

Twice as much hydrogen than oxygen is required. However, there is more than twice as much hydrogen. Thus hydrogen is the excess reactant and oxygen is the limiting reactant. If the reaction proceeds to completion, all of the oxygen will be used up, and one mole of hydrogen will remain. You can imagine this situation like this:

3H2 + O2 → 2H2O + H2

The reactant that is left over after the reaction is complete is called the "excess reactant". Often, you will want to figure out how much of the excess reactant is left after the reaction is complete. to do this, first use mole ratios to determine how much excess reactant is used up in the reaction.

Here are the ratios that need to be used:

Percent Yield

Usually, less product is made than theoretically possible. The actual yield is lower than the theoretical yield. To compare the two, one can calculate percent yield, which is .

The percent yield tells us how far the reaction actually went.

Types of Chemical Reactions

Helpful Hint!
Synthesis reactions always yield one product. Reversing a synthesis reaction will give you a decomposition reaction.

The general form of a synthesis reaction is A + B → AB. Synthesis reactions "put things together".

This is the most well-known example of a synthesis reaction—the formation of water via the combustion of hydrogen gas and oxygen gas.
Another example of a synthesis reaction is the formation of sodium chloride (table salt).

Because of the very high reactivities of sodium metal and chlorine gas, this reaction releases a tremendous amount of heat and light energy. Recall that atoms release energy as they become stable, and consider the octet rule when determining why this reaction has such favorable features.

Decomposition Reactions

These are the same number of synthesis reactions, with the format AB → A + B. Decomposition reactions "take things apart". Just as synthesis reactions can only form one product, decomposition reactions can only start with one reactant. Compounds that are unstable decompose quickly without outside assistance. Also they help other atoms to decompose better.

One example is the electrolysis of water (passing water through electrical current) to form hydrogen gas and oxygen gas.
Hydrogen peroxide slowly decomposes into water and oxygen because it is somewhat unstable. The process is sped up by the energy from light, so hydrogen peroxide is often stored in dark containers to slow down the decomposition.
Carbonic acid is the carbonation that is dissolved in soda. It decomposes into carbon dioxide and water, which is why an opened drink loses its fizz.

Single Displacement Reactions

Single displacement reaction, also called single replacement, is a reaction in which 2 elements are substituted for another element in a compound. The starting materials are always pure elements, such as a pure zinc metal or hydrogen gas plus an aqueous compound. When a displacement reaction occurs, a new aqueous compound and a different pure element are generated as products. Its format is AB + C → AC + B. Single Diplacement Adding hydrochloric acid to zinc will cause a gas to bubble out:

Double Displacement Reactions

In these reactions, two compounds swap components, in the format AB + CD → AD + CB

This is also called an "exchange". Here are the examples below:

1.) HCl + NaOH ----> NaCl + H2O


A precipitation reaction occurs when an ionic substance comes out of solution and forms an insoluble (or slightly soluble) solid. The solid which comes out of solution is called a precipitate. This can occur when two soluble salts (ionic compounds) are mixed and form an insoluble one—the precipitate.

An example is lead nitrate mixed with potassium iodide, which forms a bright yellow precipitate of lead iodide.
Note that the lead iodide is formed as a solid. The previous equation is written in molecular form, which is not the best way of describing the reaction. Each of the elements really exist in solution as individual ions, not bonded to each other (as in potassium iodide crystals). If we write the above as an ionic equation, we get a much better idea of what is actually happening.
Notice the like terms on both sides of the equation. These are called spectator ions because they do not participate in the reaction. They can be ignored, and the net ionic equation is written.

In the solution, there exists both lead and iodide ions. Because lead iodide is insoluble, they spontaneously crystallise and form the precipitate.

Acid-Base Neutralization

In simple terms, an acid is a substance which can lose a H+ ion (i.e. a proton) and a base is a substance which can accept a proton. When equal amounts of an acid and base react, they neutralize each other, forming species which aren't as acidic or basic.

For example, when hydrochloric acid and sodium hydroxide react, they form water and sodium chloride (table salt).
Again, we get a clearer picture of what's happening if we write a net ionic equation.

Acid base reactions often happen in aqueous solution, but they can also occur in the gaseous state. Acids and bases will be discussed in much greater detail in the acids and bases section.


The combustion of methane (releasing heat and light)

Combustion, better known as burning, is the combination of a substance with oxygen. The products are carbon dioxide, water, and possible other waste products. Combustion reactions release large amounts of heat. C3H8, better known as propane, undergoes combustion. The balanced equation is:

Combustion is similar to a decomposition reaction, except that oxygen and heat are required for it to occur. If there is not enough oxygen, the reaction may not occur. Sometimes, with limited oxygen, the reaction will occur, but it produces carbon monoxide (CO) or even soot. In that case, it is called incomplete combustion. If the substances being burned contain atoms other than hydrogen and oxygen, then waste products will also form. Coal is burned for heating and energy purposes, and it contains sulfur. As a result, sulfur dioxide is released, which is a pollutant. Coal with lower sulfur content is more desirable, but more expensive, because it will release less of the sulfur-based pollutants.

Organic Reactions

This is carboxylic acid. All functional groups end with an "R"—a placeholder for the rest of the molecule.

Organic reactions occur between organic molecules (molecules containing carbon and hydrogen). Since there is a virtually unlimited number of organic molecules, the scope of organic reactions is very large. However, many of the characteristics of organic molecules are determined by functional groups—small groups of atoms that react in predictable ways.

Another key concept in organic reactions is Lewis basicity. Parts of organic molecules can be electrophillic (electron-loving) or nucleophillic (nucleus, or positive loving). Nucleophillic regions have an excess of electrons—they act as Lewis bases—whereas electrophillic areas are electron deficient and act as Lewis acids. The nucleophillic and electrophillic regions attract and react with each other. Organic reactions are beyond the scope of this book, and are covered in more detail in Organic Chemistry. However, most organic substances can undergo replacement reactions and combustion reactions, as you have already learned.


The formation of hydrogen fluoride from the elements requires reduction of fluorine and oxidation of hydrogen.

Redox is an abbreviation of reduction/oxidation reactions. This is exactly what happens in a redox reaction, one species is reduced and another is oxidized. Reduction involves a gain of electrons and oxidation involves a loss, so a redox reaction is one in which electrons are transferred between species. Reactions where something is "burnt" (burning means being oxidised) are examples of redox reactions, however, oxidation reactions also occur in solution, which is very useful and forms the basis of electrochemistry.

Redox reactions are often written as two half-reactions showing the reduction and oxidation processes separately. These half-reactions are balanced (by multiplying each by a coefficient) and added together to form the full equation. When magnesium is burnt in oxygen, it loses electrons (it is oxidised). Conversely, the oxygen gains electrons from the magnesium (it is reduced).

Redox reactions will be discussed in greater detail in the redox section.

Energy Changes in Chemical Reactions

Exothermic and Endothermic Reactions

The release of energy in chemical reactions occurs when the reactants have higher chemical energy than the products. The chemical energy in a substance is a type of potential energy stored within the substance. This stored chemical potential energy is the heat content or enthalpy of the substance.

If the enthalpy decreases during a chemical reaction, a corresponding amount of energy must be released to the surroundings. Conversely, if the enthalpy increases during a reaction, a corresponding amount of energy must be absorbed from the surroundings. This is simply the Law of Conservation of Energy.

absorbtion reactions is when a chemical reaction releases more energy than it absorbs and you can also see them die on the inside.

reletion reactions is when a chemical reaction absorbs more energy than it releases.

You are already familiar with enthalpy: melting ice is endothermic and freezing water is exothermic.

When methane burns in air the heat given off equals the decrease in enthalpy that occurs as the reactants are converted to products.

