Chemical Principles/Are Atoms Real? From Democritus to Dulong and Petit

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The atomic hypothesis provides a convenient
form of speech, which succesifully
describes many of the facts in a metaphorical
manner. But the handy way in
which the atomic hypothesis lends itself
to the representation of the characteristic
features of a chemical change falls
short of constituting a proof that atoms
have any real existence.

Alexander Smith, Professor of
Chemistry, University of Chicago


In the first five chapters you encountered some of the most fundamental ideas in chemistry: atoms, molecules, moles, conservation of mass and energy, behavior of gases, kinetic theory, equilibrium, and acid-base chemistry in solution. All these ideas have been presented in a very dogmatic way, without proof of any kind. It is time now to stop being a believer and to become a skeptic. How do we know that the material in the first five chapters is true? How do we know, for example, that the molecular formula for water is H20? After all, the best chemists in the world thought it was HO for a full 58 years after the atomic theory was proposed in 1802 by John Dalton. Why did they change their minds? What gives us the right to assert that one atom of carbon is approximately 12 times as heavy as one atom of hydrogen? It is not easy to think of ways to weigh out equal numbers of atoms without the mole concept, and this concept depends on the existence of a reliable set of atomic weights, which brings us back in a circle to the relative weights of carbon and hydrogen. How can the circle be broken?

How are the atomic numbers for elements obtained? Why should atoms with the same atomic number but different atomic weights (isotopes) have so nearly identical chemical properties that they are given the same symbol and classed as one element? What evidence is there that the negative charges in an atom are on the outside, and the positive charges are grouped in a tiny central nucleus that contains virtually all the mass of the atom? And what do we mean by the radius of an atom? Is not the size of an atom as difficult to measure as its weight? What laboratory measurements can be related to such microscopic dimensions, and how can we be sure that the relationship is correct?

How, in fact, do we know that atoms exist at all? How do we really know that everything said so far is not the product of the chemist's hyperactive imagination? Perhaps Professor Smith, the author of our chapter opening quote, was right. Alchemists explained chemical reactions in terms of mythological figures or planets (the distinction was not clear in their own minds) that they associated with the reagents: gold with the sun, copper with Venus, iron with Mars, tin with Jupiter, and lead with Saturn. In what way are atoms more successful models than Greek gods? And how are hydrogen, helium, lithium, beryllium, and so on really more satisfactory as "fundamental materials" than the earth, air, fire and water of Empedocles in ancient Greece?

We have already mentioned Faraday's experiments with ions and electrolysis, and Thomson's and Millikan's measurements of electron charge and mass, in Chapter 1. The tremendous achievement of Mendeleev and Meyer in building the periodic table of the elements is the subject of Chapter 7. The work of Rutherford, Bohr, Schrödinger, and others in developing the modern theory of atomic structure and bonding is described in Chapter 8. In this chapter we shall go back even farther, and focus on two men who revolutionized chemistry: Antoine Lavoisier (1743–1794), who demonstrated that the fundamental quantity in any chemical reaction is mass) and John Dalton (1766–1844), who proposed that the fundamental units in chemical reactions are atoms. Dalton was not the first to propose the idea of atoms in principle, but he was the first to show in a convincing way that atoms do exist, and that they are a useful basis for understanding chemical reactions.

This chapter is an exercise in both chemical history and chemical understanding-the two frequently go hand in hand. One of the guiding principles of this book is that knowing how chemical concepts evolved helps to make them more comprehensible and more interesting. Such historical material is usually presented in postscripts at the ends of chapters. In effect, this chapter is one long postscript to the first five chapters. As you travel through the rest of this book, study and learn the material in the chapters, and relax and enjoy the postscripts.

The Concept of An Element[edit]

Figure 6-1 The Greeks of the fifth century B.C. pictured all material substances as composed of different proportions of the four basic elements: earth, air, fire, and water. These elements shared, in pairs, the properties of heat or cold and wetness or dryness: Earth was cold and dry, water was cold and wet, air was hot and wet, and fire was hot and dry.

One of the oldest ideas in science is that of fundamental materials out of which everything else is made. Empedocles (500 B.C.), in Greece, performed what may be the first recorded chemical analysis. He noted that when wood burns, smoke or air rises first and is followed by flame or fire. Water vapor will condense on a cool surface held near the flame. After combustion, the remains are ash or earth. Empedocles interpreted combustion as a breaking down of the burning substance into its four elements: earth, air, fire, and water. He and later writers generalized these into the four elements of which all substances were composed in varying proportions (Figure 6-1). Originally, at least, these ideas were not meant to be flights of metaphysical invention, but were attempts to explain observations. Later, among the Greek, Arabic, and medieval alchemists, the ideas become imbued with mysticism. Then earth, air, fire, and water were abandoned as fundamental elements, but varying sets of what we now would call elements or simple compounds were chosen by different alchemists as the fundamental materials of nature.

Aristotle (384 -322 B.C.) gave a definition of an element that, even now, can hardly be improved:

"Everything is either an element or composed of elements.... An element is that into which other bodies can be resolved, and which exists in them either potentially or actually, but which cannot itself be resolved into anything simpler, or different in kind."

