Besides these cases of apparent discrepancy from the law of Avogadro-Gerhardt there is yet a third, which is the last, and is very instructive. In the investigation of separate substances they have to be isolated in the purest possible form, and their chemical and physical properties, and among them the vapour density, then determined. If it be normal—that is, if D = M/2—it often serves as a proof of the purity of the substance, i.e. of its freedom from all foreign matter. If it be abnormal—that is, if D be not equal to M/2—then for those who do not believe in the law it appears as a new argument against it and nothing more; but to those who have already grasped the important significance of the law it becomes clear that there is some error in the observation, or that the density was determined under conditions in which the vapour does not follow the laws of Boyle or Gay-Lussac, or else that the substance has not been sufficiently purified, and contains other substances. The law of Avogadro-Gerhardt in that case furnishes convincing evidence of the necessity of a fresh and more exact research. And as yet the causes of error have always been found. There are not a few examples in point in the recent history of chemistry. We will cite one instance. In the case of pyrosulphuryl chloride, S2O5Cl2, M = 215, and consequently D should = 107·5, instead of which Ogier and others obtained 53·8—that is, a density half as great; and further, Ogier (1882) demonstrated clearly that the substance is not dissociated by distillation into SO3 and SO2Cl2, or any other two products, and thus the abnormal density of S2O5Cl2 remained unexplained until D. P. Konovaloff (1885) showed that the previous investigators were working with a mixture (containing SO3HCl), and that pyrosulphuryl chloride has a normal density of approximately 107. Had not the law of Avogadro-Gerhardt served as a guide, the impure liquid would have still passed as pure; the more so since the determination of the amount of chlorine could not aid in the discovery of the impurity. Thus, by following a true law of nature we are led to true deductions.
All cases which have been studied confirm the law of Avogadro-Gerhardt, and as by it a deduction is obtained, from the determination of the vapour density (a purely physical property), as to the weight of the molecule or quantity of a substance entering into chemical reaction, this law links together the two provinces of learning—physics and chemistry—in the most intimate manner. Besides which, the law of Avogadro-Gerhardt places the conceptions of molecules and atoms on a firm foundation, which was previously wanting. Although since the days of Dalton it had become evident that it was necessary to admit the existence of the elementary atom (the chemical individual indivisible by chemical or other forces), and of the groups of atoms (or molecules) of compounds, indivisible by mechanical and physical forces; still the relative magnitude of the molecule and atom was not defined with sufficient clearness. Thus, for instance, the atomic weight of oxygen might be taken as 8 or 16, or any multiple of these numbers, and nothing indicated a reason for the acceptation of one rather than another of these magnitudes;19 whilst as regards the weights of the molecules of elements and compounds there was no trustworthy knowledge whatever. With the establishment of Gerhardt's law the idea of the molecule was fully defined, as well as the relative magnitude of the elementary atom.
The chemical particle or molecule must be considered as the quantity of a substance which enters into chemical reaction with other molecules, and occupies in a state of vapour the same volume as two parts by weight of hydrogen.