Chemical Principles/Atoms, Molecules, and Ions

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According to convention there is a sweet and
a bitter, a hot and a cold, and according to
convention there is order. In truth there are
atoms and a void.

Democritus (400 B.C.)


In the trial scene in Alice in Wonderland, the White Rabbit, asked to read a document adduced as evidence, asks, "Where shall I begin, please your Majesty?" The answer is straightforward: "Begin at the beginning, and go on till you come to the end: then stop." But we shall begin in the middle, with a description of what atoms and molecules are like, before saying anything about how we know that atoms exist. When we examine the evidence for atomic and molecular structure in later chapters, you will have at least an idea of the goal of the effort. The result, we hope, will be to make this textbook more comprehensible than most of Lewis Carroll's books. (The White Rabbit's evidence did not fare very well: "If any one of them can explain it," said Alice, "I'll give him sixpence. I don't believe there's an atom of meaning in it."

The Structure of Atoms[edit]

An atom (ours, not Carroll's) consists of a positively charged nucleus, surrounded by one or more negatively charged particles called electrons. The positive charges equal the negative charges, so the atom has no overall charge; it is electrically neutral. Most of an atom's mass is in its nucleus; the mass of an electron is only 1/1836 the mass of the lightest nucleus, that of hydrogen. Although the nucleus is heavy, it is quite small compared with the overall size of an atom. The radius of a typical atom is around 0.1 to 0.25 nanometres (nm), whereas the radius of a nucleus is about 10-6 nm. * If an atom were enlarged to the size of the earth, its nucleus would be only 200 feet in diameter and could easily rest inside a small football stadium.

Table 1-1. Fundamental Particles of Matter
Particle Charge Mass (amu)
Proton break
+1 break
Neutron break
0 break
Electron break
-1 break

The nucleus of an atom contains protons and neutrons. Protons and neutrons have nearly equal masses, but they differ in charge. A neutron has no charge, whereas a proton has a positive charge that exactly balances the negative charge on an electron. Table 1-1 lists the charges of these three fundamental particles, and gives their masses expressed in atomic mass units. The atomic mass unit (amu) is defined as exactly one-twelfth the mass of the nucleus of a carbon atom consisting of six protons and six neutrons. With this scale, protons and neutrons have masses that are close to, but not precisely, 1 amu each. [As a matter of information at this point, there are approximately 6.022 X 1023 amu in 1 gram (g). This number is known as Avogadro's number, N, and later in the chapter we will show one of the ways this number can be calculated.]

The number of protons in the nucleus of an atom is known as the atomic number, Z. It is the same as the number of electrons around the nucleus, because an atom is electrically neutral. The mass number of an atom is equal to the total number of heavy particles: protons and neutrons. When two atoms are close enough to combine chemically-to form chemical bonds with one another-each atom "sees" mainly the outermost electrons of the other atom. Hence these outer electrons are the most important factors in the chemical behavior of atoms. Neutrons in the nucleus have little effect on chemical behavior, and the protons are significant only because they determine how many electrons surround the nucleus in a neutral atom. All atoms with the same atomic number behave in much the same way chemically and are classified as the same chemical element. Each element has its own name and a one- or two-letter symbol (usually derived from the element's English or Latin name). For example, the symbol for carbon is C, and the symbol for calcium is Ca. The symbol for sodium is Na-the first two letters of its Latin (and German) name, natrium- to distinguish it from nitrogen, N, and sulfur, S.

*One nanometre equals 10-9 meters (m), or 10-7 centimeters (cm). If you are not familiar with metric units, see Appendix 1 for more information on the Système International (SI), a simplified version of the metric system adopted by scientists throughout the world. We shall generally use SI units in this book. If you are not familiar with the use of exponential numbers (scientific notation), read Appendix 4.

Example 1
What is the atomic symbol for bromine, and what is its atomic number? Why isn't the symbol

for bromine just the first letter of its name? What other element preempts the symbol B?


Bromine's atomic number is 35, and its symbol is Br; B is the symbol for boron.


Although all atoms of an element have the same number of protons, the atoms may differ in the number of neutrons they have (Table 1-2). These differing atoms of the same element are called isotopes. Four isotopes of helium (He) are shown in Figure 1-1. All atoms of chlorine (Cl) have 17 protons, but there are chlorine isotopes having 15 to 23 neutrons. Only two chlorine isotopes exist in significant amounts in nature, those with 18 neutrons (75.53% of all chlorine atoms found in nature), and those with 20 neutrons (24.47%). To write the symbol for an isotope, place the atomic number as a subscript and the mass number (protons plus neutrons) as a superscript to the left of the atomic symbol. The symbols for the two naturally occurring isotopes of chlorine then would be \textstyle{\frac{35}{17}}Cl and \textstyle{\frac{37}{17}}Cl. Strictly speaking, the subscript is unnecessary, since all atoms of chlorine have 17 protons. Hence the isotope symbols are usually written without the subscript: 35Cl and 37Cl. In discussing these isotopes, we use the. terms chlorine-35 and chlorine-37. For a nucleus to be stable, the number of neutrons should (for the first few elements) equal or slightly exceed the number of protons. The more protons, the greater the ratio of neutrons to protons to ensure stability. Nuclei that have too many of either kind of fundamental particle are unstable, and break down radioactively in ways that are discussed in Chapter 23.

Figure 1-1 Four isotopes of helium (He). All atoms of helium have two protons (hence two electrons), but the number of neutrons can vary. Most helium atoms in nature have two neutrons (helium-4), and fewer than one helium atom per million in nature has just one neutron (helium-3). The other helium isotopes, helium-5, helium-6, and helium-8 (not shown) are unstable and are seen only briefly in nuclear reactions (see Chapter 23). The size of the nucleus is grossly exaggerated here. If the nucleus were of the size shown, the atom would be half a kilometer across.
Example 2
How many protons, neutrons, and electrons are there in an atom of the most stable isotope of uranium, uranium-238? Write the symbol for this isotope. Refer to Figure. 1-1.

The atomic number of uranium (see the inside back cover) is 92, and the mass number of the isotope is given as 238. Hence it has 92 protons, 92 electrons,and 238 - 92 = 146 neutrons. Its symbol is \textstyle{\frac{238}{92}}U (or 238U).

The total mass of an atom is called its atomic weight, and this is almost but not exactly the sum of the masses of its constituent protons, neutrons and electrons. * When protons, neutrons, and electrons combine to form an atom, some of their mass is converted to energy and is given off. (This is the source of energy in nuclear fusion reactions.) Because the atom cannot be broken down into its fundamental particles unless the energy for the missing mass is supplied from outside it, this energy is called the binding energy of the nucleus.

* The terms atomic weight and molecular weight are universally used by working scientists, and will be used in this book, even though these are technically masses rather than weights.

