per 100H 2 O is nearly n 1°·1 to n 1°·0 (ether, for instance, gives the last number), and consequently in dissolving in 100 grms. of water it is about 18°·0 n to 19°·0 n , taking this rule to apply to the case of a small number of n (not over 0·2 n ). If instead of water, other liquid or fused solvents (for example, benzene, acetic acid, acetone, nitrobenzene or molten naphthaline, metals, &c.) be taken and in the proportion of 100 molecules of the solvent to n molecules of a dissolved indifferent (neither acid nor saline) substance, then the depression is found to be equal to from 0°·62 n to 0°·65 n and in general K n . If the molecular weight of the solvent = m , then 100 gram-molecules will weigh 100 m grms., and the depression will be approximately (taking 0·63 n ) equal to m 0·63 n degrees for n molecules of the substance dissolved in 100 grms. of the solvent, or in general the depression for 100 grms. of a given solvent = kn where k is almost a constant quantity (for water nearly 18, for acetone nearly 37, &c.) for all dilute solutions. Thus, having found a convenient solvent for a given substance and prepared a definite (by weight) solution ( i.e. knowing how many grms. r of the solvent there are to q grms. of the substance dissolved) and having determined the depression d — i.e. the fall in temperature of freezing for the solvent—it is possible to determine the molecular weight of the substance dissolved, because d = kn where d is found by experiment and k is determined by the nature of the solvent, and therefore n or the number of molecules of the substance dissolved can be found. But if r grms. of the solvent and q grms. of the substance dissolved are taken, then there are 100 q / r of the latter per 100 grms. of the former, and this quantity = n X, where n is found from the depression and =
d / k
and X is the molecular weight of the substance dissolved. Hence X =
100qk / rd ,
which gives the molecular weight, naturally only approximately, but still with sufficient accuracy to easily indicate, for instance, whether in peroxide of hydrogen the molecule contains HO or H2O2 or H3O3, &c. (H2O2 is obtained).
Moreover, attention should be drawn to the fact that a great many substances taken as solvents give per 100 molecules a depression of about 0·63n, whilst water gives about 1·05n, i.e. a larger quantity, as though the molecules of liquid water were more complex than is expressed by the formula H2O.30
A similar phenomenon which repeats itself in the osmotic pressure, vapour tension of the solvent, &c. (see Chapter I., Notes 20 and 50), i.e. a variation of the constant (k for 100 grms. of the solvent or K for 100 molecules of it), is also observed in passing from indifferent substances to saline (to acids, alkalis and salts) both in aqueous and other solutions as we will show (according to Pickering's data 1892) for solutions of NaCl and CuSO4 in water.
For n = 0·01 0·03 0·05 0·1 0·5 molecules of NaCl the depression is d = 0°·0177 0°·0598 0°·0992 0°·1958 0°·9544 which corresponds to a depression per molecule
K = 1·77 1·96 1·98 1·96 1·91 i.e. here in the most dilute solutions (when n is nearly 0) d is obtained about 1·7n, while in the case of sugar it was about 1·1n. For CuSO4 for the same values of n, experiment gave: