The Law of Multiple Proportions GLEN WAKEHAM University of Colorado, Boulder, Colorado
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NE of the less gracious tricks for confounding a bumptious graduate student is to fire the law of multiple proportions a t him. Sometimes he will be able to recite the law in parrot-like fashion; but if confronted with an illustrative problem he is likely to begin to fiddle around with atomic weights and valences, confessing his ignorance of the fundamental relationship between facts, laws, and theories. The law of multiple proportions covers a wide range of facts and is independent of the atomic or any other theory. Classically, i t was considered as the most convincing confirmation of the atomic theory, and its discovery, or anticipation, as one of Dalton's most notable contributions to chemistry. The unlucky graduate student who finds himself suddenly floored by a deceptively simple question is not to be altogether blamed for the accident. The writer has heard several experienced teachers ask, "What's the use of the law, anyway?" One recently published text passes i t off as a "mere generalization," as if other scientific laws were not generalizations. There are important texts which ignore the law altogether. The chief reason for this neglect is probably the author's haste to get on to the theory of atomic structure which, being more fundamental, automatically takes care of classical atomism. Students easily learn to draw "bored atoms," quite mechanically, with the aid of the Periodic Chart. and think that thev have achieved a profound knowledge of ultimate chekstry. They cannot guess that they are missing entirely the historical philosophy of chemistry, some idea of which should be a prime objective of every elementary chemistry course. The law of definite proportions is, of course, the foundation of Dalton's quantitative atomic theory. As originally conceived, i t envisaged only one way in which atoms of different kinds could unite with one another. But Dalton, although not distinguished for detailed chemical knowledge, was aware of the existence of, for example, two compounds of hydrogen and carbon. He had hardly formulated his theory when he perceived that if i t was to stand, i t must account for such cases, and that if different numbers of atoms of one k i d could unite with one or the same number of atoms of another kind, the varying weights of the one element which combine with a fixed weight of the other element must be in a simple, numerical relationship to one another. Dalton's own confirmatory experiments were crude; but after the theory was published, competent technicians soon supplied ahundant proofs of its validity. The discovery was widely
recognized as one of the most brilliant triumphs'of philosophical speculation. Let any teacher who thinks the idea to he easy or obvious try to get a real comprehension of i t into the minds of average students. Most of them will understand, a t once, the concept that one atom of A might unite with one atom of B, or one atom of A with two atoms of B. But why the second weight of B uniting with a fixed weight of A should be exactly twice as great as the first weight is likely to remain an incomprehensible mystery. In presenting the topic, it is wise to stick to the simplest ratios, set forth somewhat as follows: Copper Oxygen 4 g. t 1 g. = 4_ = Red oxide of copper 8 g. i1 g. = 8 2
Black oxide of copper
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The ratio 4: 8 obviously reduces to 1:2. If the black oxide is CuO, the red oxide must be CuzO. If some student asks why it couldn't be CnO and CuOz, thank your lucky stars for one mind in the class! Proceed to the familiar oxides of sulfur, using, this time, percentages: Lower oxide of sulfur: Higher oxide of sulfur:
Oxygen Sulfur 2 50% + 50% = 1 60% + 40% = ii/; = 3
Two difficulties arise here: it is hard for some students to see that dividing the ~ercentaxesof one element by those of the other &es the weights of the first element which will unite with unit weight of the other; alsoowing to inadequate arithmetical instructionmany students will not see that 1: 1'/2 equals 2: 3still less the necessity, for the purpose of confirming atomic theory, of reducing 1: ll/z to an integral ratio, to make it match the concept of discrete atoms. The class may now he told that the atom of sulfur is believed to be twice as heavy as the atom of oxygen, from which assumption the correct molecular formulas can he derived. This is best accomplished by the cut-and-try method, as the analysis of such a problem is beyond most high-school classes. Other easy ratios are the sulfides of copper, using integral atomic weights, and the oxides of arsenic. Ambitious students may be @ven the data for longer series, such as the oxides of nitrogen, and allowed to discover that the quotients obtained may be the reciprocds of whole numbers. The important thing is to get them to see that the law is independent of atomic theory, as it is a "mere generalization" based upon facts; hut that i t is satisfactorily explained by the atomic theory, and is consequently an important confirmation of the atomic theory.
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Most teachers hesitate to use the once universally employed reduction of the oxides of copper in a current of hydrogen as an illustrative experiment, because of the possibility of an explosion. The writer has permitted many thousands of students, in Germany, England, and America to carry it out, with never a serious accident. The reduction of potassium perchlorate and chlorate by mere heating can be used; but is more difficult to explain on account of the ternary composition of the salts. One interpretation of the classical maxim, repetitio muter studiorum est, is the hope that if a principle is illustrated by a sufficient number of exercises, some comprehension of its significance will ultimately dawn in the student's mind. The educive nature of the educational process has often been emphasized: education can only draw out, or stimulate into action, potential powers already preseFt. But if there is nothing
there-you can tickle a turnip all day, hut i t will never laugh. The law of multiple proportions was a cmcial step in the development of classical atomic theory which dominated 19th-century chemistry. In this era of electrons, protons, neutrons, positrons, negatrons, neutrettos, neutrinos, etc., atoms seem t o b e going out of style, particularly in the minds and methods of elementary chemistry teachers. Two points might be * emphasized: No adequate philosophical concept of the development of the science of chemistry can be obtained without a thorough treatment of classical atomic theory; and, nearly all of the practical applications of chemistryalmost iniinite in number and variety-are still based upon the lumpy old Daltonic atoms. And the law of multiple proportions was the discovery which carried the day in favor of the greatest and most useful of all chemical theories.