Table 1-2. Composition of Typical Atoms and Ions
Electrons Protons Neutrons Atomic


Atomic Weight


Total Charge

(electron units)

Hydrogen atom, 1H or H 1 1 0 1 1.008 0
Deuterium atom, 2H or D 1 1 1 1 2.014 0
Tritium atom, 3H or T 1 1 2 1 3.016 0
Hydrogen ion, H+ 0 1 0 1 1.007 +1
Helium atom, 4He 2 2 2 2 4.003 0
Helium nucleus or alpha particle, He2+ or α 0 2 2 2 4.002 +2
Lithium atom, 7Li 3 3 4 3 7.016 0
Carbon atom, 12Ca 6 6 6 6 12.000 0
Oxygen atom, 16O 8 8 8 8 15.995 0
Chlorine atom, 35Cl 17 17 18 17 34.969 0
Chlorine atom, 37Cl 17 17 20 17 36.966 0
Naturally occurring mixture of chlorine 17 17 18 or 20 17 35.453 0
Uranium atom, 234U 92 92 142 92 234.04 0
Uranium atom, 235U 92 92 143 92 235.04 0
Uranium atom, 238U 92 92 146 92 238.05 0
Naturally occurring mixture of uranium 92 92 varied 92 238.03 0

Example 3
Calculate the mass that is lost when an atom of carbon-12 is formed from protons, electrons, and neutrons.
Since the atomic number of every carbon atom is 6, carbon-12 has 6 protons and therefore 6 electrons. To find the number of neutrons, we subtract the number of protons from the mass number: 12 - 6 = 6 neutrons. We can use the data in Table 1-1 to calculate the total mass of these particles:
Protons: 6 X 1.00728 amu = 6.04368 amu
Neutrons: 6 X 1.00867 amu = 6.05202 amu
Electrons: 6 X 0.00055 amu = 0.00330 amu
Total particle mass: 12.09900 amu
But by the definition of the scale of atomic mass units, the mass of one carbon-12 atom is exactly 12 amu. Hence 0.0990 amu of mass has disappeared in the process of building the atom from its particles.
Example 4
Calculate the expected atomic weight of the isotope of chlorine that has 20 neutrons. Compare this with the actual atomic weight of this isotope as given in Table 1-2.

The chlorine isotope has 17 protons and 20 neutrons:

Protons: 17 X 1.00728 amu = 17.1238 amu
Neutrons: 20 X 1.00867 amu = 20.1734 amu
Electrons: 17 X 0.00055 amu = 0.0094 amu
Total particle mass: 37.3066 amu
Actual observed atomic weight: 36.966 amu
Mass Loss: 0.341 amu

Each isotope of an element is characterized by an atomic number (total number of protons), a mass number (total number of protons and neutrons), and an atomic weight (mass of atom in atomic mass units). Since mass losses upon formation of an atom are small, the mass number is usually the same as the atomic weight rounded to the nearest integer. (For example, the atomic weight of chlorine-37 is 36.966, which is rounded to 37.) If there are several isotopes of an element in nature, then of course the experimentally observed atomic weight (the natural atomic weight) will be the weighted average of the isotope weights. The average is weighted according to the percent abundance of the isotopes. Chlorine occurs in nature as 75.53% chlorine-35 (34.97 amu) and 24.47% chlorine-37 (36.97 amu), so the weighted average of the isotope weights is

(0.7553 X 34.97 amu) + (0.2447 X 36.97 amu) = 35.46 amu

The atomic weights given inside the back cover of this book are all weighted averages of the isotopes occurring in nature, and these are the figures we shall use henceforth-unless we are specifically discussing one isotope. All isotopes of an element behave the same way chemically for the most part. Their behavior will differ in regard to mass-sensitive properties such as diffusion rates, which we'll look at later in this book.

Example 5
Magnesium (Mg) has three significant natural isotopes: 78.70% of all magnesium atoms have an atomic weight of 23.985 amu, 10.13% have an atomic weight of 24.986 amu, and 11.17% have an atomic weight of 25.983 amu. How many protons and neutrons are present in each of these three isotopes? How do we write the symbols for each isotope? Finally, what is the weighted average of the atomic weights?

There are 12 protons in all magnesium isotopes. The isotope whose atomic weight is 23.985 amu has a mass number of 24 (protons and neutrons), so 24 - 12 protons gives 12 neutrons. The symbol for this isotope is 24Mg. Similarly, the isotope whose atomic weight is 24.986 amu has a mass number of 25, 13 neutrons, and 25Mg as a symbol. The third isotope (25.983 amu) has a mass number of 26, 14 neutrons, and 26Mg as a symbol. We calculate the average atomic weight as follows:

(0.7870 X 23.985) + (0.1013 X 24.986) + (0.1117 X 25.983) = 24.31 amu
Example 6
Boron has two naturally occurring isotopes, lOB and 11B. We know that 80.22% of its atoms are 11B, atomic weight 11.009 amu. From the natural atomic weight given on the inside back cover, calculate the atomic weight of the lOB isotope.

If 80.22% of all boron atoms are 11B, then 100.00 - 80.22, or 19.78%, are the unknown isotope. We can use W to represent the unknown atomic weight in our calculation:

(0.8022 X 11.009) + (0.1978 X W) = 10.81 amu (natural atomic weight)
W = \textstyle{\frac{10.81-8.831}{0.1978}} = 10.01 amu


The formation of atoms from fundamental particles, interesting as this might be to the physicist, is far from being the ultimate stage in the organization of matter. As we mentioned earlier, when atoms are close enough to one another that the outer electrons of one atom can interact with the other atoms, then attractions can be set up between atoms, strong enough to hold them together in what is termed a chemical bond. In the simplest cases the bond arises from the sharing of two electrons between a pair of atoms, with one electron provided by each of the bonded atoms. Bonds based on electron sharing are known as covalent bonds, and two or more atoms held together as a unit by covalent bonds are known as a molecule. One of the principal triumphs of the theory of quantum mechanics in chemistry (see Chapter 8) has been its ability to predict the kinds of atoms that will bond together, and the three-dimensional structures and reactivities of the molecules that result. (A major section of this book, Chapters 8-14, is devoted to chemical bonding theories.)

Figure 1-2 Shapes and relative sizes of some simple molecules. Two bonded atoms appear to interpenetrate because their electron clouds overlap. By convention. a tapered bond in a drawing represents a bond pointing out toward the observer, with the wide end of the taper closest. and a dashed line is used for a bond that points back behind the plane of the page.

In molecular diagrams, a covalent, electron-sharing bond is represented by a straight line connecting the bonded atoms. In the water molecule, one atom of oxygen (0) is bonded to two hydrogen (H) atoms. The diagram for the molecule can be drawn two ways:

Chemical Principles, H20 Molecules.png

The second version acknowledges the fact that a water molecule is not linear; the two H -0 bonds make an angle of 105° with one another. Molecules of hydrogen gas, hydrogen sulfide, ammonia, methane, and methyl alcohol (methanol) have the following bond structures:

Molecules 2.png

These diagrams show only the connections between atoms in the molecules. They do not show the three-dimensional geometries (or shapes) of the molecules. Figure 1-2 shows the shapes and the relative bulk of several molecules. Note that the bond angle in molecules having more than two atoms can vary. The angle in the water molecule is 105°, and the angle in hydrogen sulfide is 92°; the four atoms connected to the central carbon in methane and methyl alcohol are directed to the four corners of a tetrahedron. The bond structure in straight-chain octane, one of the components of gasoline, is

Chemical Principles, Molecules 4.png

Each of the molecular diagrams shown can be condensed to a molecular formula, which tells how many atoms of each element are in the molecule, but provides little or no information as to how the atoms are connected. The molecular formula for hydrogen is H2; water, H20; hydrogen sulfide, H2S; ammonia, NH3; methane, CH4 ; methyl alcohol, CH30H or CH4O; and octane, C8H18. The formula for octane can also be written

Chemical Principles, Molecules 5.png

The sum of the atomic weights of all the atoms in a molecule is its molecular weight. Using the atomic weights on the inside back cover, we can calculate molecular weights. The molecular weight of hydrogen, H2, is

2 X 1.0080 amu = 2.0160 amu

A water molecule, H2O , has two atoms of hydrogen and one atom of oxygen, so:

(2 X 1.0080 amu) + (15.9994 amu) = 18.0154 amu
Example 7
Calculate the molecular weight of methyl alcohol.

The molecular formula is CH30H or CH4O. Then:

1 carbon: 1 X 12.011 amu = 12.011 amu
4 hydrogens: 4 X 1.008 amu = 4.032 amu
1 oxygen: 1 X 15.999 amu = 15.999 amu
Total particle mass: 32.04 amu

(If you wonder why the last figure has been dropped, see the discussion of significant figures in Appendix 4.)