The enthal difference between the reactants and the products is equal to the amount of energy released to the surroundings. A reaction in which energy is released to the surroundings is called an exothermic reaction. In this type of reaction the enthalpy, or stored chemical energy, is lower for the products than the reactants.

When ammonium nitrate is dissolved in water, energy is absorbed and the water cools. This concept is used in "cold packs".

The enthalpy difference between the reactants and the products is equal to the amount of energy absorbed from the surroundings. A reaction in which energy is absorbed from the surroundings is called an endothermic reaction. In endothermic reactions the enthalpy of the products is greater than the enthalpy of the reactants.

Because reactions release or absorb energy, they affect the temperature of their surroundings. Exothermic reactions heat up their surroundings while endothermic reactions cool them down. The study of enthalpy, along with many other energy-related topics, is covered in the Thermodynamics Unit.

Activation Energy

Think about the combustion of methane. It releases enough heat energy to cause a fire. However, the reaction does not occur automatically. When methane and oxygen are mixed, an explosion does not instantly occur. First, the methane must be ignited, usually with a lighter or matchstick. This reveals something about reactions: they will not occur unless a certain amount of activation energy is added first. In this sense, all reactions absorb energy before they begin, but the exothermic reactions release even more energy. This can be explained with a graph of potential energy:

This graph shows an exothermic reaction because the products are at a lower energy than the reactants (so heat has been released). Before that can happen, the energy must actually increase. The amount of energy added before the reaction can complete is the activation energy, symbolized Ea.

Predicting Chemical Reactions

Types of Reactions

There are several guidelines that can help you predict what kind of chemical reaction will occur between a mixture of chemicals.

However, not all elements will react with each other. To better predict a chemical reaction, knowledge of the reactivity series is needed.


When combining two chemicals, a single- or double-replacement reaction doesn't always happen. This can be explained by a list known as the reactivity series, which lists elements in order of reactivity. The higher on the list an element is, the more elements it can replace in a single- or double-replacement reaction. When deciding if a replacement reaction will occur, look up the two elements in question. The higher one will replace the lower one.

Elements at the very top of the series are so reactive that they can replace hydrogen from water. This explains the explosive reaction between sodium and water:

Elements in the middle of the list will react with acids (but not water) to produce a salt and hydrogen gas. Elements at the bottom of the list are mostly nonreactive.

Elements near the top of the list will corrode (rust, tarnish, etc.) in oxygen much faster than those at the bottom of the list.

The Reactivity Series

  • Red: elements that react with water and acids to form hydrogen gas, and with oxygen.
  • Orange: elements that react very slowly with water but strongly with acids.
  • Yellow: elements that react with acid to form hydrogen gas, and with oxygen.
  • Grey: elements that react with oxygen (tarnish).
  • White: elements that are often found pure; relatively nonreactive.

Most Reactive


Least Reactive

Oxidation States

Oxidation states are used to determine the degree of oxidation or reduction that an element has undergone when bonding. The oxidation state of a compound is the sum of the oxidation states of all atoms within the compound, which equals zero unless the compound is ionic.

The oxidation state of an atom within a molecule is the charge it would have if the bonding were completely ionic, even though covalent bonds do not actually result in charged ions.

Method of notation

Oxidation states are written above the element or group of elements that they belong to (when drawing the molecule), or written with roman numerals in parenthesis when naming the elements.

aluminum(III), an ion

Determining oxidation state

For single atoms or ions

Because oxidation numbers are just the sum of the electrons gained or lost, calculating them for single elements is easy.


Notice that the oxidation states of ionic compounds are simple to determine.

For larger molecules

Helpful Hint!
Remember that all the individual oxidation states must add up to the charge on the whole substance.

Although covalent bonds do not result in charges, oxidation states are still useful. They label the hypothetical transfer of electrons if the substance were ionic. Determining the oxidation states of atoms in a covalent molecule is very important when analyzing "redox" reactions. When substances react, they may transfer electrons when they form the products, so comparing the oxidation states of the products and reactants allows us to keep track of the electrons.

for hydrogen chloride
for water
for the chlorite ion

(notice the overall charge)

Determining Oxidation States

The determination of oxidation states is based on knowing which elements can have only one oxidation state other than the elemental state and which elements are able to form more than one oxidation state other than the elemental state. Let's look at some of the "rules" for determining the oxidation states.

1. The oxidation state of an element is always zero.

2. For metals, the charge of the ion is the same as the oxidation state. The following metals form only one ion: Group IA, Group IIA, Group IIIA (except Tl), Zn2+, Cd2+.

3. For monatomic anions and cations, the charge is the same as the oxidation state.

4. Oxygen in a compound is −2, unless a peroxide is present. The oxidation state of oxygen in peroxide ion , O22− is −1.

5. For compounds containing polyatomic ions, use the overall charge of the polyatomic ion to determine the charge of the cation. Here is a convenient method for determining oxidation states. Basically, you treat the charges in the compound as a simple algebraic expression. For example, let's determine the oxidation states of the elements in the compound, KMnO4. Applying rule 2, we know that the oxidation state of potassium is +1. We will assign "x" to Mn for now, since manganese may be of several oxidation states. There are 4 oxygens at −2. The overall charge of the compound is zero: K Mn O4 +1 x 4(-2)

The algebraic expression generated is: 1 + x -8 = 0

Solving for x gives the oxidation state of manganese: x - 7 = 0 x = +7 K Mn O4 +1 +7 4(-2)

Suppose the species under consideration is a polyatomic ion. For example, what is the oxidation state of chromium in dichromate ion, (Cr2O72-)?

As before, assign the oxidation state for oxygen, which is known to be -2. Since the oxidation state for chromium is not known, and two chromium atoms are present, assign the algebraic value of 2x for chromium: Cr2 O7 2- 2x 7(-2)

Set up the algebraic equation to solve for x. Since the overall charge of the ion is -2, the expression is set equal to -2 rather than 0: 2x + 7(-2) = -2

Solve for x: 2x - 14 = -2 2x = 12 x = +6

Each chromium in the ion has an oxidation state of +6. Let's do one last example, where a polyatomic ion is involved. Suppose you need to find the oxidation state of all atoms in Fe2(CO3)3. Here two atoms, iron and carbon, have more than one possible oxidation state. What happens if you don't know the oxidation state of carbon in carbonate ion? In fact, knowledge of the oxidation state of carbon is unnecessary. What you need to know is the charge of carbonate ion (-2). Set up an algebraic expression while considering just the iron ion and the carbonate ion: Fe2 (CO3)3 2x 3(-2) 2x - 6 = 0 2x = 6 x = 3

Each iron ion in the compound has an oxidation state of +3. Next consider the carbonate ion independent of the iron(III) ion: C O3 2- x 3(-2) x - 6 = -2 x = +4

The oxidation state of carbon is +4 and each oxygen is -2.


Determining oxidation states is not always easy, but there are many guidelines that can help. This guidelines in this table are listed in order of importance. The highest oxidation state that any element can reach is +8 in XeO4.

