This is usually expressed by saying that the molecular weight of water is 18 ; and in as much as it consists of two atoms of hydrogen in union with one atom of oxygen, the weight of a molecule of water-gas is equal to the sum of the weights of the atoms composing it; for, (2 x i) + 16= 18.
Molecular Weights of the Elements
The molecular weights of some of the elements have been successfully determined ; in certain cases by their density in the gaseous state, in others by the lowering of the vapour-pressure of mercury, caused by the presence of a known weight of a dissolved metal, and again in others by the depression of the freezing-point of certain metals, caused by the presence of others in known amount. These will be considered in their order.
(a) Vapour-densities. For reasons already explained on page 13, a molecule of oxygen is believed to contain two atoms, and inasmuch as the equivalents of most elements have been determined with reference to oxygen, by analysis or by synthesis of their oxides or of their chlorides, and as the ratio of the equivalent of chlorine to that of oxygen has been very accurately determined, it has been agreed to refer the atomic weights of the elements to the standard of oxygen instead of to that of hydrogen. But the atomic weight of oxygen is assumed as 16, and the same standard is applied to the densities of gases; instead of referring them to the standard of H = I, they are referred to O = 16. To find the molecular weights, the number expressing the density must be doubled in order to compare with the molecular weight of oxygen, which is 32.
The density referred to this standard is 1.006 or 1.007. There is not yet an absolute certainty, but it is clear that the molecular weight of hydrogen must be approximately 2, i.e. the molecule is di-atomic.
Lord Rayleigh found the density of nitrogen to be 14.001 ; its molecular weight is therefore 28, and its formula N 2 .
Taken as 16; formula O 2 . As these gases keep their relative densities up to a temperature of 1700, it is to be presumed that they all remain diatomic, for it is much more likely that no one of them dissociates than that all dissociate to an equal extent on rise of temperature. The case is different with fluorine, chlorine, bromine, and iodine. The density of fluorine at atmospheric tem perature is 18.3; the theoretical density for F 2 is 19. It follows, therefore, that fluorine must consist of a mixture of monatomic and diatomic molecules. Now, 19 is the molecular weight of F I , for the atom and the molecule are identical, and 38 that of F 2 ; and the gas must contain x molecules of F I +(I x) molecules of F 2 . Hence, 19x438(1 x) = 18.3 x 2 ; and x = 0.073, ** ' in ever y 1000 molecules of the gas there are 73 molecules of Fj and 927 molecules of F 2 .
Chlorine at 200 was found to have the density 35.45, the same as its atomic weight, but at 1000 the density was 27.06, and at 1560 23.3. At low temperatures, therefore, the formula of chlorine is C1 2 , but at 1560 the gas consists of 61 per cent, of molecules of CI r Similar results have been found for bromine, and for iodine, which also has the formula I at low temperatures, the density was found to be 63.7, corresponding to the molecular weight 127.4 at 1500 under low pressure ; for reducing the pressure also increases dissociation. As the atomic weight of iodine is 126.85, tne as at I 5 consists almost entirely of molecules of I r
Thallium has been weighed as gas at 1730 ; the density was 206.2, a sufficient approximation to 204.1 to warrant the conclusion that its molecule is diatomic.
Bismuth at 1640 gave the density 146.5, showing, as its atomic weight is 208.5, a P art i a l dissociation from Bi to Bi-p
Phosphorus and arsenic give densities which indicate the presence in their gases of more complicated molecules. At 313 the density of phosphorus gas is 64, and there is a gradual decrease with rise of temperature, until at 1708 the density is 45.6. As the atomic weight of phosphorus is 31.0, the density 62 would correspond to the existence of molecules of P 4 , while at 1708 there must be a con siderable admixture of molecules of a smaller complexity, probably P . Arsenic gas had the density 154.2 at 644, and 79.5 at 1700; the atomic weight of arsenic being 75, the density 150 would correspond to the formula As 4 , and at 1700 the molecules are almost all As 2 , only a small admixture of molecules of As 4 remaining undecomposed. The density of antimony gas, 141.5 at 1640, implies the presence of some molecules of Sb 4 among many molecules of Sb 2 , for the atomic weight is 120.
The elements sulphur, selenium, and tellurium show signs of even greater molecular complexity. Dumas found the density of sulphur gas at 500 to be 94.8 ; now, the atomic weight of sulphur is 32.08, and 96 is 32 x 3 ; hence, it was for long supposed that a molecule of gaseous sulphur consisted of 6 atoms ; but it has been recently found that at 193, of course under a very small pressure, 2.1 mms. (for the boiling-point of sulphur at normal pressure is 446), the density reached the high number 125.5 5 now > 32 x 4 is 128, and it must be concluded that the molecular weight of sulphur in the gaseous state is 256, and its formula at low temperatures S g . At 800 its formula is S 9 , and at 1719 the density 31.8 was found, showing no sign of further molecular simplification. Selenium, of which the atomic weight is 79.1, has the density 1 1 1 at 860, imply ing some molecular complexity, and at 1420 the density is reduced to 82.2, corresponding to the formula Se. 2 ; and tellurium, at about 1400, has the gaseous density 130; it appears, therefore, to consist of molecules of Te 9 , since its atomic weight is 127.6.