In Example 7 notice that the natural atomic weight of carbon is not 12.000 amu but 12.011 amu, since carbon occurs as a mixture of 98.89% carbon-12 and 1.11% carbon-1 3, with trace amounts of carbon-14.

Example 8
What is the molecular weight of pure octane?

Since the molecular formula is C8H18", the molecular weight is:

(8 X 12.011) + (18 X 1.008) = 114.23 amu

Forces Between Molecules[edit]

Figure 1-3 The three states of matter: (a) In a gas the individual molecules move freely through space, colliding and rebounding. A gas adapts to the shape of its container and can easily be expanded or compressed. (b) Molecules in a liquid are in contact, but free to slide past one another. A liquid also adapts to the shape of its container, but it has a relatively fixed volume. (c) In a crystalline solid. molecules are packed in to a regular array, giving the solid both a fixed volume and a definite shape. Work must be done to break or deform a crystal. Adapted from R. E. Dickerson and 1. Geis. Chemistry, Matter, and the Universe, W. A. Benjamin. Menlo Park, Calif.. 1976.

Although the strongest attractions of an atom are for other atoms to which it is bonded in a molecule, two molecules themselves exert small but appreciable attractions on one another. Molecules are slightly "sticky." These forces, caused by momentary fluctuations in electron distributions around the atoms, are known as van der Waals attractions (after Dutch physicist Johannes van der Waals). They are responsible for the existence of three states (or phases) of matter at different temperatures: solids, liquids, and gases. Temperature is just a measure of the heat energy or energy of motion that a collection of molecules possesses. At low temperatures, the molecules have little energy of motion. The van der Waals attractions hold them together in an orderly, close-packed crystalline array or lattice (Figure 1-3c). This is the solid state. If more energy is fed into the crystal so the temperature rises, the molecules will vibrate about their average or equilibrium positions in the crystal. Enough energy will cause the ordered structure of the molecular crystal to break up, and the molecules will be free to slide past one another, although they are still touching (Figure 1-3b). This is the liquid state, and the transition temperature between solid and liquid is called the melting point, Tm. The liquid is still held together by van der Waals attractions, although the molecules have too much energy of motion to be locked into a rigid array. If still more energy is given to the liquid, the molecules will begin to move fast enough to overcome the van der Waals attractions, separate entirely from one another, and travel in independent molecular trajectories through space (Figure 1-3a). This is the gas phase, and the transition temperature between liquid and gas is called the boiling point, Tb. Changes in phase are treated in more detail in Chapter 18.

The melting and boiling points of some simple molecules are compared in Table 1-3. In general, larger molecules have higher melting and boiling points, since they have larger surface areas for van der Waals attractions. Thus at 1 atm. pressure H2 boils at - 252.5°C, CH4. boils at - 164.0 °C, but C8H18 must be heated to + 125.7°C before the molecules will separate from one another and go into the gas phase.

Table 1-3. Melting and Boiling Points of Some Simple Molecular Substances
Substance Molecular


Tm(°C) Tb(°C)
Hydrogen H2 -259.1 -252.5
Oxygen O2 -218.4 -183.0
Methane CH4 -182.5 -164.0
Hydrogen Sulfide H2S -85.5 -60.7
Chlorine Cl2 -101.0 -34.6
Ammonia NH3 -77.7 -33.4
Bromine Br2 -7.2 +58.8
Methanol CH3OH -93.9 +65.0
Water H2O 0 +100
n-Octane C8H18 +185 +125.7
Iodine I2 +113.5 +184.4
Sucrose (cane sugar) C12H22O11 +185 decomposes

Figure 1-4 The 0-H bonds in water and methanol (methyl alcohol) are polar because the oxygen atom has the stronger attraction for the electron pair and pulls negative charge toward itself, leaving the hydrogen with a fractional positive charge. This polarity is of great importance in interactions between molecules.

A second kind of force between molecules also influences melting and boiling points: the polarity of the molecules. If two atoms that are connected by an electron-pair covalent bond do not have the same attraction for electrons, then the electron pair will shift toward the atom with the greater electron pulling power. This will give that atom a slight excess of negative charge (represented by δ- rather than by just a minus sign, which would imply a full electron charge), and will confer a slight positive charge (δ+) on the atom that lost out in the tug-of-war for the electron pair. Because the electron-attracting power (electronegativity) of oxygen is greater than that of hydrogen, the oxygen atom in a molecule of water or methyl alcohol is slightly negative, and the hydrogen atoms are slightly positive (Figure 1-4). Such a molecule is termed polar because it behaves like a tiny electric dipole; that is, the negative charge on the oxygen attracts other nearby positive charges, and the positive charge on each hydrogen attracts other negative charges. This is another attractive force between molecules, in addition to van der Waals attractions. Because of the forces binding its molecules, methanol melts and boils at much higher temperatures than methane, which is similar to it in molecular size. Methanol is a liquid at room temperature, whereas methane is a gas. In water, the attractions between hydrogen and oxygen from different molecules are so strong that they are given the name of hydrogen bonds. Hydrogen bonds are especially' important in proteins and other giant molecules in living organisms. If it were not for polarity and hydrogen bonding, water would melt and boil at lower temperatures even than H2S (Table 1-3). It would be a gas at room temperature, rather than the Earth's most common liquid.

Molecules and Moles[edit]

So far we have talked only about individual atoms or molecules, and about masses measured in atomic mass units. But individual molecules are hard to manipulate in the laboratory, and chemists weigh their materials in grams, not in atomic mass units. To scale up from the molecular level to the laboratory level, we use a unit called a mole. A mole of a substance is equal to as many molecules of that substance as there are atoms of carbon-12 in exactly 12 g of carbon-12. This means that 1 mole of any substance is a weight, in grams, equal to that substance's molecular weight expressed in atomic mass units. Most important of all, by this definition, 1 mole of any substance contains the same number of molecules. The chemist can count atoms and molecules in the laboratory simply by weighing them.

The word mole applies not just to molecules but also to atoms; in practice, we speak of a mole of helium atoms as well as of a mole of water molecules. The term gram-atom applied to a mole of atoms is no longer widely used.

Example 9
How many grams of each of the following substances are there in 1 mole of that substance: H2, H20 , CH3OH, octane (C8H18), and neon gas (Ne)?

The molecular weights (in atomic mass units) of most of these substances have been given in previous examples, and the atomic weight of neon is listed on the inside back cover. One mole of each substance is therefore:

H2 2.0160 g break
C8H18 114.23 g
H2O 18.0154 g break
Ne 20.179 g
CH3OH 32.04 g break

Because the weights listed in Example 9 give the correct relative weights of the molecules that are being weighed out, each of the quantities of material will contain the same number of molecules. This is what makes the concept of moles useful. It is not even necessary to know what that number is, although we know it to be 6.022 X 1023 ; it is called Avogadro's number and is given the symbol N Going from molecules to moles means a scale-up of 6.022 X 1023 times. Avogadro's number is also the conversion factor between atomic mass units and grams as units of mass: 1 g = 6.022 X 1023 amu. If we think of the molecular weight as being the mass of a mole of substance, the units for molecular weight are grams per mole; if we think of it as the actual weight of one molecule, the numerical value is unchanged but the units become atomic mass units per molecule. Both are correct.

Example 10
One molecule of H2 reacts with one molecule of Cl2 to form two molecules of hydrogen chloride gas, HCl. What weight of chlorine gas should be used in order to react completely with 1 kilogram (kg) of hydrogen gas?

