Lord Rayleigh and D. Berthelot applied corrections in the latter way to many gases. Thus, E. W. Morley had found the density of oxygen relative to hydrogen to be 15.90 at ordinary pressures; since the value of a for oxygen is 0.0009 and for hydrogen —0.0005, the corrected density becomes 15.88 (H= I ), or 16.0o (H=1.0077) in the units now adopted. (See ATOMIC WEIGHTS.) Compound gases are dealt with similarly; thus T. Batuecas (1925) corrected the densities of ethylene, nitrous oxide and nitric oxide by examination of their compressibilities (alteration of v, and hence of pv, with change in p) , and hence obtained C2H4 = N20=44.003; NO=30.006. P. A. Guye and E. Moles, among others, have determined many molecular and atomic weights by similar methods.
The principle indicated here is applicable to the determination of the molecular weight of any vaporizable substance, and it is not necessary to compare the vapour density directly with that of oxygen, for, from the "ideal" vapour density, it is only necessary to calculate the weight (in grams) which would occupy 22.41 litres (corresponding to 32 grams of oxygen) at o° C and 760 mm. pressure in order to determine the molecular weight.
The theory of solution permits the investigation of the molecular weights of substances which dissolve in water or some other solvent. It is shown in SOLUTION that a solute lowers the freezing point and raises the boiling point of the solvent in a regular manner as long as dilute solutions are dealt with. It has been shown that if one gram-molecule of a solute be dissolved in Ioo grams of solvent then the boiling point is raised by 0.02P/w (say D) degrees, where T is the absolute boiling point and w the latent heat of vaporization of the solvent; this constant is known as the molecular rise of the boiling point, and varies from solvent to solvent. If we dissolve, say, m grams of a substance of molecular weight M in 1 oo grams of the solvent and observe the elevation in the boiling point, d, then M is given by M=mD/d. Similar considerations apply to the freezing points
of solutions. In this case D = where T is the absolute freezing point of the pure solvent and w the latent heat of solidification. To apply these principles it is only necessary there fore to determine the freezing (or boiling) point of the solvent (of which a known weight is taken), add a known weight of the solute, allow it to dissolve and then notice the fall (or rise) in the freezing (or boiling) point, from which values, if the molecular depression (or elevation) be known, the molecular weight of the dissolved substance is readily calculated. The following are the molecular depressions and elevations (with, respectively, the freezing and boiling points in brackets) of the commoner solvents.
Molecular depressions: aniline 58.7; benzene 50.0; acetic acid 39.o; nitrobenzene (5.3°), 70.o; phenol 72; water (o°), 18.5.
Molecular elevations: acetic acid (II84°), 25.3 ; acetone (56°), 17.1; alcohol (78°), I1.7; ether (35°), 21.7; benzene (80°), 26.7; chloroform (60), 35.9; pyridine (I 15°), 29.5; water (Ioo°), 5.1.
Other methods are available for dissolved substances, e.g., determination of osmotic pressure, lowering of vapour pressure, and diminution of solubility, but these are little used. It must be remembered, however, that the molecular weight of a solid in solution is only apparent, for it may be affected by a great variety of factors. Thus, electrolytic dissociation of the solid if a salt will give an abnormally low value ; separation as mixed crystals (see CHEMISTRY, PHYSICAL) with the solvent will cause errors; any interaction with the solvent, such as formation of hydrates or "solvates," will affect the result; and equally important is the circumstance that the "ebullioscopic" and "cryoscopic" (boiling point and freezing point) methods just described become increas ingly inexact with increasing concentration of the solute. (See