However, this definition doesn't answer the question of how to recognize an element when you encounter one. Robert Boyle (1627–1691) gave a more practical definition: An element is a substance that will always gain weight when undergoing chemical change. This statement must be understood in the sense in which it was intended. For example, when iron rusts, the iron oxide produced weighs more than the original iron. Yet the weigh t of the iron and the oxygen that combines with it is exactly the same as the weight of the iron oxide. Conversely, when the red powder of mercuric oxide is heated, oxygen gas is emitted, and the silvery liquid mercury that remains weighs less than the original red powder. But if this decomposition takes place in an enclosed flask, one sees that there is no overall loss of weight during the reaction. (It was a century after Boyle that Lavosier made careful weighing experiments demonstrating the conservation of mass in such reactions. )

By Boyle's definition, mercuric oxide could not be an element, because it can be decomposed into parts, each of which is lighter than the original substance. Mercury could provisionally be called an element, at least until the day when someone else succeeded in separating it into components. Until the present century of spectroscopy and other laboratory techniques, it was easy to prove that a substance was not an element, but impossible to prove that one was. As the famous German chemist Justus von Liebig wrote, in 1857, "The elements count as simple substances not because we know that they are so, but because we do not know that they are not."

The elements called the rare earths provide an example of the difficulties of proving by purely chemical means that a substance is an element. In 1839, the Swedish chemist Carl Mosander extracted a new element from cerium nitrate and named it lanthanum (from the Greek lanthanein, "to lie hidden"). Two years later he showed that his lanthanum-containing preparation contained a second element which he christened didymium (from the Greek didymos, or "twin"). In 1879, Fran~ois Lecoq de Boisbaudran isolated another substance, samarium, from the didymium preparation, and all these were accepted as chemical elements. But didymium vanished from the rolls of chemistry in 1885, when the Austrian Carl von Welsbach separated it into two new elements, neodymium ("new twin") and praseodymium ("green twin"). It is only because we now have the periodic table, and understand the principles behind its construction, that we can say that there can be no other new elements between hydrogen, 1H , and element 105.

What kinds of substances are elements? The first to be recognized correctly as such were the metals. Gold, silver, copper, tin, iron, platinum, lead, zinc, mercury, nickel, tungsten, and cobalt all are metals. In fact, all but 22 of the 105 known elements have metallic properties. Five of the nonmetals (helium, neon, argon, krypton, and xenon) were discovered in the mixture of gases that remained when all the nitrogen and oxygen in air were removed. Chemists thought that these "noble" gases were inert until 1962, when it was shown that xenon combines with fluorine, the most chemically active nonmetal. The other chemically active nonmetals are either gases (such as hydrogen, nitrogen, oxygen, and chlorine) or brittle, crystalline solids (such as carbon, sulfur, phosphorus, arsenic, and iodine). Only one nonmetallic element, bromine, is liquid under ordinary conditions.

Compounds, Combustion, and the Conservation of Mass[edit]

Figure 6-2 Priestley's apparatus for preparing oxygen gas. Mercuric oxide in a small pan floating on the surface of the mercury bath is decomposed to liquid mercury and oxygen by solar heat. The arrangement of the mercury bath and bell jar prevents loss of the gas evolved.

Most eighteenth-century chemists were devoted to preparing and describing pure compounds, and to decomposing them to the elements from which they are formed. The great advances of the time were in the chemistry of gases. In 1756, Joseph Black completely changed chemists' ideas about gases when he showed, in his M.D. thesis at Edinburgh, that marble (which we know to be primarily calcium carbonate, CaCO3) could be decomposed to quicklime (calcium oxide, CaO) and a gas (carbon dioxide, CO2), and that the process could be reversed. This demonstration proved that there were different kinds of gases, and that they could take part in chemical reactions just as well as liquids and solids could. One of Black's contemporaries, John Robinson, wrote the following:

"He had discovered that a cubic inch of marble consisted of about half its weight of pure lime and as much air as would fill a vessel holding six wine gallons.... What could be more singular than to find so subtile a substance as air existing in the form of a hard stone, and its presence accompanied by such a change in the properties of the stone?"

In the following years, Henry Cavendish discovered hydrogen (1766), Daniel Rutherford found nitrogen (1772), and Joseph Priestley invented carbonated water and identified nitrous oxide ("laughing gas"), nitric oxide, carbon monoxide, sulfur dioxide, hydrogen chloride, ammonia, and oxygen. In 1781 , Cavendish proved that water is a combination of only hydrogen and oxygen, after he had witnessed Priestley explode the two gases in what Priestley later recalled as "a random experiment to entertain a few philosophical friends." The discovery of oxygen (Figure 6-2) led Antoine Lavoisier to overthrow the predominant idea of eighteenth-century chemistry, the phlogiston theory. The process by which this theory was shattered illustrates the great importance of quantitative measurements in chemistry.


When Empedocles watched wood burn, he was impressed with the idea that something left the wood; only a light fluffy ash remained. It became generally accepted that combustion was the decomposition of a substance accompanied by a loss of weight. Metal oxides are usually less dense and less compact than the metals from which they come. Even when it became known that the oxide was heavier than the original metal, a confusion between density (weight per unit volume) and weight itself compounded the error. The Germans Johann Becher and Georg Stahl proposed, in 1702, that all combustible material contains an element called phlogiston, which escapes when the material burns. According to their theory,

1. Metals, when heated, lose phlogiston and become calces. (A calx is a crumbly residue.)
2. Calces, when heated with charcoal, reabsorb phlogiston and become metals again. The charcoal is necessary because the original phlogiston has become scattered through the surrounding atmosphere and lost.
3. Charcoal must therefore be very rich in phlogiston.

By this theory, a lit match goes out when it is placed in a closed bottle because the air in the bottle becomes saturated with phlogiston; respiration in living organisms is a purification process in which phlogiston is removed; a mouse under a bell jar eventually dies when the air around him has absorbed all the phlogiston it can.

Think about these ideas for a while. So long as you make no weighing experiments, this theory explains combustion as well as our present ideas do, and seems to agree with common-sense observations about the appearance of metals and calces. Jean Rey, in France, had demonstrated that tin gains weight when it burns, but chemists, unaccustomed to attaching much importance to weight, overlooked the significance of Rey's work. In 1723, Stahl gave a clever explanation for Rey's finding:

"The fact that metals when transformed into their calces increase in

weight, does not disprove the phlogiston theory, but, on the contrary, confirms it, because phlogiston is lighter than air, and, in combining with substances, strives to lift them, and so decrease their weight; consequently, a substance which has lost phlogiston must be heavier than before."

