V.
��FREEZING POINT OF SOLUTIONS.
��j» — p' _ niM
" ioOoS ^^^ P' ^^^' From this it follows that for
the rise of boiling point dT —
��dT =
��n
��and dT =
��2niMT^ lOOOrfX
���It should be carefully noticed that T denotes the absolute temperature of the boiling point of the solvent, and X is the heat of vaporisation of a gram-molecule of it at the same temperature (compare p. 56).
Freezing Point of Solutions.— In the same way we can calculate the freezing point of a solution, as has been shown by Guldberg (1) and van't Hoflf (^). Let us consider a solvent — ^water, for example — which freezes at the tempera- ture A (Fig. 15). The vapour pressure of the liquid solvent is represented by pp, the tempera- ture being marked off as abscissa and the pressure as ordinate. At O"' (temperature A) the tension
of water vapour, represented by the point P, is 4*61 mm. ; at lower temperatures the tension is smaller, and exact measurements of this have been made by Juhlin (S). Water in the solid form, ice, also has a vapour pressure represented by PF, which at the same tem- perature is lower than that for liquid water; at the freezing point, water and ice must have the same vapour pressure. In order to prove tliis, suppose that we have a closed vessel con- taining ice, water, and water vapour at 0° (Fig. 16). If the vapour tension over the ice were smaller than that over the liquid, the water would distil over to the ice until it was all converted into ice. And, on the other liand, if the tension over the water were lower than that over the ice, then this latter would by distillation be
£
���Fio. 16.
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