In those cases where the quotient M / D proves to be less than 2, or the observed density greater than that calculated, by a multiple number of times, the matter is evidently more simple, and the fact observed only indicates that the weight of the molecule is as many times greater as that taken as the quotient obtained is less than 2. So, for instance, in the case of ethylene, whose composition is expressed by CH2, the density was found by experiment to be 14, and in the case of amylene, whose composition is also CH2, the density proved to be 35, and consequently the quotient for ethylene = 1, and for amylene = ⅖. If the molecular weight of ethylene be taken, not as 14, as might be imagined from its composition, but as twice as great—namely, as 28—and for amylene as five times greater—that is as 70—then the molecular composition of the first will be C2H4, and of the second C5H10, and for both of them M / D will be equal to 2. This application of the law, which at first sight may appear perfectly arbitrary, is nevertheless strictly correct, because the amount of ethylene which reacts—for example, with sulphuric and other acids—is not equal to 14, but to 28 parts by weight. Thus with H2SO4, Br2, or HI, &c., ethylene combines in a quantity C2H4, and amylene in a quantity C5H10, and not CH2. On the other hand, ethylene is a gas which liquefies with difficulty (absolute boiling point = +10°), whilst amylene is a liquid boiling at 35° (absolute boiling point = +192°), and by admitting the greater density of the molecules of amylene (M = 70) its difference from the lighter molecules of ethylene (M = 28) becomes clear. Thus, the smaller quotient M / D is an indication of polymerisation, as the larger quotient is of decomposition. The difference between the densities of oxygen and ozone is a case in point.
On turning to the elements, it is found in certain cases, especially with metals—for instance, mercury, zinc, and cadmium—that that weight of the atoms which must be acknowledged in their compounds (of which mention will be afterwards made) appears to be also the molecular weight. Thus, the atomic weight of mercury must be taken as = 200, but the vapour density = 100, and the quotient = 2. Consequently the molecule of mercury contains one atom, Hg. It is the same with sodium, cadmium, and zinc. This is the simplest possible molecule, which necessarily is only possible in the case of elements, as the molecule of a compound must contain at least two atoms. However, the molecules of many of the elements prove to be complex—for instance, the weight of an atom of oxygen = 16, and its density = 16, so that its molecule must contain two atoms, O2, which might already be concluded by comparing its density with that of ozone, whose molecule contains O3 (Chapter [IV].) So also the molecule of hydrogen equals H2, of chlorine Cl2, of nitrogen N2, &c. If chlorine react with hydrogen, the volume remains unaltered after the formation of hydrochloric acid, H2 + Cl2 = HCl + HCl. It is a case of substitution between the one and the other, and therefore the volumes remain constant. There are elements whose molecules are much more complex—for instance, sulphur, S6—although, by heating, the density is reduced to a third, and S2 is formed. Judging from the vapour density of phosphorus (D = 62) the molecule contains four atoms P4. Hence many elements when polymerised appear in molecules which are more complex than the simplest possible. In carbon, as we shall afterwards find, a very complex molecule must be admitted, as otherwise its non-volatility and other properties cannot be understood. And if compounds are decomposed by a more or less powerful heat, and if polymeric substances are depolymerised (that is, the weight of the molecule diminishes) by a rise of temperature, as N2O4 passes into NO2, or ozone, O3, into ordinary oxygen, O2, then we might expect to find the splitting-up of the complex molecules of elements into the simplest molecule containing a single atom only—that is to say, if O2 be obtained from O3, then the formation of O might also be looked for. The possibility but not proof of such a proposition is indicated by the vapour of iodine. Its normal density = 127 (Dumas, Deville, and others), which corresponds with the molecule I2. At temperatures above 800° (up to which the density remains almost constant), this density distinctly decreases, as is seen from the verified results obtained by Victor Meyer, Crafts, and Troost. At the ordinary pressure and 1,000° it is about 100, at 1,250° about 80, at 1,400° about 75, and apparently it strives to reduce itself to one-half—that is, to 63. Under a reduced pressure this splitting-up, or depolymerisation, of iodine vapour actually reaches a density[16] of 66, as Crafts demonstrated by reducing the pressure to 100 mm. and raising the temperature to 1,500°. From this it may be concluded that at high temperatures and low pressures the molecule I2 gradually passes into the molecule I containing one atom like mercury, and that something similar occurs with other elements at a considerable rise of temperature, which tends to bring about the disunion of compounds and the decomposition of complex molecules.[17]
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;[18] 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.
The molecular weight (which has been indicated by M) of a substance is determined by its composition, transformations, and vapour density.
The molecule is not divisible by the mechanical and physical changes of substances, but in chemical reaction it is either altered in its properties, or quantity, or structure, or in the nature of the motion of its parts.
An agglomeration of molecules, which are alike in all chemical respects, makes up the masses of homogeneous substances in all states.[19]
Molecules consist of atoms in a certain state of distribution and motion, just as the solar system[20] is made up of inseparable parts (the sun, planets, satellites, comets, &c.) The greater the number of atoms in a molecule, the more complex is the resultant substance. The equilibrium between the dissimilar atoms may be more or less stable, and may for this reason give more or less stable substances. Physical and mechanical transformations alter the velocity of the motion and the distances between the individual molecules, or of the atoms in the molecules, or of their sum total, but they do not alter the original equilibrium of the system; whilst chemical changes, on the other hand, alter the molecules themselves, that is, the velocity of motion, the relative distribution, and the quality and quantity of the atoms in the molecules.