Note 22 — Chapter VII · MOLECULES AND ATOMS. THE LAWS OF GAY-LUSSAC AND AVOGADRO-GERHARDT
George Kamensky translation
The percentage amounts of the elements contained in a given compound may be calculated from its formula by a simple proportion. Thus, for example, to find the percentage amount of hydrogen in hydrochloric acid we reason as follows:—HCl shows that hydrochloric acid contains 35·5 of chlorine and 1 part of hydrogen. Hence, in 36·5 parts of hydrochloric acid there is 1 part by weight of hydrogen, consequently 100 parts by weight of hydrochloric acid will contain as many more units of hydrogen as 100 is greater than 36·5; therefore, the proportion is as follows—x : 1 ∷ 100 : 36·5 or x = 100 / 36·5 = 2·739. Therefore 100 parts of hydrochloric acid contain 2·739 parts of hydrogen. In general, when it is required to transfer a formula into its percentage composition, we must replace the symbols by their corresponding atomic weights and find their sum, and knowing the amount by weight of a given element in it, it is easy by proportion to find the amount of this element in 100 or any other quantity of parts by weight. If, on the contrary, it be required to find the formula from a given percentage composition, we must proceed as follows: Divide the percentage amount of each element entering into the composition of a substance by its atomic weight, and compare the figures thus obtained—they should be in simple multiple proportion to each other. Thus, for instance, from the percentage composition of hydrogen peroxide, 5·88 of hydrogen and 94·12 of oxygen, it is easy to find its formula; it is only necessary to divide the amount of hydrogen by unity and the amount of oxygen by 16. The numbers 5·88 and 5·88 are thus obtained, which are in the ratio 1 : 1, which means that in hydrogen peroxide there is one atom of hydrogen to one atom of oxygen.
The following is a proof of the practical rule given above that to find the ratio of the number of atoms from the percentage composition, it is necessary to divide the percentage amounts by the atomic weights of the corresponding substances, and to find the ratio which these numbers bear to each other. Let us suppose that two radicles (simple or compound), whose symbols and combining weights are A and B, combine together, forming a compound composed of x atoms of A and y atoms of B. The formula of the substance will be AxBy. From this formula we know that our compound contains xA parts by weight of the first element, and yB of the second. In 100 parts of our compound there will be (by proportion) 100.xA / xA + yB of the first element, and 100.yB / xA + yB of the second. Let us divide these quantities, expressing the percentage amounts by the corresponding combining weights; we then obtain 100x / xA + yB for the first element and 100y / xA + yB for the second element. And these numbers are in the ratio x : y—that is, in the ratio of the number of atoms of the two substances.
It may be further observed that even the very language or nomenclature of chemistry acquires a particular clearness and conciseness by means of the conception of molecules, because then the names of substances may directly indicate their composition. Thus the term ‘carbon dioxide’ tells more about and expresses CO2 better than carbonic acid gas, or even carbonic anhydride. Such nomenclature is already employed by many. But expressing the composition without an indication or even hint as to the properties, would be neglecting the advantageous side of the present nomenclature. Sulphur dioxide, SO2, expresses the same as barium dioxide, BaO2, but sulphurous anhydride indicates the acid properties of SO2. Probably in time one harmonious chemical language will succeed in embracing both advantages.