Element Usual Oxidation State
Fluorine Fluorine, being the most electronegative element, will always have an oxidation of -1 (except when it is bonded to itself in F2, when its oxidation state is 0).
Hydrogen Hydrogen always has an oxidation of +1, -1, or 0. It is +1 when it is bonded to a non-metal (e.g. HCl, hydrochloric acid). It is -1 when it is bonded to metal (e.g. NaH, sodium hydride). It is 0 when it is bonded to itself in H2.
Oxygen Oxygen is usually given an oxidation number of -2 in its compounds, such as H2O. The exception is in peroxides (O2-2) where it is given an oxidation of -1. Also, in F2O oxygen is given an oxidation of +2 (because fluorine must have -1), and in O2, where it is bonded only to itself, the oxidation is 0.
Alkali Metals The Group 1A metals always have an oxidation of +1, as in NaCl. The Group 2A metals always have an oxidation of +2, as in CaF2. There are some rare exceptions that don't need consideration.
Halogens The other halogens (Cl, Br, I, As) usually have an oxidation of -1. When bonded to another halogen, its oxidation will be 0. However, they can also have +1, +3, +5, or +7. Looking at the family of chlorides, you can see each oxidation state (Cl2 (0), Cl- (-1), ClO- (+1), ClO2- (+3), ClO3- (+5), ClO4- (+7)).
Nitrogen Nitrogen (and the other Group 5A elements, such as phosphorus, P) often have -3 (as in ammonia, NH3), but may have +3 (as in NF3) or +5 (as in phosphate, PO43-).
Carbon Carbon can take any oxidation state from -4, as in CH4, to +4, as in CF4. It is best to find the oxidation of other elements first.

In general, the more electronegative element has the negative number. Using a chart of electronegativities, you can determine the oxidation state of any atom within a compound.


Oxidation states are another periodic trend. They seem to repeat a pattern across each period.

Redox Reactions


Redox reactions are chemical reactions in which elements are oxidized and reduced.

Specifically, at the most basic level one element gets oxidized by losing, or donating, electrons to the oxidizing agent. In doing so, the oxidizing agent gets reduced by accepting the electrons lost, or donated, by the reducing agent (i.e. the element getting oxidized).

If it seems as though there are two separate things going on here, you are correct: redox reactions can be split into two half-reactions, one dealing with oxidation, the other, reduction.


Oil Rig

Oxidation Is Loss. Reduction Is Gain



Lose Electrons Oxidation. Gain Electrons Reduction


This is the complete reaction. Iron is oxidized, thus it is the reducing agent. Copper is reduced, making it the oxidizing agent.
This is the oxidation half-reaction.
This is the reduction half-reaction.

When the two half-reactions are summed, the result is:

Helpful Hint!
If you cancel out the electrons on both sides, you get the original equation.

Balancing Redox Equations

In a redox reaction, all electrons must cancel out. If you are adding two half-reactions with unequal numbers of electrons, then the equations must be multiplied by a common denominator. This process is similar to balancing regular equations, but now you are trying to balance the electrons between two half-reactions.


The electrons don't completely cancel out. There is one electron more on the left. However, if you double all terms in the first half-reaction, then add it to the second half-reaction, the electrons will cancel out completely. That means the half-reactions for this redox reaction are actually:

Balancing Redox Equations in an Acidic or Basic Solution

If a reaction occurs in an acidic or basic environment, the redox equation is balanced as follows:

  1. Write the oxidation and reduction half reactions, but with the whole compound, not just the element that is reduced/oxidized.
  2. Balance both reactions for all elements except oxygen and hydrogen.
  3. If the oxygen atoms are not balanced in either reaction, add water molecules to the side missing the oxygen.
  4. If the hydrogen atoms are not balanced, add hydrogen ions until the hydrogen atoms are balanced.
  5. Multiply the half reactions by the appropriate number (so that they have equal numbers of electrons).
  6. Add the two equations to cancel out the electrons, as in the previous method, and the equation is balanced!

If the reaction occurs in a basic environment, proceed as if it is in an acid environment, but, after step 4, for each hydrogen ion added, add a hydroxide ion to both sides of the equation. Then, combine the hydroxide ions and hydrogen ions to form water. Then, cancel all the water molecules that appear on both sides.


Redox Reactions (review)

Redox (shorthand for reduction/oxidation reaction) describes all chemical reactions in which atoms have their oxidation number (oxidation state) changed.

This can be either a simple redox process such as the oxidation of carbon to yield carbon dioxide, or the reduction of carbon by hydrogen to yield methane (CH4), or it can be a complex process such as the oxidation of sugar in the human body through a series of very complex electron transfer processes.

The term redox comes from the two concepts of reduction and oxidation. It can be explained in simple terms:

Non-redox reactions, which do not involve changes in formal charge, are known as metathesis reactions.
  • Oxidation describes the loss of electrons by a molecule, atom, or ion
  • Reduction describes the gain of electrons by a molecule, atom, or ion

However, these descriptions (though sufficient for many purposes) are not truly correct. Oxidation and reduction properly refer to a change in oxidation number—the actual transfer of electrons may never occur. Thus, oxidation is better defined as an increase in oxidation number, and reduction as a decrease in oxidation number. In practice, the transfer of electrons will always cause a change in oxidation number, but there are many reactions which are classed as "redox" even though no electron transfer occurs noway (such as those involving covalent bonds).


Electrochemistry is a branch of chemistry that deals with the flow of electricity by chemical reactions. The electrons in a balanced half-reaction show the direct relationship between electricity and the specific redox reaction. Electrochemical reactions are either spontaneous, or nonspontaneous. A spontaneous redox reaction generates a voltage itself. A nonspontaneous redox reaction occurs when an external voltage is applied. The reactions that occur in an electric battery are electrochemical reactions.

Three components of an electrochemical reaction
  • A solution where redox reactions may occur (solutions are substances dissolved in liquid, usually water)
  • A conductor for electrons to be transferred (such as a metal wire)
  • A conductor for ions to be transferred (usually a salt bridge) e.g. filter paper dipped in a salt solution.


An electrolysis experiment forces a nonspontaneous chemical reaction to occur. This is achieved when two electrodes are submersed in an electrically conductive solution, and the electrical voltage applied to the two electrodes is increased until electrons flow. The electrode receiving the electrons, or where the reduction reactions occur, is called the cathode. The electrode which supplies the electrons, or where the oxidation reactions occur, is called the anode.

A molten salt is an example of something that may be electrolyzed because salts are composed of ions. When the salt is in its solid state, the ions are not able to freely move. However, when the salt is heated enough until it melts (making it a molten salt), the ions are free to move. This mobility of the ions in the molten salt makes the salt electrically conductive. In the electrolysis of a molten salt, for example melted , the cation of the salt (in this case ) will be reduced at the cathode, and the anion of the salt (in this case ) will be oxidized at the anode:

Cathode reaction: Na+ + e-Na
Anode reaction: 2ClCl2 + 2e-

Aqueous solutions of salts can be electrolyzed as well because they are also electrically conductive. In aqueous solutions, there is an additional reaction possible at each the cathode and the anode:

Cathode: 2H2O + 2e-H2 + 2OH- (reduction of water)
Anode: 2H2O → 4H+ + O2 + 4e- (oxidation of water)

With the addition of these two reactions, there are now two possible reactions at each electrode. At the cathode, either the reduction of the cation or the reduction of water will occur. At the anode, either the oxidation of the anion or the oxidation of water will occur. The following rules determine which reaction takes place at each electrode:

  • Cathode: If the cation is a very active metal, water will be reduced. Very active metals include Li, Na, K, Rb, Cs, Ca, Sr, and Ba. If the cation is an active or inactive metal, the cation will be reduced.
  • Anode: If the anion is a polyatomic ion, water will generally be oxidized. Specifically, sulfate, perchlorate, and nitrate ions are not oxidized; water will oxidize instead. Chloride, bromide, and iodide ions will be oxidized. If the anion in one salt is oxidized in an aqueous electrolysis, that same anion will also be oxidized in any other salt.

