56 BOILING AND FREEZING POINT. chap.
In this table dT represents the so-called molecular lowering of the freezing point, Le. that lowering produced by dissolving a gram-molecule in 100 grams of solvent.
The formula —
2 T^ 100 u
based on theory and confirmed by Eykman's results, gives the lowering of the freezing point caused by the solution of a gram-molecule in 100 gram-molecules of solvent. As above, u denotes the heat of fusion of a gram-molecule of the solvent. If the gram-molecule be dissolved in 100 grams of the solvent (and not in MlOO grams), the concentration will be M times as great, and the lowering of the freezing point will be correspondingly increased. This can also be expressed by the above formula, if we understand by u the latent heat of fusion of a gram (not, as formerly, a gram-molecule) of the solvent ; for since the value of the denominator becomes M times smaller, that of dT must become just as much greater. And the same applies to the rise of boiling point.
From what has been said, it is evident that the value of n can be ascertained either from the depression of the vapour pressure, the rise of the boiling point, or the depression of the freezing point, n being the number of dissolved molecules in the liquid. Since the quantity of dissolved substance is known, if we know n we can calculate the weight of a gram- molecule of the dissolved substance. These three methods of determining the molecular weight, particularly the method of the freezing point, on account of their simplicity and their general applicability, are fast displacing the older methods in which the gas density is determined.
Molecular Lowering of the Freezing Point — The following tables contain some data on the molecular lowering of the freezing point, taken from Eaoult's (7) results with aqueous solutions, and Beckmann's (8) extremely exact deter- minations with solutions in benzene. The value at the top of each table is that calculated by means of van't Hoff's formula.
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