Page:Text-book of Electrochemistry.djvu/105

of molecules are controlled by Guldberg and Waage's law, whilst the equilibrium relationships of one kind of molecule between two phases of a heterogeneous system are determined by the law of distribution. With the help of these two laws every equilibrium can be calculated. They have been of immense service in the investigation of dissociation phenomena at high temperature, and we shall have to apply them later in our discussion of electrolytic dissociation.

Clapeyron's Formula—For the process of evaporation,

Clapeyron, in 1834, making use of Camot's theorem, deduced the following connection:—

${\displaystyle {\frac {dp}{dT}}={\frac {l}{\left(V-V_{1}\right)T}}}$

In this formula I is the heat of vaporisation of one gram of the liquid, Tis the absolute temperature, and Fand Fi are the volumes of one gram of the vapour and liquid respectively.

It is easy to alter this formula so that it applies to a gram-molecule. If we multiply numerator and denominator of the expression by the molecular weight M of the substance, we obtain in the numerator ${\displaystyle M\times l}$ = \lambda </math>, the molecular heat of vaporisation, and in the denominator ${\displaystyle \left(MV-MV_{1}\right)=v-v_{1}}$, the difference between the molecular volumes of the vapour and the liquid. Therefore —

${\displaystyle {\frac {dp}{dT}}={\frac {\lambda }{\left(v-v_{1}\right)T}}}$

We have already (p. 48) made use of the formula in this form. If the temperature be sufficiently removed from the critical temperature, it is always permissible to neglect the molecular volume ${\displaystyle v_{1}}$ of the liquid compered with that ${\displaystyle v}$ of the gas, and by introducing at the same time ${\displaystyle pv=RT}$ we obtain —

${\displaystyle {\frac {dp}{pdT}}={\frac {\lambda }{RT^{2}}}}$

or—

${\displaystyle {\frac {d\ln {p}}{dT}}={\frac {\lambda }{RT^{2}}}}$