Galvanic Cells

The energy of a spontaneous redox reaction is captured using a galvanic cell. The following parts are necessary to make a galvanic cell:

The "ammeter" at the top measures the electrical current flowing through the wire. Electrons are flowing from copper to zinc, making zinc the oxidizing agent.
  1. Two half cells
  2. Two electrodes
  3. One electrically conductive wire
  4. One salt bridge
  5. One device, usually an ammeter or a voltmeter

A galvanic cell is constructed as shown in the image to the right. The two half-reactions are separated into two half cells. All of the reactants in the oxidation half-reaction are placed in one half cell (the anode), and all the reactants of the reduction half-reaction are placed in the other half cell (the cathode). If the half-reaction contains a metal, the metal serves as the electrode for that half cell. Otherwise, an inert electrode made of platinum, silver, or gold is used. The electrodes are connected with a wire which allows the flow of electrons. The electrons always flow from the anode to the cathode. The half cells are connected by a salt bridge which allows the ions in the solution to move from one half cell to the other, so that the reaction can continue. Since the overall reaction is spontaneous, the flow of electrons will move spontaneously through the outer circuitry from which the energy can be extirpated. The energy harnessed is useful because it can be used to do work. For example, if an electrical component such as a light bulb is attached to the wire, it will receive power from the flowing electrons.

Consistent results from a galvanic cell are dependent on three variables: pressure, temperature, and concentration. Thus, chemists defined a standard state for galvanic cells. The standard state for the galvanic cell is a pressure of 1.00 atmospheric pressure (atm) for all gases, a temperature of 298 kelvin (K) and concentrations of 1.00 molarity (M) for all soluble compounds, liquids, and solids.


Voltage is a measure of spontaneity of redox reactions, and it can be measured by a voltmeter. If the voltage of a reaction is positive, the reaction occurs spontaneously, but when negative, it does not occur spontaneously.

To compute the voltage of a redox equation, split the equation into its oxidation component and reduction component. Then, look up the voltages of each component on a standard electrode potential table. This table will list the voltage for the reduction equation. The oxidation reaction's voltage is negative of the corresponding reduction equation's voltage. To find the equation's voltage, add the standard voltages for each half reaction.

Aqueous Solutions


Types of Solutions

A solution is a homogenous mixture, composed of solvent(s) and solute(s). A solvent is any substance which allows other substances to dissolve in it. Therefore, it is usually present in the greater amount. Solutes are substances present in a solution. Note that when a solute dissolves in a solvent, no chemical bonds form between the solvent and solute.

Solutions have variable composition, unlike pure compounds whose composition is fixed. For example, a 500 mL solution of lemonade can consist of 70% water, 20% lemon juice, and 10% sugar. There can also be a 500 mL solution of lemonade consisting of 60% water, 25% lemon juice, and 15% sugar.

When two liquids can be readily combined in any proportions, they are said to be miscible. An example would be alcohol and water. Either of the two can totally dissolve each other in any proportion. Two liquids are defined as immiscible if they will not form a solution, such as oil and water. Solid solutes in a metallic solvent are known as alloys. Gold is an example of an alloy. It is too soft in its pure form, so other metals are dissolved in it. Jewelers may use 14-karat gold, which contains two-thirds gold and one-third other metals.

Variables Affecting Solubility

Factor Concept Example
Surface area More surface area gives more opportunity for solute-solvent contact Powdered sugar will dissolve in water faster than rock candy.
Temperature Solids are more soluble in hot solvents, gases are more soluble in cold solvents Sugar dissolves more readily in hot water, but CO2 dissolves better in cold soda than warm soda.
Polarity Non-polar compounds dissolve in non-polar solvents, and polar compounds dissolve in polar solvents. If one liquid is polar, and the other isn't, they are immiscible. Alcohol and water are both polar, and they are miscible. Oil is non-polar and is immiscible in water.
Pressure Gases dissolve better under higher pressure, due to greater forces pushing the gas molecules into the solvent. Leaving the cap off a soda bottle will let the carbonation out.
Agitation If a solution is agitated by stirring or shaking, there is an increase in kinetic motion and contact of particles. Therefore, the rate of solubility increases. Everyone knows to stir their coffee after adding sugar.

Dissolving at the Molecular Level

A sodium ion in solvation with water.
  1. The forces between the particles in the solid must be broken. This is an endothermic process called dissociation.
  2. Some of the intermolecular forces between the particles in the liquid must also be broken. This is endothermic.
  3. The particles of the solid and the particles in a liquid become attracted. This is an exothermic process called solvation.

Example: Dissolving NaCl

When sodium chloride is added to water, it will dissolve. Water molecules are polar, and sodium chloride is ionic (which is very polar). The positive ends of the water molecules (the hydrogens) will be attracted to the negative chloride ions, and the negative ends of the water molecules (the oxygens) will be attracted to the positive sodium ions. The attractions are strong enough to separate sodium from chloride, so the solute dissociates, or breaks apart. The solute is then spread throughout the solvent. The polar water molecules prevent the ions from reattaching to each other, so the salt stays in solution.

Important Concepts


  • When a solution can hold no more solute, it is said to be saturated. This occurs when there is an equilibrium between the dissolved and undissolved solute.
  • If more solute can be added, the solution is unsaturated.
  • If a solution has more solute than is normally possible, due to the lowering or heightening of temperature, it is said to be supersaturated. If disturbed, the solution will rapidly form solid crystals.
  • Solubility is the measure of how many grams of solute can dissolve in 100 grams of solvent (or in the case of water, solute per 100 milliliters.)


Sometimes, compounds form crystals with a specific amount of water in them. For example, copper(II) sulfate is written as CuSO4 • 5H2O. For every mole of copper(II) sulfate, there are five moles of water attached. The atoms are arranged in a crystal lattice. Even if dried, the compound will still be hydrated. It will not feel moist, but there are water molecules within the crystal structure of the solid.

Intense heat will release the water from the compound. Its color may change, indicating a chemical change. When the anhydrous compound is dissolved in water, it will become hydrated again.

Heats of Solution

Some chemicals change temperature when dissolved. This is due to a release or absorption of heat. The specific change is known as the heat of solution, measured in kJ/mol.


Some substances break up into ions and conduct electricity when dissolved. These are called electrolytes. All ionic compounds are electrolytes. Nonelectrolytes, on the other hand, do not conduct electricity when dissolved. Electrolytes are the reason that tap water conducts electricity. Tap water contains salts and other ions. If you have purified water, you will find that it does not conduct electricity at all. Upon dissolving some salt, it conducts electricity very well. The presence of ions allows electrons to move through the solution, and electricity will be conducted.

Solubility Practice Questions

1. In a mixture of 50 mL of benzene and 48 mL of octane,

a) which substance is the solute?
b) would these two substances form a solution?

2. Solutions are formed as physical reactions. Using this principle, name two ways in which solutes can be separated from solvents.

3. Three different clear, colourless liquids were gently heated in an evaporating dish. Liquid A left a white residue, liquid B left no residue, and liquid C left water. Identify each liquid solution as a pure substance or a solution.

4. Compare three bottles of soda. Bottle A was stored at room temperature (25°C), bottle B was stored at 10°C, and bottle C was stored at 30°C.

a) If you wanted a fizzy drink, which bottle would you choose?
b) If you wanted to change the gas pressure of bottle C to that of bottle B, what could you do?

Answers to Solubility Practice Questions

Properties of Solutions


The concentration of a solution is the measure of how much solute and solvent there is. A solution is concentrated if it contains a large amount of solute, or dilute if contains a small amount.


Molarity is the number of moles of solute per liter of solution. It is abbreviated with the symbol M, and is sometimes used as a unit of measurement, e.g. a 0.3 molar solution of HCl. In that example, there would be 0.3 moles of HCl for every liter of water (or whatever the solvent was).


Molality is the number of moles of solute per kilogram of solvent. It is abbreviated with the symbol m (lowercase), and is sometimes used as a unit of measurement, e.g. a 0.3 molal solution of HBr. In that example, there would be 0.3 moles of HBr for every kilogram of water (or whatever the solvent was).