The molecular weights of H2 and Cl2 are 2.0160 g mole-1 and 70.906 g mole-1, respectively. * Hence 1000 g of H2 contains:

\textstyle\frac{1000 g}{2.0160 g mole^-1} = 496.0 moles of H2 molecules

Without knowing how many molecules there are in a mole, we can still be sure that 496.0 moles of Cl2 will have the same number of molecules as 496.0 moles or 1000 g of H2. How many grams of Cl2 are there in 496.0 moles? Since the molecular weight of Cl2 is 70.906 g mole-1,

496.0 moles X 70.906 g mole-1 = 35,170 g of Cl2

One kilogram equals 1000 g, so 35,170 g is 35.17 kg. If 1.00 kg H2 is made to react with 35.17 kg of C12, the reaction will be complete and none of either starting material will be left over.

* The expression "g mole-1" should be read as "grams per mole." In this notation, a speed in miles per hour is written with units of "miles hr-I."

Example 11
How many molecules of H2 and Cl2 would be present in the experiment of Example 10?

In 496.0 moles of any substance, there will be 496.0 moles X 6.022 X 1023 molecules mole-1, which equals 2.99 X 1026 molecules.

As a sobering example of just how large Avogadro's number is, 1 mole of coconuts, each 14 centimeters (cm) in diameter, would fill a volume as large as the entire planet earth. The use of moles in chemical calculations is the subject of the next chapter, but the idea has been introduced here because we need to know how to scale up from the molecular to the laboratory level.


Figure 1-5 Common table salt (sodium chloride. NaCl) is built from closely packed sodium ions, Na+ (small spheres). and chloride ions. CI- (large. colored spheres). Each ion of one charge is surrounded by six ions of the opposite charge at the four compass points and above and below. This is a particularly stable arrangement of charges. and it occurs in many salts. From Dickerson and Geis. Chemistry, Matter. and the Universe The Benjamin / Cummings Publishing Co .. Menlo Park. Ca .. © 1976 .

The idea of a covalent bond suggests equal sharing of the electron pair by the bonded atoms, but the brief discussion of polarity in Section 1-4 indicated that the sharing is not always equal. The relative electronegativity or electron-attracting power of atoms is of great importance in explaining chemical behavior, and is treated in detail in Chapters 9 and 10. Sodium atoms (and all metals in general) have a weak hold on electrons, whereas chlorine atoms are very electronegative. Hence in common table salt (sodium chloride, NaCl), each sodium atom, Na, loses one electron (e-) to form a sodium ion, Na+. Each chlorine atom picks up one electron to become a chloride ion, Cl-:

Na → Na+ + e-wordandword\textstyle{\frac{1}{2}} Cl2 + e- → Cl-

We write \textstyle{\frac{1}{2}} Cl2 because free chlorine gas exists as diatomic (two-atom) molecules, not as free chlorine atoms. Solid sodium chloride (Figure 1-5) has sodium and chloride ions packed into a three-dimensional lattice in such a way that each positive Na+ ion is surrounded on four sides and top and bottom by negative Cl- ions, and each Cl- is similarly surrounded by six nearest neighbor Na+ ions. This is a particularly stable arrangement of positive and negative charges.

Metals in general lose one to three electrons easily to become positively charged ions, or cations:

Li Li+ + e- ttt lithium ion
Na Na+ + e- ttt sodium ion
K K+ + e- ttt potassium ion
Mg Mg2+ + 2e- ttt magnesium ion
Ca Ca2+ + 2e- ttt calcium ion
Al Al3+ + 3e- ttt aluminum ion

Some nonmetals, in contrast, pick up electrons to become negatively charged ions, or anions:

\textstyle{\frac{1}{2}} F2 + e- F- ttt fluoride ion
\textstyle{\frac{1}{2}} Cl2 + e- Cl- ttt chloride ion
\textstyle{\frac{1}{2}} O2 + 2e- O2- ttt oxide ion
\textstyle{\frac{1}{2}} S2 + 2e- S2- ttt sulfide ion

Table 1-4 Some Simple Ions of Elements

Chemical Principles, Table 1.4.png

Other simple ions made from single atoms are shown in Table 1-4. The charge on a simple, single-atom ion such as AP+ or S2- is its oxidation state or oxidation number. It is the number of electrons that must be added to reduce (or removed to oxidize) the ion to the neutral species:

Reduction: AI3+ + 3e- Al
Oxidation: S2- S + 2e-

Pulling electrons away from an atom or removing them altogether is oxidation. Adding electrons to an atom or merely shifting them toward it is reduction.

Example 12
Is chlorine oxidized or reduced in forming the chloride ion? What is the oxidation state of the ion?

Chlorine is reduced, since one electron per chlorine atom is added to form the ion. The chloride ion, Cl- , is in the - 1 oxidation state.

Example 13
When metals are converted into their ions, are they oxidized or reduced? What is the oxidation state of the aluminum ion?

Metals are oxidized to their ions, since electrons are removed. The aluminum ion, AP+, is in the +3 oxidation state.

If two or more oxidation states for a metal ion are possible, they are differentiated by writing the oxidation state in Roman numerals after the name of the atom. An older nomenclature, still in use, identifies the higher oxidation state by the ending -ic and the lower by -ous. Hence,

Fe2+ tt
iron(II) or ferrous break
Fe3+ tt
iron(III) or ferric
Cu+ tt
copper(I) or cuprous break
Cu2+ tt
copper(II) or cupric
Sn2+ tt
tin(II) or stannous break
Sn4+ tt
tin(IV) or stannic
Example 14
When the ferric ion is converted to the ferrous ion, is this an oxidation or reduction? Write the equation for the process.

The equation is Fe3+ + e- Fe2+ . The process is a reduction since an electron is added.

The modern nomenclature with Roman numerals is easier to use because it does not require you to remember what the two oxidation states of a metal are, in order to know what a compound is from its name.

A salt is a compound made up of positive and negative ions. Because a salt must be electrically neutral, the total charge on its positive and negative ions must be zero. Since each ion of Sn2+ has a charge of +2, twice as many chloride ions with -1 charge each are required to produce a zero net charge. Hence the salt of Sn2+ and Cl- ions has the overall composition SnCl2, rather than SnCl or SnCl3. It is called stannous chloride or tin (II) chloride. The formula for stannic chloride or tin(IV) chloride is SnCl4.

In addition to these simple ions, compound or complex ions can be formed between a metal or nonmetal and oxygen, chlorine, ammonia (NH3), the hydroxide ion (OH-), or other chemical groups. The sulfate ion, SO\textstyle{\frac{2-}{4}}, has four oxygens at the corners of a tetrahedron around the central sulfur atom, and an overall charge of -2. The nitrate ion, NO\textstyle{\frac{}{3}}, has three oxygen atoms in an equilateral triangle around the nitrogen, and a -1 charge. The ammonium ion, NH\textstyle{\frac{+}{4}}, has four hydrogens at the corners of a tetrahedron, and a +1 charge. These ions are thought of as units because they form salts the way single-atom ions do, and go through many chemical reactions unchanged. Silver nitrate, AgN03, is a salt containing equal numbers of Ag+ and NO\textstyle{\frac{}{3}} ions. Ammonium sulfate is a salt with twice as many ammonium ions, NH\textstyle{\frac{+}{4}}, as sulfate ions, SO\textstyle{\frac{2-}{4}}, and the chemical formula (NH4)2S04. Other typical complex ions are shown in Table 1-5.

Table 1-5 Some Common Complex Ions

Chemical Principles, Table 1.5.png

When a central atom is surrounded by several equally spaced atoms, the number of surrounding atoms is called the coordination number. The most important factor is size. Nitrogen in the nitrate ion, NO\textstyle{\frac{ }{3}}, has room for three oxygen atoms around it, and hence a coordination number of 3 for oxygen. The sulfur atom is larger than a nitrogen atom, and can accommodate one more oxygen atom in the sulfate ion, SO\textstyle{\frac{2-}{4}}. Hence the coordination number of sulfur for oxygen is 4.

