-je GENERAL CONDITIONS OF EQUILIBRIUM, chap.
calculations (see p. 29), must be so weighted that it exerts on the solution a pressure (P per square centimetre) equal to the osmotic pressure. By raising the piston, in doing which work must be done, a volume dv of the solvent is caused to pass into the solution. Since solid substance is present in contact with the solution, the concentration, and consequently also the osmotic pressure, remain constant, and the work done during the solution process is, like that done by evaporation of a liquid —
dA = Pdv.
When a gram-molecule of a solid substance dissolves, the work done is, according to van't HoflTs law, the same as for a liquid which is vaporised —
A =Pr=l-99Tcal.,
where V is the volume occupied by a gram-molecule, and T denotes the absolute temperature. This work, like that done during the evaporation of a liquid, is independent of the pressure under which the vaporisation takes place, but is proportional to the absolute temperature.
This does not, of course, apply to the solution of those substances (salts, strong acids and bases) which exert an osmotic pressure greater than that which can be calculated by van't HoflTs law. In such cases a correction must be introduced, and this can easily be done. If it has been ascertained by experiment that the osmotic pressure of the solution in question is i times greater than it should be according to van't Hoff's law, we must multiply by this factor, and obtain —
A = VmiT caL
Let us now take the case of a solution containing a certain amount of a dissolved substance and no solid in contact with it. As before, let the solution be contained in a vessel with a piston above which there is pure solvent. By raising the piston we allow some of the solvent to enter the solution.
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