Page 234 - MODERN ELECTROCHEMISTRY

170 CHAPTER 2

However, this is only the excess number of nonelectrolyte molecules per unit
volume at a distance r from the ion. What is required is the total excess number per
unit volume throughout the region outside the primary solvation sheath, i.e., in region
2. One proceeds as follows: the excess number, not per unit volume, but in a spherical
shell of volume dr around the ion, is

and therefore the total excess number of nonelectrolyte molecules per ion in region 2
is (with equal to the radius of the primary hydration sheath)

If one sets then the excess number of nonelectrolyte molecules caused
to be in solution per ion is

The excess number of nonelectrolyte molecules in a real solution containing
moles of binary electrolyte is given by Eq. (2.148), multiplied by the number of
moles per cubic centimeter in the solution, namely, The expression

where is the number of nonelectrolyte molecules per cubic centimeter in the
solution after addition of the electrolyte.
Hence,

42
A factor of 2 has been removed from the denominator of this equation, compared with Eq. (2.148), because
there are two ions in the binary electrolyte, each of which is assumed to give the same effect on the
solubility.