Mole Fraction

The mole fraction is simply the moles of solute per moles of solution. As an example, you dissolve one mole of NaCl into three moles of water. Remember that the NaCl will dissociate into its ions, so there are now five moles of particles: one mole Na+, one mole Cl-, and three moles water. The mole fraction of sodium is 0.2, the mole fraction of chloride is 0.2, and the mole fraction of water is 0.6.

The mole fraction is symbolized with the Greek letter (chi), which is often written simply as an X.


Dilution is adding solvent to a solution to obtain a less concentrated solution. Perhaps you have used dilution when running a lemonade stand. To cut costs, you could take a half-full jug of rich, concentrated lemonade and fill it up with water. The resulting solution would have the same total amount of sugar and lemon juice, but double the total volume. Its flavor would be weaker due to the added water.

Chemists often keep highly concentrated solutions of useful chemicals. They can quickly obtain more dilute solutions of known concentration by this method.

The key concept is that the amount of solute is constant before and after the dilution process. The concentration is decreased (and volume increased) only by adding solvent.

Thus, the number of moles of solute before and after dilution are equal.
By definition of molarity, you can find the moles of solvent.
Substituting the second equation into the first gives the dilution equation.

To determine the amount of solvent (usually water) that must be added, you must know the initial volume and concentration, and the desired concentration. Solving for in the above equation will give you the total volume of the diluted solution. Subtracting the initial volume from the total volume will determine the amount of pure solvent that must be added.

Ionic Solutes

When ionic compounds dissolve in water, they separate into ions. This process is called dissociation. Note that because of dissociation, there are more moles of particles in the solution containing ions than there would be with the solute and solvent separated.

If you have two glasses of water, and you dissolve salt into one and sugar into the other, there will be a big difference in concentration. The salt will dissociate into its ions, but sugar (a molecule) will not dissociate. If the salt were NaCl, the concentration would be double that of the sugar. If the salt were MgCl2, the concentration would be triple (there are three ions).

Solubility Rules

Not all ionic compounds are soluble. Some ionic compounds have so much attractive force between their anions and cations that they will not dissociate. These substances are insoluble and will not dissolve. Instead, they clump together as a solid in the bottom of solution. Many ionic compounds, however, will dissociate in water and dissolve. In these cases, the attractive force between ion and water is greater than that between cation and anion. There are several rules to help you determine which compounds will dissolve and which will not.

Solubility Rules
  1. All compounds with Group 1 ions or ammonium ions are soluble.
  2. Nitrates, acetates, and chlorates are soluble.
  3. Compounds containing a halogen are soluble, except those with fluorine, silver, or mercury. If they have lead, they are soluble only in hot water.
  4. Sulfates are soluble, except when combined with silver, lead, calcium, barium, or strontium.
  5. Carbonates, sulfides, oxides, silicates, and phosphates are insoluble, except for rule #1.
  6. Hydroxides are insoluble except when combined with calcium, barium, strontium, or rule #1.

Sometimes, when two different ionic compounds are dissolved, they react, forming a precipitate that is insoluble. Predicting these reactions requires knowledge of the activity series and solubility rules. These reactions can be written with all ions, or without the spectator ions (the ion that don't react, present on both sides of the reaction), a format known as the net ionic equation.

For example, silver nitrate is soluble, but silver chloride is not soluble (see the above rules). Mixing silver nitrate into sodium chloride would cause a cloudy white precipitate to form. This happens because of a double replacement reaction.


When solutes dissociate (or if a molecule ionizes), the solution can conduct electricity. Compounds that readily form ions, thus being good conductors, are known as strong electrolytes. If only a small amount of ions are formed, electricity is poorly conducted, meaning the compound is a weak electrolyte.

Colligative Properties

Some properties are the same for all solute particles regardless of what kind. These are known as the colligative properties. These properties apply to ideal solutions, so in reality, the properties may not be exactly as calculated. In an ideal solution, there are no forces acting between the solute particles, which is generally not the case.

Vapor Pressure

All liquids have a tendency for their surface molecules to escape and evaporate, even if the liquid is not at its boiling point. This is because the average energy of the molecules is too small for evaporation, but some molecules could gain above average energy and escape. Vapor pressure is the measure of the pressure of the evaporated vapor, and it depends on the temperature of the solution and the quantities of solute. More solute will decrease vapor pressure.

The vapor pressure is given by Rauolt's Law, where is the mole fraction of the solvent. Notice that the vapor pressure equals that of the pure solvent when there is no solute (). If , there would be no vapor pressure at all. This could only happen if there were no solvent, only solute. A solid solute has no vapor pressure.
If two volatile substances (both have vapor pressures) are in solution, Rauolt's Law is still used. In this case, Rauolt's Law is essentially a linear combination of the vapor pressures of the substances. Two liquids in solution both have vapor pressures, so this equation must be used.

The second equation shows the relationship between the solvents. If two liquids were mixed exactly half-and-half, the vapor pressure of the resulting solution would be exactly halfway between the vapor pressures of the two solvents.

Another relation is Henry's Law, which shows the relationship between gas and pressure. It is given by Cg = k Pg , where C is concentration and P is pressure. As the pressure goes up, the concentration of gas in solution must also increase. This is why soda cans release gas when they are opened - The decrease in pressure results in a decrease in concentration of CO2 in the soda.

Exercise for the reader

At 50 °C the vapor pressure of water is 11 kPa and the vapor pressure of ethanol is 30 kPa. Determine the resulting vapor pressure if a solution contains 75% water and 25% ethanol (by moles, not mass).

Boiling Point Elevation

A liquid reaches its boiling point when its vapor pressure is equal to the atmosphere around it. Because the presence of solute lowers the vapor pressure, the boiling point is raised. The boiling point increase is given by:

The reduced vapor pressure increases the boiling point of the liquid only if the solute itself is non-volatile, meaning it doesn't have a tendency to evaporate. For every mole of non-volatile solute per kilogram of solvent, the boiling point increases by a constant amount, known as the molal boiling-point constant (). Because this is a colligative property, is not affected by the kind of solute.

Freezing Point Depression

This explains why roads are salted in the winter.

A liquid reaches its freezing temperature when its vapor pressure is equal to that of its solid form. Because the presence of the solute lowers the vapor pressure, the freezing point is lowered. The freezing point depression is given by:

Again, this equation works only for non-volatile solutes. The temperature of the freezing point decreases by a constant amount for every one mole of solute added per kilogram solvent. This constant () is known as the molar freezing-point constant.


Osmosis results from the tendency for concentration to distribute itself evenly.

If you studied biology, you would know that osmosis is the movement of water through a membrane. If two solutions of different molarity are placed on opposite sides of a semipermeable membrane, then water will travel through the membrane to the side with higher molarity. This happens because the water molecules are "attached" to the solvent molecules, so they cannot travel through the membrane. As a result, the water on the side with lower molarity can more easily travel through the membrane than the water on the other side.

The pressure of this osmosis is given in the equation

Where pi is the pressure, M is molarity, R is the gas constant, and T is temperature in Kelvin.

Electrolytes and Colligative Properties

When one mole of table salt is added to water, the colligative effects are double those that would have occurred if sugar were added instead. This is because the salt dissociates, forming twice as many particles as sugar would. This dissociation, called the Van't Hoff Factor describes how many particles that are dissociated into the solution and must be multiplied into the Boiling Point Elevation or Vapor Pressure Lowering equations.

Sugar is a covalent molecule. No dissociation occurs when dissolved.
Table salt is an ionic compound and a strong electrolyte. Total dissociation occurs when dissolved, doubling the effects of colligative properties.
Magnesium bromide is also ionic. The colligative effects will be tripled.