It is no wonder that hydrogen, when it was discovered, was hailed as the first preparation of pure phlogiston! Again there was a confusion between the two ideas of weight and of density (in terms of buoyancy).

Conservation of Mass[edit]

Lavoisier discovered that mercuric calx lost weight when it was heated and free mercury and a gas were produced. He measured the volume of gas released. Then he showed that when mercury was reconverted to calx, the same volume of this gas was reabsorbed and there was a weight increase equal to the earlier loss. On the basis of careful weighing experiments such as these, Lavoisier proposed that combustible materials burn by adding oxygen, thus increasing in weight. (Oxygen was his name for the gas. Priestley called it dephlogisticated air since it could apparently absorb even more phlogiston than atmospheric air could.) Lavoisier demonstrated that the products obtained from burning wood, sulfur, phosphorus, charcoal, and other substances were gases whose weight always exceeded that of the solids that burned. His rebuttal to the metallurgical explanations of Becher and Stahl was as follows:

1. Metals combine with oxygen from the air to form calces, which are oxides.
2. Hot charcoal removes oxygen from calces to form a metal and a gas, 02 (at that time called fixed air).
3. Charcoal, therefore, does not combine with the metal)· rather, it removes the oxygen that had previously been combined with the metal in the calx.

The key to this theory was the chemical balance. Lavoisier was the first chemist to realize the importance of the principle of the conservation of mass. In his Traite Etementaire de Chimie) he wrote:

"We must lay it down as an incontestable axiom, that in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment .... Upon this principle, the whole art of performing chemical experiments depends."

Lavoisier was a businessman first and a chemist second. His full-time occupation was as a member of the Ferme Generale) an agency that collected taxes on a commission basis for the French government before the revolution. One of his biographers has called his conservation of mass dictum the "principle of the balance sheet," and has claimed to see its origin in his role as tax collector. Be that as it may, in 1794, his connection with the Ferme Generale cost him his life. *

*Hailed before a revolutionary tribunal because of his past aristocratic associations, Lavoisier heard Coffinhal, president of the tribunal, reject a plea for clemency: "The Republic has no need of chemists and savants. The course of justice shall not be interrupted." This was surely one of the most serious governmental cutbacks in the history of science.

Lavoisier published his textbook, Traite Etementaire de Chimie) in 1789, and it would be difficult to overemphasize the impact that it had on chemistry. In addition to setting forth the principle of conservation of mass in chemical reactions and overthrowing the phlogiston theory, the book contained in an appendix what is essentially our present system of nomenclature. For a generation, therefore, chemistry became "the French science" (the phrase lingered longer in France than elsewhere).

Does a Compound Have a Fixed Composition?[edit]

After Lavoisier, chemists began an intensive study of quantities in chemical reaction, that is, masses. The distinction between compounds and mixtures or solutions gradually became clear. A feud developed between those who claimed that the ratios of elements in compounds were fixed and those who believed that a continuous range of proportions was possible. The French chemist Berthollet cited alloys of metals in support of the idea of variable composition. But]. L. Proust, in Madrid, insisted that compounds had fixed composition, and correctly recognized alloys as solid solutions, not compounds:

"The properties of true compounds are invariable as is the ratio of their constituents. Between pole and pole, they are found identical in these two respects; their appearance may vary owing to the manner of aggregation, but their [chemical] properties never. No differences have yet been observed between the oxides of iron from the South and those from the North. The cinnabar of Japan is constituted according to the same ratio as that of Spain. Silver is not differently oxidized or muriated in the muriate of Peru than in that of Siberia."

This principle has been called the law of constant composition. The dispute between Berthollet and Proust had the good effect of sending chemists to the laboratory to prove the ideas of one or the other camps, and incidentally to compile rapidly a body of knowledge about chemical composition. *Of course, Proust was right; yet there are solid crystalline materials in which, because of defects in the crystal structure, the same ratio of atoms is not quite that predicted by the ideal chemical formula. For example, iron sulfide can vary from Fe1.1S to FeS1.1, depending on how the sample is prepared. Such substances are called nonstoichiometric solids, although it has been suggested that they be called "berthollides" after the loser in the debate just discussed.

*The orthodox viewpoint is that they went to the laboratory to decide between two conflicting theories. Let us be honest: Scientists are people, and science is seldom conducted in such a nonpartisan vacuum.

Equivalent Proportions[edit]

Between 1792 and 1802, an obscure German chemist named Jeremias Richter made an important discovery that was almost completely ignored by his contemporaries. His idea was the one of the equivalent proportions: The same relative amounts of two elements that combine with on another will also combine with a third element (assuming that the reactions are possible at all). This concept is easy to understand from a few examples:

1 g oh hydrogen combines with 8 g of oxygen to form water.
1 g of hydrogen combines with 3 g of carbon to form methane.
1 g of hydrogen combines with 35.5 g of chlorine to form hydrogen chloride.
1 g of hydrogen combines with 25 g of arsenic to form arsine.

The chemical reactions and formulas (which were not known at the time) are, in fact,

2H2 + O2 2H2O
2H2 + O2 2H2O
H2 + O2 2H2O
3H2 + O2 2H2O

Using modern atomic weights, verify that the preceding statements about weights involved in the reactions are true.

