Page 326 - MODERN ELECTROCHEMISTRY

262 CHAPTER 3

where is the mole fraction of the solvent. One allows for the nonideal behavior of
the solvent in respect to its vapor pressure by writing

As Thus, the “standard state” is the pure solvent.
At this point, one calls into play the Gibbs–Duhem equation of thermodynamics,
according to which 10

Or, for a two-component system (solvent and electrolyte)

where the subscript 1 represents the solvent and the subscript 2 represents the
electrolyte solute.
It follows from ln , that

or

Thus, if one measures a number of values of the vapor pressure of the solvent
at a corresponding number of solute concentrations, (to which there are matching
solvent concentrations one can plot the ln values against the ratios. Then
the area of that plot will give ln the being the solute activity corresponding to
the limit of the integral at (this being the measured solvent activity for a solution
containing a solute, the activity of which is
The left-hand side of Eq. (3.98) came from

10
Any initial impression that there is something unreasonable about the Gibbs–Duhem equation should be
instantly quelled. It merely tells one that (for a two-component system) when an increase in occurs,
it causes a decrease in of equal magnitude, a typically powerful and general result of thermody-
namic reasoning.