Though extremely useful for calculating the general Van't Hoff Factor, this system of calculation is slightly inaccurate when considering ions. This is because when ions are in solution, they may interact and clump together, lessening the effect of the Van't Hoff factor. In addition, more strongly charged ions may have a smaller effect. For example, CaO would be less effective as an electrolyte than NaCl.

Acids and Bases

Acid-Base Reaction Theories

Acids and bases are everywhere. Some foods contain acid, like the citric acid in lemons and the lactic acid in dairy. Cleaning products like bleach and ammonia are bases. Chemicals that are acidic or basic are an important part of chemistry.

Helpful Hint!
You may need to refresh your memory on naming acids.

Several different theories explain what composes an acid and a base. The first scientific definition of an acid was proposed by the French chemist Antoine Lavoisier in the eighteenth century. He proposed that acids contained oxygen, although he did not know the dual composition of acids such as hydrochloric acid (HCl). Over the years, much more accurate definitions of acids and bases have been created.

Arrhenius Theory

The Swedish chemist Svante Arrhenius published his theory of acids and bases in 1887. It can be simply explained by these two points:

Arrhenius Acids and Bases
  1. An acid is a substance which dissociates in solvent to produce one or more hydrogen ions (H+).
  2. A base is a substance which dissociates in solvent to produce one or more hydroxide ions (OH-).
Svante Arrhenius

Based on this definition, you can see that Arrhenius acids must be soluble in water. Arrhenius acid-base reactions can be summarized with three generic equations:

An acid will dissociate in water producing hydrogen ions.
A base (usually containing a metal) will dissociate in water to produce hydroxide ions.
Acids and bases will neutralize each other when mixed. They produce water and an ionic salt, neither of which are acidic or basic.

The Arrhenius theory is simple and useful. It explains many properties and reactions of acids and bases. For instance, mixing hydrochloric acid (HCl) with sodium hydroxide (NaOH) results in a neutral solution containing table salt (NaCl).

However, the Arrhenius theory is not without flaws. There are many well known bases, such as ammonia (NH3) that do not contain the hydroxide ion. Furthermore, acid-base reactions are observed in solutions that do not contain water. To resolve these problems, there is a more advanced acid-base theory.

Brønsted-Lowry Theory

The Brønsted-Lowry theory was proposed in 1923. It is more general than the Arrhenius theory—all Arrhenius acids/bases are also Brønsted-Lowry acids/bases (but not necessarily vice versa).

Brønsted-Lowry Acids and Bases
  1. An acid is a substance from which a proton (H+ ion) can be removed. Essentially, an acid donates protons to bases.
  2. A base is a substance to which a proton (H+) can be added. Essentially, a base accepts protons from acids.

Acids that can donate only one proton are monoprotic, and acids that can donate more than one proton are polyprotic.

These reactions demonstrate the behavior of Brønsted-Lowry acids and bases:

An acid (in this case, hydrochloric acid) will donate a proton to a base (in this case, water is the base). The acid loses its proton and the base gains it.
Water is not necessary. In this case, hydrochloric acid is still the acid, but ammonia acts as the base.
The same reaction is happening, but now in reverse. What was once an acid is now a base (HCl → Cl-) and what was once a base is now an acid (NH3 → NH4+). This concept is called conjugates, and it will be explained in more detail later.

Two examples of acids (HCl and H3O+) mixing with bases (NaOH and OH-) to form neutral substances (NaCl and H2O).
A base (sodium hydroxide) will accept a proton from an acid (ammonia). A neutral substance is produced (water), which is not necessarily a part of every reaction. Compare this reaction to the second one. Ammonia was a base, and now it is an acid. This concept, called amphoterism, is explained later.

The Brønsted-Lowry theory is by far the most useful and commonly-used definition. For the remainder of General Chemistry, you can assume that any acids/bases use the Brønsted-Lowry definition, unless stated otherwise.

This Brønsted-Lowry acid donates a proton (in green) to water (the base).

Lewis Theory

The Lewis definition is the most general theory, having no requirements for solubility or protons.

Lewis Acids and Bases
  1. An acid is a substance that accepts a lone pair of electrons.
  2. A base is a substance that donates a lone pair electrons.

Lewis acids and bases react to create an adduct, a compound in which the acid and base have bonded by sharing the electron pair. Lewis acid/base reactions are different from redox reactions because there is no change in oxidation state.

This reaction shows a Lewis base (NH3) donating an electron pair to a Lewis acid (H+) to form an adduct (NH4+).

Amphoterism and Water

Substances capable of acting as either an acid or a base are amphoteric. Water is the most important amphoteric substance. It can ionize into hydroxide (OH-, a base) or hydronium (H3O+, an acid). By doing so, water is

  1. Increasing the H+ or OH- concentration (Arrhenius),
  2. Donating or accepting a proton (Brønsted-Lowry), and
  3. Accepting or donating an electron pair (Lewis).
H+ ions actually exist as hydronium, H3O+.

Water will dissociate very slightly (which further explains its amphoteric properties).

The presence of hydrogen ions indicates an acid, whereas the presence of hydroxide ions indicates a base. Being neutral, water dissociates into both equally.
This equation is more accurate—hydrogen ions do not exist in water because they bond to form hydronium.


Another common example of an amphoteric substance is ammonia. Ammonia is normally a base, but in some reactions it can act like an acid.

Ammonia acts as a base. It accepts a proton to form ammonium.
Ammonia also acts as an acid. Here, it donates a proton to form amide.

Ammonia's amphoteric properties are not often seen because ammonia typically acts like a base. Water, on the other hand, is completely neutral, so its acid and base behaviors are both observed commonly.

Conjugate Acids and Bases

In all the theories, the products of an acid-base reaction are related to the initial reactants of the reaction. For example, in the Brønsted-Lowry theory, this relationship is the difference of a proton between a reactant and product. Two substances which exhibit this relationship form a conjugate acid-base pair.

Brønsted-Lowry Conjugate Pairs
  • An acid that has donated its proton becomes a conjugate base.
  • A base that has accepted a proton becomes a conjugate acid.
Hydroiodic acid reacts with water (which serves as a base). The conjugate base is the iodide ion and the conjugate acid is the hydronium ion. The acids are written in red, and the bases are written in blue. One conjugate pair is written bold and the other conjugate pair is in cursive.
Ammonia (basic) reacts with water (the acid). The conjugate acid is ammonium and the conjugate base is hydroxide. Again, acids are written in red, and the bases are written in blue. The conjugate pairs are distinguished with matching fonts.

Strong and Weak Acids/Bases

A strong acid is an acid which dissociates completely in water. That is, all the acid molecules break up into ions and solvate (attach) to water molecules. Therefore, the concentration of hydronium ions in a strong acid solution is equal to the concentration of the acid.

The majority of acids exist as weak acids, an acid which dissociates only partially. On average, only about 1% of a weak acid solution dissociates in water in a 0.1 mol/L solution. Therefore, the concentration of hydronium ions in a weak acid solution is always less than the concentration of the dissolved acid.

Strong bases and weak bases do not require additional explanation; the concept is the same.

This explains why, in all of the above example reactions, the reverse chemical reaction does not occur. The stronger acid/base will prevail, and the weaker one will not contribute to the overall acidity/basicity. For example, hydrochloric acid is strong, and upon dissociation chloride ions are formed. Chloride ions are a weak base, but the solution is not basic because the acidity of HCl is overwhelmingly stronger than basicity of Cl-.

Helpful Hint!
Although the other halogens make strong acids, hydrofluoric acid (HF) is a weak acid. Despite being weak, it is incredibly corrosive—hydrofluoric acid dissolves glass and metal!

Most acids and bases are weak. You should be familiar with the most common strong acids and assume that any other acids are weak.