Richter's law of equivalent proportion states that if carbon and oxygen combine they should do so in the ratio of 3 to 8 by weight. This is true for what we now know to be CO2. If they react, carbon and chlorine should do so in the ratio of 3 to 35.5, and this is true for the liquid that we now know as carbon tetrachloride, CCl4. In a similar way, arsenic forms AsCl3, and As2O3 and chlorine and oxygen form Cl2O.

Combining Weights[edit]

Figure 6-3 Weights of elements that combine with one another in form ing the compounds indicated. We can pred ict from the diagram that 25.0 g of arsenic, for example, will combine with 35.5 9 of chlorine or 16.0 9 of sulfur. This, in fact, does occur. Arsenic and chlorine react In the predicted weight ratio to give arsenic trichloride (AsCl3). whereas arsenic and sulfur react in the predicted ratio to give the compound arsenous sulfide (As2S3).

A combining weight can be defined for each element as the weight of the element that combines with 1 g of hydrogen. If no hydrogen compound exists, it is the weight that combines with 8 g of oxygen or with one combining weight of some other element that does form a hydrogen compound. In this way a branching network of reactions can lead to a table of combining weights for all the elements. Richter's principle, if true, assures us that there will be no contradictions within the table. Such a set of combining weights for all the elements. Richter's principle, if true, assures us that there will be no contradictions within the table. Such a set of combining weights is shown in Figure 6-3 and Table 6-1.

There is one serious flaw to this scheme, which is why no one took Richter very seriously. The flaw is that many elements appear to have more than one combining weight. Carbon forms a second oxide (we know it now as carbon monoxide, CO), in which the ratio of carbon to oxygen is only 3 to 4. Either the combining weight of carbon has risen to 6, or that of oxygen has fallen to 4. In ethane (C2H6) the combining weight of carbon is 4, in ethylene (C2H4) it is 6, and in acetylene (C2H2) it is 12. The expected oxide of sulfur, SO, does not appear, and in the two most common oxides (SO2 and SO3) sulfur has combining weights of 8 and 5(Figure 6-4).

Figure 6-4 Variable combining weights for sulfur and carbon. Note that in this figure and in Figure 6-3 there are three combining weights for sulfur: 5.33 g, 8.00 g, and 16.0 g. These weights are in the ratios of 2:3:6. The two combining weights for carbon are in the ratio of 1:2.

Chemical Principles Table 6.1.png

Nitrogen is particularly troublesome. In ammonia it has a combining weight of 4, and in the three oxides known since Priestley's time its combining weights are 3, 7, and 14. If you know chemical formulas, the combining weights are easy to calculate, and you should be able to check them. But if you know only the combining weights, could you deduce the formulas? The significance of the ratios of elements in compounds was obscured even more by the habit of reporting composition in percent by weight; it was John Dalton who developed the trick of writing them as ratios to one common element and setting up combining weight tables, . which we still do. When Humphry Davy reported that the three oxides of nitrogen contained 29.50%, 44.05%, and 63.30% nitrogen by weight, no one noticed that the nitrogen was combining in the relative ratios of 1 to 2 to 4. (These percentages are Davy's experimental values. What are the correct percentages?) By 1802, it was established that compounds had fixed compositions, and that there could be several such definite compositions between the same two elements. Yet no one knew why, or where to go from there.

John Dalton and the Theory of Atoms[edit]

Figure 6-5 Dalton's original symbolism for reactions that form simple compounds. Modern symbols appear beneath them. The names to the right are Dalton's. When either the formula or the name of the product is different today, the modern formula or name is given in parentheses.

John Dalton, a science (or "natural philosophy") teacher in the Manchester, England, schools was compelled by such data as those in Section 6-3 to propose a theory of atoms, which he presented to the Literary and Philosophical Society of Manchester in 1802 and published three years later. His theory was as follows:

1. All matter is made up of atoms. These are the ultimate particles, and are indivisible and indestructible.
2. All atoms of a given element are identical, both in weight and in chemical properties.
3. Atoms of different elements have a different weights and different chemical properties.
4. Atoms of different elements can combine in simple whole numbers to form compounds.
5. When a compound is decomposed, the recovered atoms are unchanged and can form the same or new compounds.

Dalton also emphasized weights, as had Lavoisier; furthermore, Dalton invented a convenient symbolism for atoms, shown in Figure 6-5. Dalton's symbol for hydrogen represents more than merely an unspecified amount of hydrogen. It represents either one atom of hydrogen or some standard weight of hydrogen containing a standard number of atoms (such as the atomic weight containing Avogadro's number of atoms). Chemical formulas and equations are therefore not merely symbolic, but quantitative.

The Greek Atomic Theory[edit]

The idea of atoms was far from new. Democritus and the Epicureans in Greece had proposed an atomic theory, about 400 B.C., that contained virtually all of Dalton's ideas on the subject. The original writings are lost, but we know of this theory from attacks by its opponents and from a long poem written, in 55 B.C., by a Roman Epicurean, Lucretius. (The poem is entitled De Rerum Natura, "On the Nature of Things.") After Lucretius, the ideas of atomism drifted in and out of alchemy for nearly 1900 years without making a significant impact on it. Isaac Newton and Lavoisier both believed in atoms, but more as philosophical concepts or figures of speech that helped in thinking about reactions than as a theory requiring experiment.

There is an important point here that cannot be overstressed. A theory in science is important if, and only if, it makes the understanding of the behavior of the real world clearer. Describing bronze as a substitutional alloy of tin and copper is superior to describing it as the confluence of Jupiter and Venus, in alchemical terminology, because the tin-copper theory suggests experiments by which the properties of bronze might be explained, predicted, and even improved, whereas the "celestial marriage" theory leads nowhere. But perhaps it is less apparent that Democritus' atomic theory, and even Newton's, was not much of an improvement on this celestial marriage idea; it was Dalton's measurements, explanations, and predictions that made atomic theory valuable.