These examples show that the molecules of many elements in the gaseous state are more or less complex. It is probable that sulphur, selenium, and tellurium would exist as octo-atomic molecules could the temperature be sufficiently reduced ; even with sulphur at its boiling-point under normal pressure, the temperature is so high that many of these complex molecules are already decomposed. Probability is also in favour of the supposition that elements of the phosphorus group, phosphorus, arsenic, antimony, and possibly bismuth, have molecules consisting of 4 atoms ; these too dissociating with rise of temperature into di-atomic molecules. Oxygen, nitrogen, and hydrogen consist of di-atomic molecules, no sign of dissociation having been remarked even at the highest attainable temperatures; but fluorine, though consisting mostly of di-atomic molecules, contains some mono-atomic ones ; and chlorine, bromine, and iodine, though probably CJ 9 , Br 2 , and I 2 at low temperatures, dissociate into molecules identical with their atoms if the temperature is sufficiently raised. The fact of reduction in the molecular complexity of the molecules of elements prepares us for the existence of elements which in the gaseous state are already mono-atomic ; and many such are known.
Mono-atomic Cad elements
Sodium. Potassium. Zinc. Mium. Mercury. Gas-density 12.7 18.8 3415 57-oi 100.94 Temperature Red heat Red heat 1400 1040 446 and 1730 Atomic weights 23.05 39-!4 65.4 112.0 200.3 Density x 2 25.4 37.6 68.3 114.02 201.88
The presumption from these numbers is that the elements are all mono-atomic. It must be remembered that their specific heats all point to the atomic weights given.
There is, however, another argument for the mono atomicity of gaseous mercury. On the assumption of the " kinetic theory of gases," that the pressure of a gas on the walls of the vessel containing it is due to the bombardment of the sides by repeated and enormously numerous impacts of the molecules, it can be calculated that the amount of heat necessary to raise the temperature of the molecular weight expressed in grams of an ideal gas the molecules of which are supposed to be hard smooth elastic spheres, must be 3 calories, provided the gas be not allowed to expand. If, however, it be allowed to expand, it will cool itself, and more heat must be added to restore the temperature ; this extra amount of heat is two additional calories. To heat the molecular weight of the gas in grams through I , allowing it to expand at constant pressure, requires therefore 5 calories.
The " molecular heat at constant volume" is thus 3 calories; the "molecular heat at constant pressure" is 5 calories. The ratio between the two is 3 : 5, or I : 1.66. This has been found to be the case for mercury gas, the mono-atomicity of whose molecule is proved on other grounds ; and the inactive gases of the atmosphere, helium, neon, argon, krypton, and xenon, exhibit the same ratio between their atomic heats. It therefore follows that the atoms of these gases are also identical with their molecules ; and that their atomic weights are to be deduced from their densities by doubling the numbers representing the latter. Confirmatory of this view, the ratio between the molecular heats of oxygen, hydrogen, nitrogen, and gases which are known to be di-atomic, like NO, CO, &c., is as 5 : 7 or i : 1.4. Such gases require more heat to raise their temperature than an equal number of molecules of the mono-atomic gases do ; the reason is, that the heat applied to diorpoly-atomic gases is used, not merely in transporting the atoms from place to place and raising pressure by causing them to bombard the walls of the containing vessel, but some heat is required to cause the atoms to move within the molecule, in some rotatory or vibratory manner ; and consistently with this it has been found that gases consisting of a greater number of atoms in the molecule require still more heat to raise the temperature of weights proportional to their molecular weights ; in other words, their molecular heats at constant volume are higher the greater the number of atoms in the molecule.
For these reasons the densities of the inactive gases must be multiplied by 2 to obtain their atomic weights.
() Lowering of Freezing-Point, or Lowering of Vapour-Pressure of Solvent. The molecular weights of some of the elements have been determined by Raoult's method, either by the lowering of the vapour-pressure of mercury, or by the depression in the freezing-point of some other metal or solvent in which the element has been dissolved. Lithium, sodium, potassium, calcium, barium, magnesium, cadmium, gallium, thallium, manganese, silver, and gold appear to be mono-atomic, while tin, lead, aluminium, antimony, and bismuth show tendency in con centrated solution to associate to di-atomic molecules. These results were obtained by measuring the lowering of vapourpressure of mercury produced by known weight of the metals named. By measurement of the depression in the freezing-point of tin, in which metals were dissolved, zinc, copper, silver, cadmium, lead, and mercury appeared to be mono-atomic, while aluminium was found to be di atomic. These results, however, are not to be regarded with the same confidence as those obtained by means of measurements of the vapour-density, for it is not certain whether the molecular weight of the solvent should be taken as identical with its atomic weight. All that can be certainly affirmed is, that the molecular weights of the elements which have been placed in the same class above correspond to formulas with the same number of atoms in the molecule. Thus, if zinc is mono-atomic, so is cadmium ; if di-atomic,
cadmium has also a di-atomic molecule ; and similarly with the rest.
A method has also been devised, depending on the capillary rise of liquids in narrow tubes, by means of which it is possible to estimate the molecular complexity of liquids. This method is applicable to only a few elements ; but by its use it has been found that in the liquid state bromine consists chiefly of di-atomic molecules mixed with a few tetra-tomic molecules ; and that phosphorus in the liquid, as in the gaseous condition, forms molecules corresponding to the formula P 4 .