Page 360 - MODERN ELECTROCHEMISTRY

296 CHAPTER 3

solutions, this is the hydration number). Then, if there are n moles of electrolyte in the
water, the change in free energy due to the removal of the water to the ions’ sheaths
is per mole of electrolyte.
One now comes to the second kind of work and realizes why the calculation is
best done as a thought process in which the interionic attraction is shut off while the
work is calculated. One wants to be able to use the ideal-solution (no interaction)
equation for the work done, and not Thus, using the latter
expression would be awkward; it needs a knowledge of the activities themselves and
that is what one is trying to calculate.
Now, the change in free energy change due to the change in the concentration of
the ions after the removal of the effective solvent molecule is

where x is the mole fraction of the electrolyte in the solution.
Before the water is removed,

where n is the number of moles of electrolyte present in moles of water. Then after
the water is removed to the sheaths,

The change in free energy is

Hence, the total free-energy change in the solution, calculated per mole of the
electrolyte present, is

Now, one has to switch back to the Coulombic interactions. If the expression for
the work done in building up an ionic atmosphere [e.g., Eq. (3.120)] were still valid
in the region of relatively high concentrations in which the effect of change of
concentration is occurring, then, 20

20
Here has been written instead of the of Eq. (3.119). For 1:1 electrolytes, c and I are identical.