Fixed Ratios[edit]

Dalton took the table of combining weights as his point of departure and asked why the ratios of elements in compounds should be fixed. His answer was that a compound consists of a large number of identical molecules, each of which is built up from the same small number of atoms, arranged in the same way. Yet Dalton still needed to know how many atoms of carbon and oxygen combined in each molecule of an oxide of carbon, and how many hydrogen and oxygen atoms combined in a water molecule. Lacking any other guide, he proposed a "rule of simplicity" that started him off well but eventually landed him in serious trouble. The most stable two-element molecule, he reasoned, would be the simple diatomic one, AB. If only one compound of two elements were known, it would be an AB compound. Next most stable would be the triatomic molecules, AB2 and A2B. If only two or three compounds of two elements were known, they would be of these three types. This rule was one of those principles of economy, like the minimization of energy in mechanics or the principle of least action in physics, which are sometimes right, and sometimes wrong. Dalton was wrong.

Dalton began by mistakenly assuming from his rule of simplicity that water had a diatomic formula, HO. This made the atomic weight of oxygen equal to its combining weight of 8 (all relative to 1 for hydrogen). He then turned to the oxides of carbon and nitrogen; the possible choices are shown in Table 6-2. (All atomic weights in this discussion are based on the true numerical values, not on Dalton's values. He was a notoriously poor experimentalist. The atomic weight of oxygen, even on his own terms, began at 6.5 and slowly worked up to 8.) One oxide of carbon had a carbon-to-oxygen ratio of 0.75, and the other had a ratio of 0.375. If the first oxide were CO- he assumed that one of them had to be-then, as Table 6-2 shows, the other would be CO2 , Thus, the atomic weight of carbon would be 6. If the second oxide were CO, the first would have to be C20. (Can you prove this?) Then carbon would have an atomic weight of 3. Since oxide A was more stable to decomposition, he argued that this one must be CO, and correctly chose possibility 1. For the oxides of nitrogen, he similarly ruled out possibilities 1 and 3 because the five-atom molecules clashed with his rule of simplicity; and he again made the correct assignment of an atomic weight of 7 for nitrogen. (Correct, that is, relative to 8 for oxygen.)

Chemical Principles Table 6.2.png

Dalton should have sensed trouble as soon as he came to ammonia. He assumed by the rule of simplicity that the molecular formula for ammonia was NH. However, since 4 g of nitrogen combines with 1 g of hydrogen, this assumption would have meant an atomic weight of 4 for nitrogen, a value in conflict with the number 7 calculated from the oxides. As an alternative, he could have kept the atomic weight of 7 and worked out the formula for ammonia:

Hydrogen: = 1 mole of hydrogen atoms
Nitrogen: = 0.667 mole of nitrogen atoms

With the molar ratio of hydrogen to nitrogen (and therefore the ratio of atoms as well) being 1:0.667, or 3:2, the chemical formula would have to be N2H3, N4H6, or some higher multiple. Such a result would have shaken Dalton's faith in the rule of simplicity, and might have forced him to go back and find the right track. Yet he was undone by the poor quality of his experimental data. His initial value for the combining weight of oxygen was 6.5, which he raised to 7 in 1808. Davy increased it 7.5, and Proust finally arrived at the correct figure (given Dalton's assumptions) of 8. Dalton refused to believe their values (a stubborn attitude for such a poor experimentalist), and all the nitrogen calculations described here were carried out by Dalton with a nitrogen atomic weight of 5 rather than 7.

Law of Multiple Proportions[edit]

It is easy to be critical of a man who has gone astray because of bad data. But the real achievement of the atomic theory, which made people accept it almost at once, was not the calculation of atomic weights. It was the atomic theory explained perfectly a principle that had lain unnoticed in he published literature for over 15 years, relating elements that combine to form more than one compound. This was Dalton's law of multiple proportions.

The law of multiple proportions states that if two elements combine to form more than one compound, then the amounts of one element that combine with a fixed amount of the other will differ by factors that are the ratios of small whole numbers. (Or, that you can multiply the amounts by a suitable constant and produce a set of integers.) Since we have been using combining weights, perhaps a more meaningful statement is that if an element shows several combining weights, these weights will differ among themselves by ratios of small whole numbers. For example, the combining weights of carbon in Table 6-1 differ in the ratios of 3 to 4 to 6 to 12, or, more revealingly, in the ratio of 1/4 to 1/3 to 1/2 to 1. The combining weights for sulfur are in the ratios of 1 to 1/2 to 1/3, and the ones for nitrogen are 1/3 to 1/4 to 1/2 to 1 in NH3, NO2, NO, and N2O. Dalton's explanation of these simple fractions was that one, or two, or small number of atoms could combine with one of another kind, but that a molecule with 1.369... atoms combined with 1 atom of another was physically impossible according to atomic theory. The combining weights differ by small whole number fractions because the atoms combine in small whole numbers.

A search through the chemical literature showed that this law was the universal rule. It is one thing to prove your theory with new data that you have collected, but it is much more impressive to prove it with everyone else's; this is what Dalton did. The acceptance of the atomic theory was rapid and almost unanimous.

Equal Numbers In Equal Volumes: Gay-Lussac and Avogadro[edit]

As chemists tried to deduce formulas for more and more compounds, the flaws in Dalton's atomic weights and in his rule of simplicity became more and more obvious. No one could come up with dependable method of deciding on chemical formulas. Of the three pieces of molecular information -combining weights of the elements, atomic weights of the elements, and molecular formulas- any one could be calculated if the other two were known. Yet only one, the combining weight, was directly measurable. Dalton's wrong assumptions about formulas led to wrong atomic weights, which led back again to wrong formulas were assigned to acetic acid, the common acid of vinegar. The confusion was so great that some chemists despaired for the atomic theory. Jean Dumas wrote:

"If I were in charge, I would efface the word atom from science, for I am persuaded that it goes far beyond experience, and chemistry must never go beyond experience."

