The new quantity of liquid, which still contains a gram- molecule of dissolved gas, is united with the liquid in -4 — the gas and liquid in this vessel having previously been separated. A volume, v, of liquid is now forced out through a semi-permeable membrane, whilst the a gram-molecule remains in the vessel A. The work then done will be —
^6= -l'99aT= --48.
Finally, the dissolved a gram-molecule of gas is permitteil to evolve from the liquid in A into the gas above at pressure p, and the work —
Ae= 199aT = -^a
is done, the same as when the gas was forced into the liquid, but with the sign changed. The condition in A is now the same as initially.
Summing up, we have
Ai + A^=^ l'99aT fin ?? -Hn^LH =r
L pi vj
or — ^ = = constant,
Pi TTl
i,e, the osmotic pressure of the dissolved gas is proportional to the pressure of the gas above the solution.
Since the osmotic pressure is proportional on the one hand to the concentration, and on the other hand to the pressure of the gas, it is clear that the concentration of the gas in the solution must stand in a constant ratio to the concentration, or density, of the gas over the solution. This law is called, after its discoverer, Henry's law.
The same development would lead to a different result if the substance in the gaseous state and when dissolved had difTerent molecular weights. If, for instance, the substance when dissolved had a molecular weight double that in the gaseous state, the work A^ would consist in changing
the osmotic pressure of « gram-molecule from osmotic pressure m to osmotic pressure rr, and we should obtain —
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