The most common coordination numbers are 2, 3, 4, and 6, (See Table 1-6.) An ion or molecule with a central atom having a coordination number of 2 can be either linear, as carbon dioxide with O-C-O in a straight line, or bent, as in water, H20. Possible structures for ions or molecules with coordination numbers of 3, 4, and 6 are shown in Table 1-6.

Table 1-6 Common Coordination Numbers

Chemistry Principles Table 1.6.png

Figure 1-6 Geometry of atoms around central atoms with coordination numbers 3, 4, and 6. If L is any peripheral atom and M is the central atom, then the bond angle L - M - L is 120° for trigonal planar, 109.5° for tetrahedral, and typically around 109.5° for trigonal pyramidal geometries. Square planar and octahedral geometries have two L - M - L angles, 90° and 180°.

It is not strictly correct to talk about molecular formulas and molecular weights of salts, since there are no molecules in salts-only ordered lattices of ions. No one sodium ion in the sodium chloride structure shown in Figure 1-5 "belongs" to a particular chloride ion. It is correct, however, to speak of the chemical formula of a salt, and the formula weight that corresponds to it. Since the chemical formula for sodium chloride is NaCl, the formula weight of sodium chloride is the sum of the atomic weights of one atom of sodium and one atom of chlorine:

1 sodium: tt
22.990 amu
1 chlorine: tt
35.453 amu
Total: tt
58.443 amu

It is conventional to call this the "molecular weight" of sodium chloride, and no confusion results as long as you realize what a salt structure is like. A mole of sodium chloride is 58.443 g. It will contain 6.022 X 1023 sodium ions and 6.022 X 1023 chloride ions. Even though they are not paired off into molecules, the ratio is strictly one to one.

Example 15
What is the molecular weight of ammonium sulfate?

The chemical formula of ammonium sulfate is (NH4)2SO4, so the molecular weight (actually the formula weight) is

2 nitrogens: tt
2 X 14.007 amu= tt
28.014 amu
8 hydrogens: tt
8 X 1.008 amu= tt
8.064 amu
1 sulfur: tt
1 X 32.06 amu= tt
32.06 amu
4 oxygen: tt
4 X 15.999 amu= tt
63.996 amu
Total: tt
132.13 amu

The simple anions are named by adding -ide to the name of the element, as in the fluoride (F-), chloride (Cl-), oxide (O2-), and sulfide (S2-) ions. Where more than one complex anion of an element with oxygen can be formed, the suffixes -ate and -ite are used for the higher and lower oxidation states, respectively. Thus,

Sulfate ion: tt
SO\textstyle{\frac{2-}{4}} word
Sulfite ion: tt
Nitrate ion: tt
NO\textstyle{\frac{ }{3}} word
Nitrite ion: tt
NO\textstyle{\frac{ }{2}}
Arsenate ion: tt
AsO\textstyle{\frac{3-}{4}} word
Arsenite ion: tt

If more than two such anions exist, then the prefixes hypo- ("under") and per- ("beyond") are used:

Perchlorate ion: tt
ClO\textstyle{\frac{ }{4}}
Chlorate ion: tt
ClO\textstyle{\frac{ }{3}}
Chlorite ion: tt
ClO\textstyle{\frac{ }{2}}
Hypochlorite ion: tt
ClO\textstyle{\frac{ }{ }}

Melting Points and Boiling Points of Salts[edit]

A salt crystal represents a particularly stable balance of positive and negative charges, with each type of ion being kept out of the way of others of like charge. Melting a salt crystal means upsetting this delicate balance of charges, and allowing mutually repelling ions to come closer together from time to time as the ions flow past one another. This disruption of structure requires large amounts of energy to accomplish, so the melting points of salts are higher than those of molecular solids. The melting points of two salts, sodium chloride (NaCI) and potassium sulfate (K2SO4), are compared in Table 1-7 with those of the elements from which the salts are made.

Table 1-7. Melting and Boiling Points of Two Salts and Their Component Elements
Substance Chemical


Tm(°C) Tb(°C)
Sodium metal Na 97.8 882.9
Chlorine Gas Cl2 -101.0 -34.6
Sodium Chloride (salt) NaCl 801 1413
Potassium metal K 64 774
Sulfur S 119 445
Oxygen gas O2 -218 -183
Potassium sulfate (salt) K2SO4 1069 1689

Metallic sodium melts at 97.8°C, and solid chlorine melts at -101°C, but their combination, sodium chloride (common table salt), requires a temperature of 801°C before it will melt. Boiling or vaporizing a salt is even more difficult. The ions remain ions in the liquid state, tumbling past one another as in any other liquid; but before the gas phase can be attained, Na+ and CI- ions must pair off into neutral NaCl molecules. To accomplish this pairing, electrons have to be pulled away from CI- ions, which have a strong attraction for them, and pushed toward Na+ ions, which do not want them. The NaCl bond in sodium chloride vapor is extremely polar, with the electron pair skewed strongly toward the chlorine atom, but the separation still is not as complete as in Na+ and CI- ions. Much energy is required to push electrons where they are not wanted and to make NaCl molecules from Na+ and CI- ions, so high temperatures are required before this can happen. Hence the very high boiling points of salts in comparison with molecular compounds, as illustrated in Table 1-7.

Ions in Solution[edit]

Figure 1-7 Breakup of a salt crystal by water molecules. with hydration of ions. Each salt ion in solution is surrounded by polar water molecules with the opposite charge to that of the ion turned toward it. This electrostatic hydration energy compensates for the loss of attractions between ions in the salt crystal. From Dickerson and Geis. Chemistry, Matter, and the Universe.

Although salts are hard to melt and even harder to vaporize, many can be dissolved easily in a polar liquid such as water. The reason for this is simple. The water molecules help to dismantle the salt crystal, since the partial positive and negative charges on the polar water molecules (Figure 1-4) provide a substitute for the positive and negative charges that were present in the crystal lattice. Figure 1-7 illustrates what happens when a crystal such as sodium chloride is dissolved in water. Each positively charged Na+ is surrounded by water molecules with their negatively charged oxygens turned toward it, and each negatively charged Cl- ion is surrounded by water molecules with their positively charged hydrogens closest. The ions from the salt crystal are said to be hydrated. If the stability that hydration gives the ions in solution is greater than the stability of the crystal lattice, then the salt will dissolve. Sodium chloride is a familiar example of a soluble salt. In contrast, if the hydration energy is too small, then the crystal will be the more stable form, and it will not dissolve in water. Silver chloride (AgCl) and barium sulfate (BaS04) are examples of insoluble salts. When a salt crystal dissolves, it does not simply come apart into ions; it is taken apart by the molecules of the liquid in which it is dissolved (the solvent). This is why salts will not dissolve in nonpolar liquids such as gasoline (octane, C8H18); there are no charges on the solvent molecules to make up for the loss of charge attractions within the crystalline salt.

Salt solutions conduct electricity, and this property was extremely important early in the development of theories of chemical bonding. Electrical conduction in metals takes place by means of moving electrons; the metal ions remain in place. Crystalline salts do not conduct electricity at all, but if the salt is melted, then positive ions can migrate one way through the liquid and negative ions can move the other way in the presence of an electric field. This mobility of ions is even greater if the salt is dissolved in water and the ions consequently are hydrated.