The great German chemist Friedrich Wöhler complained, even as early as 1835, that

" chemistry just now is enough to drive one mad. It gives me the impression of a primeval tropical forest, full of the most remarkable things, a monstrous and boundless thicket, with no way to escape, into which one may well dread to enter."

However, the key to dilemma was already in the chemical literature, and had been since 1811. The first step was provided by Gay-Lussac, and the second by Avogadro.


Figure 6-6 Gay-Lussac's results on the combining volumes of gases and the explanations by (a) Dalton and (b) Avogadro. Gay-Lussac found that one volume of hydrogen and one of chlorine produce two volumes of HCl gas, and that two volumes of hydrogen react with one of oxygen to produce two volumes of steam. (a) Dalton agreed that if the volume of HCl is twice the volume of either hydrogen or chlorine there must be half as many molecules per volume unit in HCL. Similarly, if there are n molecules of hydrogen per unit of volume, and if each of these molecules produces a water molecule in the same total volume, there will also be n molecules per volume unit in water. But only half the volume of oxygen is required, so the density of oxygen must be 2n molecules per volume unit. Thus. in hydrogen chloride, hydrogen, chlorine, water, and oxygen, the numbers of molecules per volume unit are n/2, n, n, and 2n. (b) Avogadro proposed that each molecule of hydrogen, chlorine. or oxygen contains two atoms. All the participants in the HCl reaction would therefore have the same number of molecules per volume unit of gas. Applying this same assumption to the water reaction led to a new formula for water, H2O, and ultimately to a complete revision of Dalton's atomic weight scale.

In 1808, Joseph Gay-Lussac (1778–1850) began a series of experiments with the volumes of reacting gases. He found that equal volumes of HCL gas and ammonia form neutral, solid ammonium chloride. An initial excess of either gas is left over at the end of the reaction. Two volumes of hydrogen react with one of oxygen to form two volumes of steam; three volumes of hydrogen react with one of nitrogen to yield two volumes of ammonia; and one volume of hydrogen reacts with one of chlorine to produce two volumes of HCl gas. In these and other experiments, in which the gas reactions were usually explosions triggered by a spark in an enclosed container, Gay-Lussac always found that gases react [in simple whole number units of volume units 1 provided that after the explosion the products are brought back to the temperature and pressure of the initial gases.

Gay-Lussac was a cautious man and a protégé of Berthollet, who as we have seen did not believe in compounds with fixed compositions. Gay-Lussac drew no conclusions in his Memoire, but the possibility of a connection with Dalton's atomic theory was apparent.


Dalton used Gay-Lussac's data to "prove" that equal volumes of gas do not have equal numbers of molecules, another wrong turn, like his rule of simplicity. Dalton's argument is illustrated in Figure 6-6a. The Italian physicist Amedeo Avogadro (1776–1856) saw another path. He began by assuming that equal volumes of gas (at the same temperature and pressure) contain equal numbers of molecules. As Figure 6-6b shows, this assumption requires that gases of the reactive elements such as hydrogen, oxygen, chlorine, and nitrogen be composed of two-atom molecules instead of single, isolated atoms. If Avogadro had been believed when he published his ideas in 1811, a half-century of confusion in chemistry would have been avoided. To many people, though, his ideas seemed like one shaky assumption (equal numbers in equal volumes) buttressed by an even shakier one (diatomic molecules). At that time, ideas of chemical bonding were based almost entirely on electrical attraction and repulsion, and it was difficult for scientists to understand how two identical atoms could do anything but repel each other. And if they did attract, why did they not form larger molecules, such as H3 and H4? Jöns Jakob Berzelius (1779–1848) used data on the vapors of sulfur and phosphorus to undercut Avogadro. Yet Berzelius did not realize that these were examples of just such higher aggregates (S8 and P4). Avogadro himself did not help matters; he mixed terminology so much that it sometimes appeared as if he were splitting hydrogen atoms ("elementary molecules") rather than separating atoms in a diatomic molecule ("integral molecules").

Cannizzaro and A Rational Method Of Calculating Atomic Weights[edit]

By 1860, the confusion about atomic weights was so widespread that nearly every chemist of any repute had his own private method of writing chemical formulas. August Kekulé (the inventor of the Kekulé structure for benzene) called a conference in Karlsruhe, Germany, to try to reach some kind of an agreement. The man who settled the entire issue was the Italian Stanislao Cannizzaro (1826–1910), who based a rigorous method for finding atomic weights on the long-ignored work of his countryman Avogadro.

Cannizzaro's reasoning, based on Avogadro's principle that equal volumes of gas contain equal numbers of molecules, was as follows:

1. Assume that the atomic weight of hydrogen is 1.0, and that hydrogen gas is made up of diatomic molecules, as Gay-Lussac's gas volume experiments suggest.
2. Assume that Avogadro was correct in deducting that oxygen gas is also diatomic, O2, and hence that the molecular formula for water is H2O, not HO. (See Figure 6-6b.) Since the combining weight of oxygen in water is 8.0, the atomic weight of oxygen must be 16.0, and the molecular weight of O2 must be 32.0.
3. If equal volumes of all gases contain equal numbers of molecules, then the molecular weight (m) of a gas is proportional to the density (D) of the gas: M = k D. Use H2 and O2 to evaluate the proportionality constant, k:
Density, D Molecular Weight, Constant, k
Gas (g liter−1) M (g mole−1 (liters mole−1)
H2 0.0894 2.0 22.37
O2 1.427 32.0 22.42
Average Value: 22.4

(The fact that k is the same or both H2 and O2 indicated that Cannizzaro was on the right track.)