Formula Strong Acid
HClO4 Perchloric acid
HNO3 Nitric acid
H2SO4 Sulfuric acid
HCl, HBr, HI Hydrohalic acids

Within a series of oxyacids, the ions with the greatest number of oxygen molecules are the strongest. For example, nitric acid (HNO3) is strong, but nitrous acid (HNO2) is weak. Perchloric acid (HClO4) is stronger than chloric acid (HClO3), which is stronger than the weak chlorous acid (HClO2). Hypochlorous acid (HClO) is the weakest of the four.

Common strong bases are the hydroxides of Group 1 and most Group 2 metals. For example, potassium hydroxide and calcium hydroxide are some of the strongest bases. You can assume that any other bases (including ammonia and ammonium hydroxide) are weak.

Formula Strong Base
LiOH Lithium hydroxide
NaOH Sodium hydroxide
KOH Potassium hydroxide
RbOH Rubidium hydroxide
CsOH Cesium hydroxide
Ca(OH)2 Calcium hydroxide
Sr(OH)2 Strontium hydroxide
Ba(OH)2 Barium hydroxide


Properties of Acids and Bases

Now that you are aware of the acid-base theories, you can learn about the physical and chemical properties of acids and bases. Acids and bases have very different properties, allowing them to be distinguished by observation.


Bromothymol blue is an indicator that turns blue in a base, or yellow in acid.

Made with special chemical compounds that react slightly with an acid or base, indicators will change color in the presence of an acid or base. A common indicator is litmus paper. Litmus paper turns red in acidic conditions and blue in basic conditions. Phenolphthalein purple is colorless in acidic and neutral solutions, but it turns purple once the solution becomes basic. It is useful when attempting to neutralize an acidic solution; once the indicator turns purple, enough base has been added.


A less informative method is to test for conductivity. Acids and bases in aqueous solutions will conduct electricity because they contain dissolved ions. Therefore, acids and bases are electrolytes. Strong acids and bases will be strong electrolytes. Weak acids and bases will be weak electrolytes. This affects the amount of conductivity.

However, acids will react with metal, so testing conductivity may not be plausible.

Physical properties

The physical properties of acids and bases are opposites.

Acids Bases
Taste sour bitter
Feel stinging slippery
Odor sharp odorless

These properties are very general; they may not be true for every single acid or base.

Another warning: if an acid or base is spilled, it must be cleaned up immediately and properly (according to the procedures of the lab you are working in). If, for example, sodium hydroxide is spilled, the water will begin to evaporate. Sodium hydroxide does not evaporate, so the concentration of the base steadily increases until it becomes damaging to its surrounding surfaces.

Chemical Reactions


Acids will react with bases to form a salt and water. This is a neutralization reaction. The products of a neutralization reaction are much less acidic or basic than the reactants were. For example, sodium hydroxide (a base) is added to hydrochloric acid.

This is a double replacement reaction.


Acids react with metal to produce a metal salt and hydrogen gas bubbles.
Acids react with metal carbonates to produce water, CO2 gas bubbles, and a salt.
Acids react with metal oxides to produce water and a salt.


Bases are typically less reactive and violent than acids. They do still undergo many chemical reactions, especially with organic compounds. A common reaction is saponification: the reaction of a base with fat or oil to create soap.

Saponification converts an "ester" into an "alcohol" and salt. This is an organic reaction outside the scope of General Chemistry.

Practice Questions

1. Name the following compounds that will form, and identify as an acid or base:

a) Br + H
b) 2H + SO3
c) K + H
d) 2H + SO6
e) 3H + P2
f) H + BrO2
g) Na + Cl

2. What are the conjugate acids and bases of the following:

a) water
b) ammonia
c) bisulfate ion
d) zinc hydroxide
e) hydrobromic acid
f) nitrite ion
g) dihydrogen phosphate ion

3. In a conductivity test, 5 different solutions were set up with light bulbs. The following observations were recorded:

Solution A glowed brightly.
Solution B glowed dimly.
Solution C glowed dimly.
Solution D did not glow.
Solution E glowed brightly.
a) Which solution(s) could contain strong bases?
b) Which solution(s) could contain weak acids?
c) Which solution(s) could contain ions?
d) Which solution(s) could contain pure water?
e) Based solely on these observations, would it be possible to distinguish between acidic and basic solutions?

4. Identity the conjugate base and conjugate acid in these following equations:

a) HCl + H2O → H3O+ + Cl-
b) HClO + H2O → ClO- + H3O+
c) CH3CH2NH2 + H2O → CH3CH2NH3+ + OH-

5. Identify these bases as Arrhenius, Brønsted-Lowry, or both.

a) strontium hydroxide
b) butyllithium (C4H9Li)
c) ammonia
d) potassium hydroxide
e) potassium iodide

6. Based on the Brønsted-Lowry Theory of Acids and Bases, would you expect pure water to have no dissolved ions whatsoever? Explain, using a balanced chemical equation.




  1. ^ Brown, Theodore E.; Lemay, H. Eugene; Bursten, Bruce E.; Murphy, Catherine; Woodward, Patrick (2009), Chemistry: The Central Science (11th ed.), New York: Prentice-Hall, ISBN 0136006175.

Answers to Properties of Acids and Bases Practice Questions

Titration and pH

Ionization of Water

Water is a very weak electrolyte. It will dissociate into hydroxide and hydronium ions, although only in a very small amount. Because pure water is completely neutral, it always dissociates in equal amounts of both hydroxide and hydronium. Once acidic or basic substances have been added to pure water, the concentration of the ions will change. Regardless of which acid-base theory is used, acids and bases all have one important thing in common:

  • All acids increase the H+ concentration of water.
  • All bases increase the OH- concentration of water.

Furthermore, the concentration of hydrogen ions multiplied by the concentration of hydroxide ions is a constant. This constant is known as the ionization constant of water, or Kw. At room temperature it equals 10-14 mol2/L2. Thus:

In a neutral solution, the concentrations of H+ and OH- are both equal to 10-7. Using the above equation, the concentration of one ion can be determined if the concentration of the other ion is known. This equation further demonstrates the relationship between acids and bases: as the acidity (H+) increases, the basicity (OH-) must decrease.

The pH Scale

To measure the acidity or basicity of a substance, the pH scale is employed.

The pH Scale
  • A completely neutral substance has a pH of 7.
  • Acids have a pH below 7
  • Bases have a pH above 7.

pH usually ranges between 0 and 14, but it can be any value. Battery acid, for example, has a negative pH because it is so acidic.

Various pH values.

Definition of pH

The pH scale is mathematically defined as:

Substances that release protons or increase the concentration of hydrogen ions (or hydronium ions) will lower the pH value.


There is also a less common scale, the pOH scale. It is defined as:

Substances that absorb protons or increase the concentration of hydroxide ions will lower the pOH value.

The sum of pH and pOH is always 14 at room temperature:

Calculating pH

A strong acid or strong base will completely dissociate in water, so the concentration of the acid/base is equal to the concentration of H+ or OH-. If you know the concentration of the acid or base, then you can simply plug that number into the pH or pOH formula. The sum of pH and pOH will always equal 14 at room temperature, so you can interconvert these two values.

If you know the H+ concentration and need to know the OH- concentration (or vice versa), use the definition of Kw above. The product of the two ion concentrations will always equal 10-14 at room temperature.


Titration is the controlled mixing of a solution with known concentration (the standard solution or titrant) to another solution (called the analyte) to determine its concentration. One solution is acidic and the other is basic. An indicator is added to the mixture. An indicator must be selected so that it changes color when equal amounts of acid and base have been added. This is known as the equivalence point. This does not necessarily mean that the pH is 7.0.