Some of the first concrete ideas about the nature of chemical bonding came from the electrolysis experiments of the English scientist Michael Faraday (1791-1867). (Electrolysis means "breaking apart with electricity.") If sodium chloride is melted (above 801°C) and if two electrodes (the cathode and the anode) are inserted into the melt as shown in Figure 1-8 and an electric current is passed through the molten salt, then chemical reactions take place at the electrodes: Sodium ions migrate to the cathode, where electrons enter the melt, and are reduced to sodium metal:

Figure 1-8 A commercial electrolysis cell for the production of metallic sodium and chlorine gas from molten NaCl. Liquid sodium floats to the top of the melt above the cathode and is drained off into a storage tank. Chlorine gas bubbles out of the melt above the anode. From Dickerson and Geis. Chemistry. Matter. and the Universe.
Figure 1-9 Schematic diagram of an electrolysis cell. For current to be carried , the fluid must contain mobile ions, either as a molten salt or as hydrated ions in solution , A substance capable of carrying current by migration of ions is called an electrolyte. If the electrolyte is a solution of CuCl2 , which dissociates (breaks apart) to give Cu2+ and CI- ions, then as current is passed through the cell. Cu2+ ions migrate to the cathode and are reduced to metallic copper, and CI- ions migrate to the anode, where they are oxidized to Cl2 gas. Platinum electrodes are used because they are chemically inert and will not react.
Na+ + e-(from cathode) Na

Chloride ions migrate the other way, toward the anode, give up their electrons to the anode, and are oxidized to chlorine gas:

Cl- \textstyle{\frac{1}{2}}C12 + e-(to anode)

The overall reaction is the breakdown of sodium chloride into its elements:

Na+ + CI- Na + \textstyle{\frac{1}{2}}C12

Sodium ions are reduced and chloride ions are oxidized. Electrolysis can also be carried out by passing electric current through solutions of salts (Figure 1-9). If a solution of sodium chloride in water is electrolyzed, chlorine gas is given off at the anode as in the case of molten sodium chloride, but the cathode product is hydrogen gas rather than metallic sodium:

Na+ + Cl- + H2O Na + \textstyle{\frac{1}{2}}C12 + \textstyle{\frac{1}{2}}H2 + OH- (1-1)

This is the same result that would be obtained if liquid sodium chloride was first electrolyzed to give metallic sodium:

Na+ + Cl- Na + \textstyle{\frac{1}{2}}C12 (1-2)

and the sodium was then dumped into water:

Na + H2O Na+ + \textstyle{\frac{1}{2}}H2 + OH- (1-3)

Equation 1-1 is just the sum of equations 1-2 and 1-3, since the sodium metal that is produced in equation 1-2 is used up in equation 1-3. There is nothing mysterious about the different cathode products during electrolysis of sodium chloride in a melt or in solution, If water is present, some of the H2O molecules will be dissociated into H+ and OH- ions. Because H+ has a greater affinity for electrons than Na+ does, the H+ ions will take electrons away from metallic sodium, making the anode product H2 rather than Na, and leaving Na+ ions in solution. In contrast, Cu2+ ions have a greater affinity for electrons than H+ ions do, so the anode product of electrolysis of CuCl2 is metallic copper, whether the process is carried out in the melt or in solution (Figure 1-9). Typical products of electrolysis of solutions and melts are given in Table 1-8. Electrochemical reactions and cells are discussed in detail in Chapter 19. At the moment, we are focusing on what electrochemical reactions tell us about chemical bonding.

Table 1-8. Products of Electrolysis
Cathode Producttt
Anode Product
Sulfuric acid (H2SO4) in H2Ott
Sodium sulfate (Na2SO4) in H2Ott
Sodium chloride (NaCl) in H2Ott
Potassium iodide (Kl) in H20tt
Copper sulfate (Cu2SO4) in H20tt
Silver nitrate (AgNO3) in H2Ott
Mercuric nitrate [Hg(NO3)2] in H20tt
Lead nitrate [Pb(NO3)2] in H20tt
O2 and some PbO2
Molten lye (NaOH); not in H2Ott

Faraday found that there was a quantitative relationship between the amount of electricity passed through an electrolytic cell and the amount of chemical change produced. He formulated Faraday's laws of electrolysis, which in terms of the modern theory of atoms and ions can be expressed as follows:

1. Passing the same quantity of electricity through a cell always leads to the same amount of chemical change for a given reaction. The weight of an element deposited or liberated at an electrode is proportional to the amount of electricity that is passed through.

2. It takes 96,485 coulombs of electricity to deposit or liberate 1 mole of a substance that gains or loses one electron during the cell reaction. If n electrons are involved in the reaction, then 96,485n coulombs of electricity are required to liberate a mole of product.

The quantity 96,485 coulombs of electricity has become known as 1 faraday in his honor, and has been given the symbol \mathcal{F}. Faraday's laws become self-evident when you realize that 1 \mathcal{F} is simply the charge on 1 mole of electrons, or 6.022 X 1023 electrons. The scale-up factor of 6.022 X 1023 from molecules to moles is paralleled by the same scale-up factor from 1 electron charge to 1 \mathcal{F} of charge. At the time, of course, Faraday knew neither the value of Avogadro's number nor the charge on an electron. His experiments did tell him, however, that charges on ions came in multiples of a fundamental unit, such that 96,485 coulombs corresponded to a mole of these units. The word electron first appeared in 1881, when the British physicist G. J. Stoney coined it to denote this fundamental unit of ionic charge. Its application to a real negatively charged particle came a decade later.

Example 16
Write equations for the reactions that occur when current is passed through molten NaCl. How many grams of sodium and chlorine are released when 1 \mathcal{F} of charge is passed through the cell?

The cathode reaction is Na+ + e- Na, and the anode reaction is Cl- \textstyle{\frac{1}{2}}Cl2 + e-. When 1 mole of electrons (1\mathcal{F}) passes through molten NaCI, each electron reduces one sodium ion, so 1 mole of sodium atoms is produced. Hence 22.990 g of Na are deposited at the cathode. At the anode, 1 mole of electrons is removed from 1 mole of chloride ions, leaving 1 mole of chlorine atoms, which combine pairwise to make \textstyle{\frac{1}{2}} mole of Cl2 molecules. Hence the weight of chlorine gas released is 35.453 g (the atomic weight of Cl, half the molecular weight of Cl2).

Example 17
How many grams of magnesium metal and chlorine gas are released when 1 \mathcal{F} of electricity is passed through an electrolytic cell containing molten magnesium chloride, MgC12?

The cathode reaction is Mg2+ + 2e- Mg, and the anode reaction is this: 2Cl- Cl2 + 2e-. Since two electrons are required to reduce each ion of Mg2+, 1 mole of electrons will be sufficient to reduce half a mole of magnesium ions, depositing 12.153 g of magnesium. (The atomic weight of magnesium is 24.305 g mole-1.) As in Example 16, 1 mole of Cl- ions is oxidized, liberating half a mole or 35.453 g of Cl2 gas.

Example 18
The main commercial source of aluminum metal is the electrolysis of molten salts of Al3+. How many faradays of charge, and how many coulombs, must be passed through the melt to deposit 1 kg of metal?

One kilogram of aluminum is 1000 g/26.98 g mole-1, or 37.06 moles. Since each atom of aluminum deposited requires three electrons, 37.06 moles will require 3 X 37.06, or 111.2, moles of electrons. Hence 111.2\mathcal{F} or 10,730,000 coulombs will be needed.

Example 19
Electron flow at the rate of 1 coulomb per second (coulomb sec-1) is a current of 1 ampere (A). Currents in industrial electrolytic production of aluminum are ordinarily in the range of 20,000 to 50,000 A. If a cell is operated at 40,000 A (40,000 coulombs sec-1), how long will it take to produce the kilogram of aluminum metal mentioned in Example 18?