4. Evaluate the molecular weights of a series of compounds containing the elements whose atomic weights are to be determined. Starting with percent composition by weight from chemical analyses, and molecular weights calculated from gas densities, calculate the weight of each element per molecular unit. Look over these weights for a given element to see if the numbers can be interpreted as integral multiples of some common factor, which may then be the atomic weight.

In the data given in Table 6-3, carbon occurs only in multiples of 12, hydrogen in multiples of 1, and chlorine in multiples of 35.3. Hence the atomic weight of carbon cannot be greater than 12, although it could be an integral submultiple of 12, such as 6, 4, or 3.

Chemical Principles Table 6.3.png

The atomic weights obtained by Cannizzaro's method are either the true atomic weights or integral multiples of them. If just ethane, benzene, and ethyl chloride had been included in the table, then the conclusion might have been drawn that the atomic weight of carbon was 24. If information from other carbon compounds had been added to the table, and just one analysis gave a weight of 6 for carbon, then the lower value would have to have been accepted, making the probable formulas C2H4, C4H6, C12H6, C2HCl3, and so on. However, no matter how many carbon compounds were analyzed by Cannizzaro's method, the weight per molecular unit always came out to be an integral multiple of 12. Hence this value was accepted as the atomic weight of carbon.

Cannizzaro's achievement was the last link in the chain of logic that began with Proust and the law of constant composition. The battle was over, save for the computing. Scientists could find accurate atomic weights for any element that appeared in compounds having measurable vapor densities. With these atomic weights, the percent composition of a new compound would lead unambiguously to the chemical formula. The mole was defined as we have stated in Chapter 1, that is, as the number of grams of a compound equal to its molecular weight on Cannizzaro's scale (which is the one we use today, with improvements in accuracy). It was realized that a mole of any compound would have the same number of molecules. Although the value of that number was not then known, it was named Avogadro's number, N, in belated recognition of his contribution.

With the hindsight that comes from knowledge of the ideal gas law, we can see that Cannizzaro's constant k is simply RT/P:

PV = nRT =
k =
where P = pressure w = weight in grams
V = volume M = molecular weight
n = number of molecules D = density = w/V
R = constant k = constant = M/D
T = temperature

The gas density values that were used in the previous demonstration of Cannizzaro's argument are those at standard temperature and pressure or STP: 1.00 atm and 273 K. Thus,

k = liters mole-1 = 22.4 liters mole-1
Example 1
At STP, the following vapor densities and percent compositions are observed for three compounds of C, H, and S:
 Density Percent by weight
Compound  (g liter−1) C H   S
x  3.40 16.0 0.0   84.0
y  2.14 25.0 8.4   66.6
z   2.77 38.7 9.7   51.6

Assuming atomic weights of 12 for C and 1 for H, as just found, calculate the probable atomic weight of sulfur, S, and the probable formulas for molecules x, y, and z.


For each compound, first calculate the molecular weight (mol wt) from the gas density, and the weight of each element per molecule:

Weight per molecule Probable
Compound  Mol wt C H   S formula
x  76.1 12.2 0.0   63.9 CS2
y  48.0 12.0 4.0   32.0 CH4S
z   62.1 24.0 6.0 32.0 C2H6S
  Greatest common fa ctor for sulfur =   32.0

The probable atomic weight of sulfur is therefore 32.0 g mole-1.

Example 2
Suppose that another compound, w, has a vapor density of 1.38 g liter−1, and an analysis of 38.7% C, 9.4% H, and 51.6% S by weight. How would this force you to revise your conclusions for Example 1?

The molecular weight of compound w would be 31.0 g mole−1, and the percent composition would indicate 12.0 g or 1 mole of C per mole, 2.9 g or 3 moles of H, and only 16.0 g of sulfur. Hence the revised atomic weight of S would be 16.0 g mole−1 and the formula for molecule w would be CH3S. The formula for x then would be CS4; for y, CH4S2 ; and for z, C2H6S2. Needless to say, a compound such as w has never been observed, and the atomic weight of 32.0 for sulfur is valid.

By calculations such as these, a consistent set of atomic weights was obtained for the lighter elements that can be found in gaseous molecules.

Atomic Weights for the Heavy Elements: Dulong and Petit[edit]

One problem remained: What does one do about the heavy elements, especially metals, that cannot be prepared readily in gaseous compounds? The problem can be illustrated by considering lead and silver.

Example 3
The combining weight of lead (amount per 8.00 g of oxygen) in lead oxide is 51.8 g. What is the atomic weight of lead?

We know that 103.6 of lead combine with 16 g, or 1 mole, of oxygen atoms, but we can go no further without knowing the chemical formula for lead oxide. Hence, we are caught in the same vicious circle from which Cannizzaro escaped for the lighter atoms. If the formula is PbO, then the atomic weight oflead is 103.6. But if the formula is Pb2O, the atomic weight is 51.8, and if PbO2, 207.2. Can you show that, in general, if the formula for lead oxide is PbxOy, the atomic weight of lead will be 103.6 (y/x)? The problem has several solutions.

Example 4
Silver oxide is 93.05% silver by weight. What is the atomic weight of silver?

If we take, for simplicity, a specimen sample of 100 g, there will be 93.05 g of silver for every 6.95 g of oxygen. The combining weight of silver (amount per 8.00 g of oxygen) is then 93.05 g (8.00 g/6.95 g) = 107.1 g. One mole of oxygen atoms combines with twice this amount, or 214.2 g, of silver. The choice of atomic weight now is limited to a set of multiples or fractions of 107.1 g, depending on what we assume the formula to be.

