the osmotic pressure of which is vaiiable, and follows van't Hoff's law—
where V is the (variable) volume in which a gram-molecule is dissolved. The pressure which the substance exerts on the piston is the same as that which would be exerted by the same number of gram-molecules in the gaseous state, instead of dissolved, contained in the same volume. If, therefore, by the introduction of solvent, the volume of the solution increases from vq to vi (whilst the osmotic pressure diminishes from po to pi) at constant temperature, the work done by the solution during this process will be the same as that done by a mass of gas containing the same number of mole- cules when it increases in volume by the same amount. At constant temperature T this work amounts for each gram- molecule of dissolved substance to —
A = 1-99^ In ^ = 1-99^ In ??
Vq p{
For substances which deviate from van't HoflTs law the value given must be multiplied by i, just as before.
As no known gas exactly follows the law of Avogadro (and also those of Boyle and Gay-Lussac), we often consider a so-called ideal gas which exactly obeys these laws ; in the same way there is no solution which absolutely obeys van't HoflTs law, and so we often make use of the ideal (dilute) solution td which we assume the law rigidly applies.
Heiuy's Law. — In the following development of the laws of equilibria we start with the fundamental doctrine that, when a substance is transferred from one system to another, and then at the same temperature is brought back to its original condition, the sum of the works done is zero. Thus : if we have a gas, e.g. oxygen, at pressure p, in contact with a liquid, e.g. water, in a closed vessel. A, the gas dissolves to a certain extent; let the osmotic pressui^e which it exerts when equilibrium is established be rr. In another closed vessel, B, let there be the same gas, but at a
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