[18] And so it was in the fifties. Some took O = 8, others O = 16. Water in the first case would be HO and hydrogen peroxide HO2, and in the second case, as is now generally accepted, water H2O and hydrogen peroxide H2O2 or HO. Disagreement and confusion reigned. In 1860 the chemists of the whole world met at Carlsruhe for the purpose of arriving at some agreement and uniformity of opinion. I was present at this Congress, and well remember how great was the difference of opinion, and how a compromise was advocated with great acumen by many scientific men, and with what warmth the followers of Gerhardt, at whose head stood the Italian professor, Canizzaro, followed up the consequences of the law of Avogadro. In the spirit of scientific freedom, without which science would make no progress, and would remain petrified as in the middle ages, and with the simultaneous necessity of scientific conservatism, without which the roots of past study could give no fruit, a compromise was not arrived at, nor ought it to have been, but instead of it truth, in the form of the law of Avogadro-Gerhardt, received by means of the Congress a wider development, and soon afterwards conquered all minds. Then the new so-called Gerhardt atomic weights established themselves, and in the seventies they were already in general use.
[19] A bubble of gas, a drop of liquid, or the smallest crystal, presents an agglomeration of a number of molecules, in a state of continual motion (like the stars of the Milky Way), distributing themselves evenly or forming new systems. If the aggregation of all kinds of heterogeneous molecules be possible in a gaseous state, where the molecules are considerably removed from each other, then in a liquid state, where they are already close together, such an aggregation becomes possible only in the sense of the mutual reaction between them which results from their chemical attraction, and especially in the aptitude of heterogeneous molecules for combining together. Solutions and other so-called indefinite chemical compounds should be regarded in this light. According to the principles developed in this work we should regard them as containing both the compounds of the heterogeneous molecules themselves and the products of their decomposition, as in peroxide of nitrogen, N2O4 and NO2. And we must consider that those molecules A, which at a given moment are combined with B in AB, will in the following moment become free in order to again enter into a combined form. The laws of chemical equilibrium proper to dissociated systems cannot be regarded in any other light.
[20] This strengthens the fundamental idea of the unity and harmony of type of all creation and is one of those ideas which impress themselves on man in all ages, and give rise to a hope of arriving in time, by means of a laborious series of discoveries, observations, experiments, laws, hypotheses, and theories, at a comprehension of the internal and invisible structure of concrete substances with that same degree of clearness and exactitude which has been attained in the visible structure of the heavenly bodies. It is not many years ago since the law of Avogadro-Gerhardt took root in science. It is within the memory of many living scientific men, and of mine amongst others. It is not surprising, therefore, that as yet little progress has been made in the province of molecular mechanics; but the theory of gases alone, which is intimately connected with the conception of molecules, shows by its success that the time is approaching when our knowledge of the internal structure of matter will be defined and established.
[21] If Be = 9, and beryllium chloride be BeCl2, then for every 9 parts of beryllium there are 71 parts of chlorine, and the molecular weight of BeCl2 = 80; hence the vapour density should be 40 or n40. If Be = 13·5, and beryllium chloride be BeCl3, then to 13·5 of beryllium there are 106·5 of chlorine; hence the molecular weight would be 120, and the vapour density 60 or n60. The composition is evidently the same in both cases, because 9 : 71 ∷ 13·5 : 106·5. Thus, if the symbol of an element designate different atomic weights, apparently very different formulæ may equally well express both the percentage composition of compounds, and those properties which are required by the laws of multiple proportions and equivalents. The chemists of former days accurately expressed the composition of substances, and accurately applied Dalton's laws, by taking H = 1, O = 8, C = 6, Si = 14, &c. The Gerhardt equivalents are also satisfied by them, because O = 16, C = 12, Si = 28, &c., are multiples of them. The choice of one or the other multiple quantity for the atomic weight is impossible without a firm and concrete conception of the molecule and atom, and this is only obtained as a consequence of the law of Avogadro-Gerhardt, and hence the modern atomic weights are the results of this law (see Note [28]).
[22] 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.
[23] This formula (which is given in my work on ‘The Tension of Gases,’ and in a somewhat modified form in the ‘Comptes Rendus,’ Feb. 1876) is deduced in the following manner. According to the law of Avogadro-Gerhardt, M = 2D for all gases, where M is the molecular weight and D the density referred to hydrogen. But it is equal to the weight s0 of a cubic centimetre of a gas in grams at 0° and 76 cm. pressure, divided by 0·0000898, for this is the weight in grams of a cubic centimetre of hydrogen. But the weight s of a cubic centimetre of a gas at a temperature t and under a pressure p (in centimetres) is equal to s0p/76(1 + at). Therefore, s0 = s.76(1 + at)/p; hence D = 76.s(1 + at)/0·0000898p, whence M = 152s(1 + at)/0·0000898p, which gives the above expression, because 1/a = 273, and 152 multiplied by 273 and divided by 0·0000898 is nearly 6200. In place of s, m/v may be taken, where m is the weight and v the volume of a vapour.
[24] The above formula may be directly applied in order to ascertain the molecular weight from the data; weight of vapour m grms., its volume v c.c., pressure p cm., and temperature t°; for s = the weight of vapour m, divided by the volume v, and consequently M = 6,200m(273 + t)/pv. Therefore, instead of the formula (see Chapter II., Note 34), pv = R(273 + t), where R varies with the mass and nature of a gas, we may apply the formula pv = 6,200(m/M)(273 + t). These formulæ simplify the calculations in many cases. For example, required the volume v occupied by 5 grms. of aqueous vapour at a temperature t = 127° and under a pressure p = 76 cm. According to the formula M = 6,200m(273 + t)/pv, we find that v = 9,064 c.c., as in the case of water M = 18, m in this instance = 5 grms. (These formulæ, however, like the laws of gases, are only approximate.)