about 13'4 mm. At any given temperature the pressure and composition of the phases are fixed. If the composition of the liquid phase were given, such a saturated solution could only be obtained at a single temperature and with a single pressure of water vapour.
If the number of co-existing phases is the same as the number of bodies present in the system, then two of the external conditions may be chosen {e,g, temperature and pressure), but the composition of the phases is then deter- mined. If, therefore, we have two bodies, salt and water, in two phases, namely, solution and vapour, and the system is to have a particular temperature and pressure, the composition of the solution can only have one value. In other words, there is only one concentration of the solution which at a given temperature possesses a particular vapour pressure.
Osmotic Work. — In order to derive the various con- ditions of equilibria it is necessary to know how much work is done when a dissolved substance passes from one concen- tration to another by removal of the solvent. This removal may be carried out in different ways, as by evaporation, by freezing out, or by forcing solvent out from the solution by means of a semi-permeable piston which does not allow the dissolved substtmce to pass through. In our derivation we shall make use of this last method. We premise that a 8emi-permeable membrane can be found for every substance which will allow this but no other substance present in the solution to pass through. In reality this is not quite the case, but in general an arrangement can be made which closely approximates to the condition of semi-permeability.
The simplest case is ofiTered by a solid substance which dissolves in a liquid, so that the solution in contact with the solid is always saturated. Suppose a piston, permeable by the solvent but not by the dissolved substance, resting on the surface of the solution, and suppose further that there is solvent above the piston. In order that there may be a condition of equilibrium so that the pure solvent does not pass into the solution, the piston, according to our previous
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