The time required will be

\textstyle{\frac{10,730,000 coulombs}{40,000 coulombs sec^-1}} = 268 sec or 4.5 min
Figure 1-10 Illustrations of Faraday's laws of electrolysis (a) Two electrons are required to reduce each ion of Cu2+, or 2 moles of electrons (2\mathcal{F}) for each mole of copper. Each faraday is enough to oxidize 1 mole of Cl- ions to \textstyle{\frac{1}{2}} mole of Cl2 gas. (b) Only 1\mathcal{F} of charge is required to reduce 1 mole of Ag+ ions to metallic silver. since the ionic charge on Ag+ is only +1. Chlorine gas is liberated at the same rate per faraday as before.

Faraday's laws are represented diagrammatically in Figure 1-10. We have been using these laws with a prior knowledge of the charges on different ions, and the knowledge that 96,485 coulombs is the total charge on 6.022 X 1023 electrons. History actually operated in reverse: Faraday and others used electrolysis experiments to find out what the charges on ions were. The reasoning used is illustrated in Table 1-9. If twice as much electricity is required to liberate a mole of copper as a mole of silver (assuming that you know the atomic weights of the two metals and can calculate the weights of a mole of each), then the copper ion must have twice the charge of the silver ion. In Table 1-9, the number of faradays of charge required to liberate 1 mole of an element is the same as the number of charges, positive or negative, on the ion.

Table 1-9. Deduction of Ionic Charge by Electrolysis
Product of


Electrode Faradays per mole

of atoms deposited

Ion in


Silver (Ag) Cathode 1a Ag+
Chlorine (Cl2) Anode 1 Cl-
Copper (Cu) Cathode 2 Cu2+
Hydrogen (H2) Cathode 1 H+
Iodine (I2) Anode 2 I-
Oxygen (O2)b Anode 2 O2-
Zinc (Zn) Cathode 2 Zn2+

a For example, electrolysis of silver nitrate solution for 1 hour by using a current of 0.5 A deposits 2.015 g of silver; 2.015/107.9 = 0.0187 mole of silver.

(0.5 coulomb sec^-1) x 3600 sec = 0.0187 \mathcal{F}

96.485 coulombs \mathcal{F}-1

b Actually, oxygen (02) is produced by a complicated electrode reaction. The species 02- can exist in molten oxides, but in water 02- becomes 20H- by reaction with a water molecule.

Gaseous Ions[edit]

Figure 1-11 A Crookes tube. When a high voltage (about 10,000 volts) is applied across two electrodes in a sealed glass tube containing gas at low pressure, the voltage induces the breakdown of gas molecules into electrons and positive ions. The electrons stream toward the anode and are known as cathode rays, and the positive ions stream toward the cathode and are termed canal rays. If the cathode is perforated, the positive ions will pass through it and cause a glow where they strike the glass walls. If a lightweight pinwheel is placed in the path of the cathode rays. they can cause it to rotate . As the electrons of the cathode rays move toward the anode. they strike other gas molecules and set up a glow discharge that is familiar in neon signs.

It was proposed even as far back as the time of Ben Franklin and John Dalton that the forces between particles of matter must be electrical in some way. But because like charges repel one another, it was believed, wrongly, that bonds could not exist between identical atoms, whereas we now know that most common gases occur as diatomic molecules: H2, N2, 02, F2, Cl2, and so on. This one blunder led to nearly a half-century of confusion about molecular structure and atomic weights, during which it was thought that hydrogen gas was H instead of H2 water was HO instead of H2O, and oxygen had an atomic weight of 8 rather than 16. Electron pairs as the "glue" that holds atoms together in covalent bonds were not even proposed systematically until 1913, by G. N. Lewis; they were not explained theoretically for still another 20 years. Faraday's experiments showed that the charges on ions did occur naturally in fundamental pieces or units such that a mole of these charges equaled 1 \mathcal{F}, and Stoney named this elemental unit the electron. But Stoney's electron was not necessarily a particle that could be isolated and studied.

The people who first showed that electrons were real particles that could be added to or removed from atoms were physicists studying the effects of electricity on gases. They found that if they set up an electrical potential of 10,000 volts between two electrodes in a sealed tube (a Crookes tube) containing gas at low pressure, they observed a glow discharge (Figure 1-11). This discharge is what makes neon signs glow. The electrical potential strips electrons from atoms of the gas, sending the electrons streaming toward the anode and positive ions toward the cathode. These moving electrons (the cathode rays) can be detected by watching the flashes of light on a zinc sulfide screen placed in the tube. If a lightweight pinwheel is set up in the path of the electrons inside the tube, the electrons even make the pinwheel rotate. On their way to the anode, the cathode rays strike other atoms of the gas, causing the emission of light in a glow discharge. The color of the glow discharge will vary, depending on the gas used· inside the tube.

If a metal plate with a slit is placed in front of the cathode, then the electrons in the cathode ray will be confined to a thin beam. This beam is deflected by electric and magnetic fields in a way that indicates that the particles in the beam carry a negative charge. The relative amount of bending of the canal rays (positive ions) and cathode rays (negative electrons) shows that the cathode ray particles are extremely light, whereas the positive ions are roughly as heavy as the original atoms from which they came. The exact nature of the canal rays depends on what gas is used in the tube, but the cathode rays are the same for all gases. J. J. Thomson (1856- 1940) suggested that the particles in the cathode rays might in fact be Stoney's "electrons," and in 1897 he found a way to use the deflection of the beam by electric and magnetic fields to calculate the charge-to-mass ratio (elm) of the particles. He found that

\textstyle{\frac{e}{m}} = 1.76 x 108 coulombs g-1
Figure 1-12 The mass spectrometer, Electrons emitted by an ionizing source bombard gas molecules and produce positive ions . These ions are accelerated by an electric field. and they are then passed through collimating slits (51 and 52), which direct the ions into parallel beams. These beams are bent in an electric field. resulting in diverging beams of ions moving with different speeds. The collimating slits are aligned so that only ions headed straight along the tube arrive at the point of divergence. A magnetic field refocuses the beams in such a way that all ions of the same charge-to-mass ratio strike the same spot on the photographic plate.

Example 20
Assume that Thomson's cathode ray particles are in fact the same as Stoney's and Faraday's electrons, and that 1\mathcal{F} is a mole of electrons. Calculate the mass of one electron.

The charge on one electron is

e = \textstyle{\frac{1\mathcal{F}}{N}} = \textstyle{\frac{96,485 coulombs mole^-1}{6.022 X 10^23 electrons mole^-1}}
= 1.602x 1019 coulomb
m = \textstyle{\frac{1.602x 10^19coulomb}{1.76 X 10^8 coulomb g^-1}} = 0.910 x 10-27 g

Figure 1-13 Millikan's oil-drop experiment. Tiny droplets of oil are introduced between two plates that can be given an electrostatic charge. A drop of oil is allowed to fall freely through the air, and its path is monitored . The radius of the drop is calculated from the terminal velocity of its fall and the viscosity of air The air is ionized by x rays. and negatively charged particles (electrons) stick to the oil drops. The charge on a drop can be determined from the voltage that must be applied across the condenser plates to make the drop hang motionless, with electrostatic and gravitational forces in balance.

A modern descendant of the Crookes tube and Thomson's apparatus is the mass spectrometer (Figure 1-12). It is a valuable research tool for measuring the mass per unit charge of any substance that can be given a positive charge. Mass spectrometry offers the most direct measurement of atomic weights of elements, and it is the method by which isotopes can be both identified and separated. By looking at the masses of the fragments into which molecules are broken down during electron bombardment in the spectrometer, organic chemists can obtain useful information about the molecular structure of a substance. (During the development of the atomic bomb in World War II, mass spectrometry was used to separate fissionable 235U from 238U, although the extremely low pressures that mass spectrometry requires were not practical for large-scale production.)

