THE FAIRY STORY OF ATOMIC WEIGHTS ANTHONY STANDEN The Interscience Encyclopedia, Bmoklyn, New York
INELEMENTAFX chemistry textbooks the description of the determination of atomic weights is entirely inadequate. Here is the usual account: The method was invented by Cannizzaro and depends upon Avogadro's hypothesis. From the densities and combining volumes of oxygen, hydrogen, and chlorine the atomic weights of these elements are determined, and i t is found that a gram molecular weight of a gas occupies 22.4 liters. Atomic weights of other elements can then be found by determining the smallest weight of the element ever found in 22.4 liters of a gaseous compound. The next step is a generalization called Dulong and Petit's law, and by assuming the general truth of this law, we can calculate the atomic weights of all the other elements, even if they do not have convenient gaseous compounds. This description has only one flaw, and that is that i t will not work. The difficulty is in deriving Dulong and Petit's law. Any law should be derived from experimental data, and the experimental data on which Dulong and Petit's law is based ought to be presented. This could be done in the form of a table, having the following columns: (1) name of element, (2) gaseous compounds used (for the methods of atomic weight determination described up to now all require gaseous compounds), (3) atomic weight so determined, (4) specific heat, and (5) product of atomic weight and specific heat. But in no text hook can such a table be found. Some textbooks give a list of elements whose atomic weights can be determined by the methods suggested by Cannizzaro. Popular elements for this table are nonmetals, such as H, C1, 0,C, P, and N. Many books also give a table of atomic weights and specific heats, thus recognizing an obligation to show how Dulong and Petit's law is deduced from experiment, but popular elements for this group are metals, such as Li, Ag, Au, Cu, Bi, Pb, Fe, etc., and they are never the same elements as those in the first group. How were their atomic weights determined? The second column suggested above, the gaseous compounds used in the atomic weight determinations, is never given. The reason for this is that the atomic weights of the elements in the second table were not determined by Cannizzwm methods a t all, but either by entirely different methods or by the use of Dulong and Petit's law. Thus this extraordinary law is used to prove itself! In some textbooks the gap between Cannizzaro and Dulong and Petit's law is quite explicit. Thus ?The problem of iinding the relative weights of the atoms remained unsolved for 52 years after the formulation of Dalton's atomic theory in 1808," and then later in
the same book "In 1819 Dulong and Petit pointed out that the product of the atomic weight and the specific heat of an element in the solid state is approximately equal to a constant." How could they have done this in any other way than pure prophecy? Since there may he even students who notice this remarkable discrepancy, one would have thought that the telltale dates would have been prudently concealed. Here is an attempt to deduce Dulong and Petit's law from atomic weight determinations on some elements which have readily available gaseous compounds. Elemat
Atmnic weiaht
Sveeific heat
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It will be seen that there is no trace of Dulong and Petit's famous law. Now anyone who knows all the answers can easily say "Oh, but the permanent gases should have been cooled way below ordinary temperatures, solidified in fact, and the remaining 'exceptions' should have been heated up several hundred degrees." But this is hindsight, which is much easier than foresight. It would he quite easy to prove that "All gases have the same density" by choosing conditions of measurement no further apart than this. We are trying to show how Dulong and Petit's law was deduced, or a t least how i t could have been deduced. If we cannot deduce it, then we shall have to determine the atomic weights of the metals somehow; we cannot leave so large a group of elements dangling, as it were, from a sky hook. Nor is any solid support placed under the sky hook by the introduction, a t this point, of modern physical methods, such as the mass spectrograph. In comparing, say, magnesium and hydrogen in this apparatus, lines are obtained corresponding to two sorts of particles, one about 24 times as heavy as the other. But how do we know that these particles are singly charged atoms of magnesium and hydrogen and not somethmg else? Only by knowing, beforehand, that the atomic weight of magnesium is 24, and not 12, and how did we know that? There are two steps in an atomic weight determination. The first is the determination of the equivalent weight. This is a pure experimental determination
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involving the analysis of a compound of the element, either with oxygen or with some element whose equivalent weight is known. The second step is the selection, in the light of further experimental evidence, of a multiple of the equivalent weight, which is the atomic weight. The multiplier used is called the "valence," and i t can be seen that i t is equal to the number of "hooks" or "linkages" that the atom must be supposed to use. Most textbooks refrain from using the word "valence" a t this point, but introduce it a chapter or two later. This is on account of the historical accident that the word "valence" was not used until 1852. But the concept of valence must have been present in the mind of whoever it was that first suggested that the atomic weight of oxygen might be 16 and not 8, for this necessarily implies that an atom of oxygen can unite with two atoms of hydrogen, and the fact that there are such things as equivalent weights (the so-called law of reciprocal proportions) shows that there is a considerable degree of constancy, from one compound to another, of the number of "hooks" used by an atom. The fact that the word "valence," and perhaps