Polyprotic acids have multiple equivalence points.

Once the equivalence point has been reached, the unknown concentration can be determined mathematically.

Practice Questions

1) 5.00g of NaOH are dissolved to make 1.00L of solution.

a What is the concentration of H+?
b What is the pH?

Answers for Titration and pH

Buffer Systems


Buffer systems are systems in which there is a significant (and nearly equivalent) amount of a weak acid and its conjugate base—or a weak base and its conjugate acid—present in solution. This coupling provides a resistance to change in the solution's pH. When strong acid is added, it is neutralized by the conjugate base. When strong base is added, it is neutralized by the weak acid. However, too much acid or base will exceed the buffer's capacity, resulting in significant pH changes.

Consider an arbitrary weak acid, HA, and its conjugate base, A-, in equilibrium.
The addition of a strong acid will cause only a slight change in pH due to neutralization.
Likewise, the addition of a strong base will cause only a slight change in pH.

Buffers are useful when a solution must maintain a specific pH. For example, blood is a buffer system because the life processes in a human only function within a specific pH range of 7.35 to 7.45. When, for example, lactic acid is released by the muscles during exercise, buffers within the blood neutralize it to maintain a healthy pH.

Making a Buffer

Once again, let's consider an arbitrary weak acid, HA, which is present in a solution. If we introduce a salt of the acid's conjugate base, say NaA (which will provide the A- ion), we now have a buffer solution. Ideally, the buffer would contain equal amounts of the weak acid and conjugate base.

Instead of adding NaA, what if a strong base were added, such as NaOH? In that case, the hydroxide ions would neutralize the weak acid and create water and A- ions. If the solution contained only A- ions, then a strong acid like HCl were added, they would neutralize and create HA.

As you can see, there are three ways to create a buffer:

  • 1 HA + 1 A-
  • 1 HA + ½ OH-
  • 1 A- + ½ H+
  • 1 B + 1 HB+
  • 1 B + ½ H+
  • 1 HB+ + ½ OH-

All six of the combinations will create equal amounts of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Buffers and pH

To determine the pH of a buffer system, you must know the acid's dissociation constant. This value, (or for a base) determines the strength of an acid (or base). It is explored more thoroughly in the Equilibrium unit, but for now it suffices to say that this value is simply a measure of strength for acids and bases. The dissociation constants for acids and bases are determined experimentally.

The Henderson-Hasselbalch equation allows the calculation of a buffer's pH. It is:

For a buffer created from a base, the equation is:

Using these equations requires determining the ratio of base to acid in the solution.

Reactions of Acids and Bases


To summarize the properties and behaviors of acids and bases, this chapter lists and explains the various chemical reactions that they undergo. You may wish to review chemical equations and types of reactions before attempting this chapter.

The following reactions are net ionic equations. In other words, spectator ions are not written. If an ion does not partake in the reaction, it is simply excluded. The spectator ions can be found because they occur on both the reactant and the product side of the equation. Cross them out and rewrite the equation without them. Of course, the coefficients must be equal.

Canceling out the spectator ions explains the net of net ionic equations. The ionic part means that dissolved compounds are written as ions instead of compounds. Acids, bases, and salts are all ionic, so they are written as separate ions if they have dissociated.

Net Ionic Equations
  • Soluble salts are written as ions.
e.g.: Na+ + Cl-
  • Solids, liquids, and gases are written as compounds.
e.g.: NaCl(s), H2O(l), HCl(g)
  • Strong acids and strong bases are written as ions (because they dissociate almost completely).
e.g.: H+ + NO3-
  • Weak acids and weak bases are written as compounds (because they barely dissociate).
e.g.: HNO2

As an example, sodium bicarbonate (NaHCO3) would be written as Na+ and HCO3- because the salt will dissociate, but the bicarbonate will not dissociate (it's a weak acid).


When an acid and a base react, they form a neutral substance, often water and a salt.

First, let's examine the neutralization of a strong acid with a strong base.

Solid potassium hydroxide is added to an aqueous solution of hydrochloric acid. Notice how the solid is written as a compound, but the acid is written as ions because it dissociates.
The hydrogen ions will react with hydroxide ions to form water.
Ignoring spectator ions, this is the net ionic equation.

Now, let's see some examples involving weak acids and weak bases.

Excess hydrochloric acid is added to a solution of sodium phosphate. Phosphoric acid is weak, so the phosphate ions will react with hydrogen ions. The result is a solution with some, but much less, hydrogen ions, so it is much closer to neutral than either of the original reactants.
Equimolar amounts of sodium phosphate and hydrochloric acid are mixed. Notice the difference between this reaction and the previous one.
A strong base is added to a solution of calcium bicarbonate. (Bicarbonate is a weak acid.)
A strong acid is added to a solution of calcium bicarbonate. Gas bubbles appear.

Many reactions result in the formation of gas bubbles or a solid precipitate that will make the solution cloudy. The last equation brings up an interesting application. Many rocks and minerals contain calcium carbonate or calcium bicarbonate. To identify these rocks, geologists can perform the "acid test". A drop of acid is applied, and the presence of gas bubbles indicates carbonate.

Here are more examples of neutralization reactions.

Solid ammonium chloride crystals are dissolved into a solution of sodium hydroxide. The smell of ammonia is detected.
Ammonia gas is bubbled through a solution of hydrochloric acid. This reaction is essentially the opposite of the previous. In that reaction, ammonium ions react with base to form ammonia gas. In this reaction, ammonia gas reacts with acid to form ammonium ions.
Ammonia (a weak base) reacts with acetic acid (also weak). The resulting solution is nearly neutral, but it will be slightly basic because ammonia is stronger than acetic acid.
Hydrogen sulfide gas is bubbled into a strong base.
A strong acid is added to the above result, and hydrogen sulfide gas is released.


An anhydride is a substance that does not contain water. More specifically, it is a substance that reacts with water to form an acid or base. Anhydrides are usually in the form of a gas that dissolves into water and reacts to form an acid or base. They can also be solids that will react with water.

Gaseous dinitrogen pentoxide is bubbled through water to form nitric acid.
Dinitrogen trioxide is mixed with water to form nitrous acid.

The main difference between those two equations is the fact that nitrous acid is weak and thus does not dissociate, whereas nitric acid is strong and dissociates into ions.

Here are a few more examples of anhydride reactions.

Solid potassium oxide is added to water to form a strong base.
Phosphorus(V) oxide powder is mixed into water to form a weak acid.

It is important to remember which acids are strong and which are weak. Review this if necessary.

For example, sulfur dioxide gas (acidic anhydride) is bubbled through a solution of calcium hydroxide (basic).

First, determine the reaction of the anhydride with water.
Then, determine the reaction of the acid and base. This is a double replacement reaction.
Add the two reactions together.
Cancel out spectators. Also, calcium hydroxide should be ionized (but calcium sulfite is a solid precipitate). This is the final net ionic equation.

Here are more examples.

Calcium oxide crystals (basic anhydrides) are added to a strong acid. Notice that it does not matter what the acid is (nitric, sulfuric, etc.) because it is strong and this reaction only requires the hydrogen ions. In other words, the anions of the strong acid are spectators and are not written.
Excess sulfur dioxide gas is bubbled into a dilute solution of strong base. The base is the limiting reactant.
Sulfur dioxide gas is bubbled into an excess of basic solution.

Remember that water is involved in these reactions, but it is not written if it occurs on both sides of the equation.

Solid calcium oxide (basic anhydride) is exposed to dry ice gas (acidic anhydride). The resulting solid is a salt.
Solid calcium oxide is exposed to a stream of sulfur trioxide gas. The resulting solid is a neutral salt.


A salt of a weak acid and strong base dissociates and reac