MOLECULE 621 illustration is supplied by mellitic acid. For a long time the formula C 4 H 2 O 4 was used for this acid, and by means of it all the then known derivatives were repre sented. But later investigations by Baeyer proved that this formula must be multiplied by three, the new deriva tives obtained by him not being capable of representation with any formula simpler than C 12 H 6 O 12 . Very many ex amples of the same kind might be adduced, but those given may serve to show the nature of the difficulty of settling the formula and with it the molecular weight of a sub stance. It need scarcely be said that the multiple formula represents everything which the simple formula represents and something more, and that chemists as a rule take the simplest formula which will answer the purpose. These chemical methods of determining the formula and mole cular weight apply equally to all pure substances, but they do not give us absolute values, only numbers to which the molecular weights are proportional. And for purely chemical purposes these are all that we requjre. Thus, when a chemist speaks of acting on a molecule of suc- cinic acid with two molecules of pentachloride of phos phorus, he means that he mixes them in the proportion of 118 parts of the former to 2 x 177 5 of the latter. For the sake of precision we sometimes speak of a mole cule of water (or other substance) in grammes, or even of & gramme-molecule, a, grain-molecule, c. Thus, in the case just mentioned a gramme-molecule of succinic acid means 118 grammes- of succinic acid, tfcc. But, while for practical purposes these proportional numbers are quite sufficient, we cannot leave out of view their relation to the actual constitution of matter. There is good reason to believe that matter consists of discrete particles, and that every pure substance is made up of small portions of matter, all alike, so that one of them, if we could examine it, would give us a complete idea of the chemical composition, constitution, and character of the substance. These small portions, of which the smallest quantity of the substance which we can examine contains many millions, we may call molecules. From the character which we have supposed this molecule to possess viz., that it fully represents all the chemical properties of the sub stance it will be seen that these real, ultimate molecules must be proportional to the molecular weights ascertained by chemical means ; so that, while for practical laboratory or manufacturing purposes we use the gramme, the pound, or the ton as our unit, and speak of 18 grammes, pounds, or tons, as the case may be, of water, as a molecule (or gramme-molecule, ton-molecule, &c.), in dealing with the actual constitution of matter we should use as our unit the mass of a single atom of hydrogen, and our gramme- molecule would then be a definite, very large, but not yet accurately ascertained, number of real molecules. It has been already shown above that, on the kinetic theory of gas, a gas consists of a number of particles moving about in straight lines in all directions, and that in a homogeneous gas which follows Boyle s and Charles s laws these particles are all alike. The masses of the particles of different gases are therefore to one another in the same proportion as the densities of the gases, tempera ture and pressure being the same. Thus, in gases, the in dependently moving particles of the kinetic theory are the molecules of which the chemist is in search, and it becomes important that we should compare our chemically found molecular weights with the densities. Theoretically accu rate results could be obtained only in the case of a perfect gas ; but small deviations from Boyle s and Charles s laws do not interfere with the application of this method. Chemical methods, as we have already seen, lead us to a particular number, or a multiple of it, so that our choice is as a rule limited to two or three numbers widely differing from one another. We find that if we do not exceed the limits of chemical stability a gas approaches the state of a perfect gas as the temperature increases, or as the pres sure diminishes. Now if one of the numbers rendered probable by chemical evidence nearly coincides with that given by comparison of gas densities, under conditions where the substance sensibly deviates from Boyle s and Charles s laws, we find that by diminishing the pressure or increasing the temperature within the limits of chemical stability, and thus bringing the substance nearer the state of a perfect gas, the correspondence between these two numbers becomes closer. This has already been pointed out and illustrated in the article CHEMISTRY, vol. v. p. 469. We can now compare the results, in the case of gases, of the chemical and of the physical determination of molecular weight, by giving some examples, placing side by side the formula and molecular weight adopted by chemists, and the mass, in grammes, of the gas occupying the volume of 22-33 x 760/^5 x (273 + Z)/273 litres. This volume is that which one gramme of an ideal gas having the molecular weight 1, and perfectly following Boyle s and Charles s laws, would occupy at pressure p millimetres of mercury and temperature t C. If, then, w be the mole cular weight of any gas, iv grammes of it should occupy this volume, and slight deviation from this would indicate slight deviation from Boyle s and Charles s laws. In the annexed table iv is the molecular weight and m the mass contained in 22 33 x 760/p x (273-M)/273 litres. Where the temperature is not specially stated, the determinations were made under the usual atmospheric conditions. Name. Formula. ia. m. Sulphuretted hydrogen . . . Nitrous oxide H 2 S N-,0 34 44 34-04 44-08 Ammonia NH 3 17 17 12 Carbonic acid CO, 44 44-14 Marsh gas CH 4 16 16-13 Olefiant gas C,H 4 28 28-44 Hydrogen Ho 2 2 Oxvffen .. 0, 32 32 Chlorine C1 2 71 71-27 at 100 C Phosphorus Pi 124 125-9 500 C Arsenic As* 300 294-5 860 C Sulphur f s 6 192 194 500 C. Bromide of aluminium . . . Ferric chloride
s,
Al 2 Br 6 Fe 9 Cl 64 534 325 63 5 537-5 328-8 1000 C. 440 C. 440 C Sal-ammoniac NH 4 C1 53 5 29 6 at 350 C Oil of vitriol H.,S0 4 98 SO 24 440 C Pentachloride of phos- phorus j PC1 5 208-5 (140
4
200 C. 300 C Sulphide of ammonium ... (NH 4 ),S 68 22-76 80 C. A comparison of the values of w and m leads to the following conclusions : (1) In the case of a very great number of substances, of which only a few specimens are given in the table, the two determinations agree, the slight differences often observed being evidently due to deviation of the sub stance from the state of a perfect gas. (2) In a consider able number of substances, physical evidence leads to a multiple of the simplest number satisfying the chemical conditions. This cannot be looked upon as a disagreement between the methods, because, if a particular formula satis fies the chemical conditions, any multiple of it will neces sarily do so ; and indeed, in many of the cases we are now considering, it is possible from chemical considerations to justify the higher molecular weight after it has been sug gested, although such chemical considerations might not in all cases have warranted its adoption without external
support. Thus, we are not without chemical evidence in