Although the ratio of electron charge to electron mass was measured in 1897 by Thomson, the charge itself was not measured until 1911 , when Robert A. Millikan (1868-1953) obtained the charge by the ingenious experiment illustrated in Figure 1-13. He used x rays to irradiate a spray of tiny oil droplets between two chargeable plates. Electrons from ionization of the air around the drops adhered to the drops, giving them one, two, or more electron charges. Millikan measured first the rate of free fall of the charged drops through air of known viscosity. Then he measured the voltage across the plates that was sufficient to suspend the drops motionless between the plates. He calculated that the charge on anyone drop was always an integral multiple of 1.6022 X 10-19 coulomb, and he concluded correctly that this was the charge on a single electron.

Example 20 actually was presented the wrong way around. We can solve it only because we know the value of Avogadro's number, whereas in fact Millikan's results furnished one way of calculating Avogadro's number.

Example 21
Assume that you do not know the value of Avogadro's number, but that you recognize that the faraday is the charge necessary to reduce 1 mole of Na+ ions, with one of Millikan's electrons combining with each ion. Calculate the number of ions in a mole, or Avogadro's number.

The charge on one electron is

N =\textstyle{\frac{96,485 coulombs mole^-1}{1.6022 X 10^-19 coulomb ion^-1}} = 6.022 x 1023 ions mole-1


An atom consists of a positively charged nucleus surrounded by enough negatively charged electrons to yield zero net charge. The nucleus is constructed from positively charged protons and neutral neutrons, each of mass approximately 1 amu. The mass of an electron is approximately 1/ 1836 the mass of a proton; the charge on an electron is equal but opposite in sign to the charge on a proton. The total number of protons in the nucleus (and electrons in a neutral atom) is the atomic number, Z. The total number of both protons and neutrons is the mass number, and the mass of the atom, in atomic mass units, is its atomic weight. The atomic weight is always slightly less than the sum of masses of the particles that go into making an atom, because mass is converted to energy and lost when the atom is formed.

All atoms with the same number of protons, and therefore the same atomic number, are classified as the same element and represented by a one- or two-letter symbol. Atoms of the same element with varying numbers of neutrons are called isotopes of the element. Isotopes are identified by placing the mass number as a superscript to the left of the symbol of the element (e.g., 37Cl). The atomic number is sometimes added as a subscript (e.g., \textstyle\frac{37}{17}Cl), although it is actually not necessary since the element's name and atomic number are known from the symbol. Each isotope of an element has its own atomic weight, and the natural atomic weight is the weighted average of these isotopic values, the weighting being according to the natural abundance of each isotope.

A collection of atoms held together by chemical bonds is a molecule Usually, but not always, the bonding in a molecule can be explained in terms of electron pairs, each holding two atoms together. Such an electronpair bond is a covalent bond. The sum of the atomic weights of all the atoms in a molecule is its molecular weight. Although atoms in different molecules are not directly bonded to one another, all molecules are slightly "sticky," and are attracted to other molecules. These van der Waals attractions will make the molecules of a gas adhere to one another to form a liquid if the temperature falls low enough, and make the molecules of a liquid fit together in a regular crystalline array in a solid if the temperature falls lower still. The temperatures at which these two transitions occur are the boiling point, Tb , and the melting point, Tm' respectively.

If two atoms differ in their intrinsic electron-pulling power or electronegativity, then the electron pair of the bond between them will be shifted toward the atom with the greater attraction, giving it a negative charge and the other atom a positive charge. The bond, and molecules that contain such bonds, are said to be polar. Polar molecules can attract one another, and they can also attract positively and negatively charged ions. Melting and boiling points of polar molecules are higher than would be expected from van der Waals attractions alone, because their polarity provides a second type of intermolecular attraction.

Atomic and molecular weights are measured on a scale of atomic mass units (amu), where 1 amu is defined as exactly one-twelfth of the mass of a I2C atom. A quantity of a chemical substance (atoms, molecules, or ions) equal to the atomic weight expressed in grams is defined as 1 mole of that substance. One mole of any substance-atoms, molecules or ions-contains the same number of particles of that substance. This property makes the mole a useful means of counting out particles merely by weighing them. The units of atomic and molecular weights are either grams per mole or amu per molecule (or atom).

Some atoms, those of metals in particular, have a weak hold on their electrons and can lose one, two, or more electrons to become positively charged ions, or cations. Many nonmetals or groups of atoms can acquire one or more negative charges to become negatively charged ions, or anions. A salt is a compound of the relative number of cations and anions that will produce zero overall charge. Common table salt, NaCl, contains equal numbers of Na+ and Cl- ions. The pulling away or outright removal of electrons is termed oxidation, and the addition to or shifting of electrons toward an atom is reduction. Since electrons are never created or destroyed in chemical reactions, whenever one substance is oxidized, some other substance must be reduced.

Simple anions made by adding electrons to single atoms have names ending in -ide, as chloride, Cl-, and sulfide, S2-, ions. For complex ions of a nonmetal atom with oxygen, the higher and lower oxidation state ions are differentiated by the suffixes -ate and -ite. The oxidation state of a metal cation (see Chapter 10) is indicated by a Roman numeral after the name of the metal, as in Fe3+, iron(III), or by the suffixes -ic and -ous.

Although salts do not have separate molecules and, strictly speaking, cannot have molecular weights, they do have chemical formulas that express their overall composition in the simplest possibJe way. The weight of 1 mole of these atoms is the formula weight of the salt, but it is customary to refer to this as the salt's "molecular weight." Thus magnesium chloride has one Mg2+ ion for every two Cl- ions, a net charge of zero, a chemical formula of MgCl2, and a molecular weight of 95.211 g mole-1.

The coordination number in a complex ion or molecule is the number of atoms or chemical groups bonded directly to the central atom. These bonding groups can be simple ions such as O2- and Cl- or molecules such as ammonia (NH3) and water (H2O). The maximum coordination number for a given central atom depends on the size of the atom and the size of its surrounding groups. The most common coordination numbers are 2, 3, 4, and 6.

Salts have higher melting and boiling points than molecular substances, because heat energy must be supplied to break apart the stable crystal lattice, and even more heat energy is required to force positive and negative ions to pair off and share electrons in neutral molecules that can go into a gas phase. Salts often dissolve readily in water, however, because polar attractions by the water molecules can compensate for the attractions of other ions in the crystal. Ions surrounded by polar water molecules in solution are said to be hydrated. Gasoline and similar nonpolar liquids cannot dissolve salts because they cannot hydrate (or solvate, if the solvent is other than water) the ions.

If a current of electricity is passed through molten salt or a salt solution, the current is carried by ions migrating in opposite directions. At the cathode, where electrons enter the salt medium, metal cations can be reduced to pure metal. At the anode, where electrons flow out of the salt and back into the external circuit, anions can be oxidized to liberate pure nonmetallic elements. This is the process of electrolysis. Faraday found a quantitative relationship between the amount of charge passed through a cell and the amount of chemical change produced: 96,485 coulombs of charge will bring about 1 mole of a change that involves one electron per ion. The quantity, 96,485 coulombs, is simply the charge on 1 mole of electrons and is called 1 faraday (\mathcal{F}) of charge.

Electrons as separate particles were studied by physicists interested in low-pressure gas discharges under high voltages. Cathode rays consist of a beam of electrons stripped away from the gas atoms. J. J. Thomson showed, by means of deflecting magnetic and electrostatic fields, that the cathode rays were made of negatively charged particles, and he measured the charge-to-mass ratio of the particles. R. A. Millikan completed the process, in his oil-drop experiment, by successfully measuring the charge on the electron. This, combined with Faraday's results, led to the calculation of Avogadro's number, the number of electrons in a faraday of charge, or the number of particles in a mole of any substance. The mass spectrometer, a descendant of Thomson's gas-discharge tubes, is a modern analytical tool and a means of finding the charge-to-mass ratio for any atomic or molecular species that can be given a charge.