Formula: Ag2O Ag3O2 AgO Ag2O3 AgO2
Atomic Weight: 107.1 142.8 214.2 321.3 428.4

We need some means of deciding among these values. Without further information a choice cannot be made.

Pierre Dulong (1785–1838) and Alexis Petit (1791–1820) had discovered a method of estimating atomic weights of the heavier elements in 1819, but it had been overlooked in the general confusion that attended chemistry at that time. They made a systematic study of all physical properties that could possibly have a correlation with atomic weight, and found a good one in the heat capacities of solids. The gram heat capacity of a substance is the number of joules of heat needed to raise the temperature of 1 g of the substance by 1 °C. It is an easily measured property. The product of the gram heat capacity and the atomic weight of an element is the heat required to raise the temperature of 1 mole by 1 °C, or the molar heat capacity. Dulong and Petit noticed that for many solid elements whose atomic weight was known the molar heat capacity was very close to 25 J deg−1 mole−1 (Table 6-4). This indicates that the process of heat absorption must be related more strongly to the number of atoms of matter present than to the mass of matter. Later work on the theory of heat capacities of solids has shown that there should be such a constant molar heat capacity for simple solids. Dulong and Petit gave no explanation, however.

Since they advanced no reason for this phenomenon, at the time it was regarded by most chemists as being as dubious as Dalton's rule of simplicity (which was wrong) or Avogadro's principle of equal volumes/equal number of molecules (which was right). It was not until Cannizzaro prepared the way with light atoms that the method of Dulong and Petit was appreciated for heavy atoms.

We now can choose among the possible precise values of atomic weight derived from analytical data by using an approximate value obtained by assuming, with Dulong and Petit, that the molar heat capacity is approximately constant for all solids, 25 J deg−1 mole−1.

Chemical Principles Table 6.4.png

Example 5
The heat capacities of lead and silver, as tabulated by Dulong and Petit, are 0.123 and 0.233 J deg−1 g−1, respectively. Use this information to choose the proper atomic weights for Examples 3 and 4.
Approximate atomic weight of lead = = 203
Approximate atomic weight of silver = = 107

The correct choices from the previous examples must be 207.2 for lead and 107.1 for silver; the chemical formulas then are PbO2 and Ag2O.

Example 6
A common cobalt-containing mineral, linnaeite, contains 58.0% cobalt and 42.0% sulfur by weight. The heat capacity of cobalt metal is 0.434 J deg−1 g-l. Assuming that you know the atomic weight of sulfur to be 32.06, compute the atomic weight of cobalt and write the correct empirical formula for linnaeite.

The correct answers are 59 and Co3S4.

Combining Capacities, "Valence," and Oxidation Number[edit]

With Dalton's atomic theory, and with the contributions of Avogadro, Dulong and Petit, and Cannizzaro, it became possible to deduce atomic weights for elements from chemical analyses and physical data such as vapor densities and heat capacities. These deductions have given us the table of atomic weights shown on the inside back cover. The next great task of chemistry was to explain the formulas that could be derived.

The most primitive concept in chemical bonding is probably the idea of combining capacity, sometimes called "valence." The combining capacity of an element in a given compound is defined as the ratio of its true atomic weight to its combining weight in that compound:

Combining capacity =

Hydrogen has a combining capacity of 1, by definition. Oxygen has a combining capacity of 2 in H2O and most other compounds, but a combining capacity of 1 in hydrogen peroxide, H2O2. Using the data in Table 6-1, we can see that Cl and Br have combining capacities of 1; Ca, 2; and As, 3; carbon shows several combining capacities: 4, 3, 2, and 1. Sulfur has a combining capacity of 2 in H2S, 4 in S02, and 6 in SO3. Nitrogen has a combining capacity of 3 in ammonia, 4 in NO2, 2 in NO, and 1 in N2O. Notice that in these two-element compounds the total combining capacity of one element exactly balances the total combining capacity of the other. In SO3 one sulfur atom with a combining capacity of 6 balances three oxygen atoms having a capacity of 2 each. The formulation of the concept of combining capacity or "valence" was the first step toward a theory of chemical bonding. The second step was to assign plus and minus signs to these combining capacities so that the sum of the signed capacities for a molecule is zero. Hydrogen was assigned the value +1; therefore the value for oxygen had to be -2 so the sum for water, H2O, would be zero. The formula for sulfuric acid, H2SO4, requires that sulfur be associated with the value +6:

H:   2 +1 = +2
O:   4 -2 = -8
S:   1 +6 = +6
Sum:        0

These signed combining capacities are just the oxidation numbers that we encountered in Chapter 1. They are important in theories of chemical bonding because they describe how electrons are shifted toward or away from atoms in a molecule.


This chapter has chronicled the process by which scientists deduced that chemical compounds are made up of specific numbers of atoms of different kinds having specific atomic weights, and slowly worked out a set of reliable atomic weights. The theory of atoms originated as a philosophical concept rather than as a means of manipulating substances and reactions. Antoine Lavoisier laid the foundation by establishing that mass was the fundamental quantity in chemical reactions. John Dalton turned the philosophy into reality by showing that the atomic theory would account for the experimental observations that were summarized in the laws of equivalent proportions and multiple proportions.

The task of deciding upon a set of consistent atomic weights was not an easy one, and Dalton himself went astray. The circular argument involving assumed atomic weights and assumed molecular formulas was not broken until 1860, when Cannizzaro applied a principle that had been discovered in 1811 by Avogadro but had been ignored: Under the same conditions of temperature and pressure, equal volumes of all gases contain equal numbers of molecules. Since this meant that gas density was proportional to molecular weight, the way was open for establishing the standard atomic weight scale that we still use today. The quantitative foundations of modern chemistry had been laid.