even the full realization of the concept, was not developed until much later is no excuse for not bringing in the word and the concept here, where they logically belong. There is no reason why chemical education should retrace the tortuous steps of chemical history. (Valence, of course, is an Expanding Concept, like "acid" or "oxidation!' The word is here being used in its original core meaning, which applies only to binary compounds. It is only by an extension of the meaning that we can speak of the valence of, say, Mn in KMnO,. I n all atomic weight determinations, these two steps, the determinatidn of the equivalent weight and the selection of the valence, are present. I n some methods of atomic-weight determination the prior determine tion of the equivalent weight is easily.lost sight of, but it is always there. Thus, in the classical determination of the atomic weights of H, 0, and C1, the experimental data required are the relative densities and the combining volumes of the gases. From these data the equivalent weights follow immediately, without the use of any theory whatever. Then, assuming Avogadro's hypothesis and entering upon a chain of theoretical reasoning, we arrive a t a representation of the molecule of water and of hydrogen chloride, thence the valence of the elements, and thence their atomic weights. I n the method which depends upon determinations of the analyses and vapor densities of a number of gaseous compounds of the element, the analyses alone yield values for the equivalent weights. In the method which depends upon Dulong and Petit's law, the prior determination of the equivalent weight is quite explicit. The two stages in atomic weight determination are very different. The equivalent weight of an element can never be altered, although it can be determined with ever-increasing precision. The atomic weights of elements can be altered, and have been altered, many times. Mendeleeff boldly altered several of them, i n order to make them fit his theory. He could not possibly
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do that to an equivalent weight. The great atomic weight determiners, such as Richards and Honigschmid, in reality determined equivalent weightethat is to say, they concentrated their attention on stage (1) of atomic weight determinations, because stage (2), the selection of the valence, had already been decided to everybody's satisfaction. The determinationof equivalent weights does not present di5culties other than those that arise in the mechanics of experimentation. The real diEculties, the intellectual di5culties, only arise in step (2) of atomic weight determinations. In the history of atomic weight determinations (which is not quite the same as the history of equivalent weight determinations) Cannizzaro did not speak the first word. Instead he spoke the last word. I n his time most of the atomic weights were accepted a t values not far from the present ones; his work cleared up the last remaining difficulties, one of the most troublesome of which was whether oxygen was 8 or 16. Now, if someone can genuinely deduce Dulong and Petit's law from atomic weights deduced by Cannizzaran methods, then we do not need to bother further, in chemical education, about the first half of the 19th century, and we can leave out the whole uncomfortable period from Dalton to Cannizzaro. But if this cannot be done, and i t is far from easy, thenin order to obtain the atomic weights of the metals, we shall be forced to pay some attention topre-Cannizzaranmethods. In Dulong and Petit's time, the equivalent weights were known with a moderate degree of precision. The problem was to find the multiplier, equal to the valence, that gives the atomic weight. One such method available to Dulong and Petit is absurdly easy; it depends upon the obvious fact that if anelement has two equivalent weights, then its atomic weight must be amultiple of both of them. Thus, iron has the equivalent weights 27.92 and 18.62 in ferrous and ferric compounds. From this, its atomic weight must be either 55.85, and its valences 2 and 3, or else 111.7, and the valences 4 and 6 or higher multiples. It is true there is an ambiguity in this method, but so there is in all methods. The Cannizzaro analysis only shows that there must be at least two atoms of chlorine in the molecule; there might be four, or six. Vapor density determinations on a number of carbon compounds rule out the possibiity of the atomic weight's being 24, but it still might be 6; the method based on Dulong and Petit's law appears to give a univocal answer, hut actually it has all the ambiguity of the determinations the law is based on. The method just illustrated for iron is applicable to any element that has more than one valence. It is by far the most straightforward of all methods of atomic weight determination, and it can easily be understood as soon as the relationship between atomic weight and equivalent weight is grasped. +other method which was, historically, extremely useful is based on isomorphism. Thus, for example, the atomic weight of silver was reduced from 215.8 to 107.9 in order to account for the isomorphism of silver sulfide with cuprous sulfide.
MARCH. 1947 The student of the history of chemistry might possibly 6nd several other methods of atomic weight determination of equal validity with all the foregoing and just as useful for deducing the atomic weights of the metals from experiment. But since we are not bound, in teaching, by the mistakes and uncertainties of the past, we can look on this side of Cannizzaro, as well as before his time; for example, the Hardy-Schulze law
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could be used very neatly to justify an atomic weight determination. By these methods, or others which may suggest themselves to ingenious chemists, i t should be easily possible to present an account of how atomic weights actually could have been determined. The present account is neither historically true nor even logically possible. It is nothing better than a fairy story.
