Change of Solubility with Temperature.— It has been shown that the solution of a sabstance corresponds exactly with the vaporisation of a liquid into a vacuum if the osmotic pressure be introduced in place of the vapour pressure ; conse- quently for the solution there must be a connection analogous to that expressed by the Clapeyron formula, that is —
dlnir X
��-_.-i:_ f
��dT " iRT
where ir is the osmotic pressure of the saturated solution and t, as before, denotes the coefficient which occurs in the formula tt F = iRT for the osmotic pressure. If we replace
F, the volume, by ^ * the reciprocal of the concentration, we
obtain —
TT = iCRT,
and from this we further obtain —
d In TT = rf(ln C + In T) = rf In (7 + ^; one step more leads to —
din C ' X - iRT Ai
��— •
��dT " iRT' " iRT'
X denotes the heat which is taken up when a gram- molecule of liquid passes into gas at constant pressure, i,€. with increase of volume, and the external work done amounts to iRT = 2iT (see p. 76). On the other hand, for the solution we consider the heat, Xi, which is required when the process takes place without doing external work, i.e. at constant volume. During the solution the volume of the liquid is not appreciably altered.
Now,
Xi = X - iRT,
i.e. the heat of vaporisation or of solution at constant volume differs from that at constant pressure by the amount of the external work done.
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