Page 52 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

2 FUNDAMENTAL THEORETICAL PRINCIPLES OF REACTIONS IN SOLUTION

concentrations. Substituting in the above equation, we obtain:

This is the rigorously correct expression for the Law of Mass Action as applied
to weak electrolytes.
The activity coefficient varies with the concentration. For ions it also varies
with the ionic charge, and is the same for al1 dilute solutions having the same
ionic strength, the latter being a measure of the electrical field existing in the
solution. The term ionic strength, designated by the symbol I, is defined as equal
to one half of the sum of the products of the concentration of each ion multiplied
by the square of its charge number, or I =0.5Cciz2, where ci is the ionic
concentration in moles per litre of solution and zi is the charge number of the
ion concerned. An example will make this clear. The ionic strength of
0.1 M HNO, solution containing 0.2M Ba(NO,), is given by:
0.5{0.1 (for H+)+0.1 (for NO;)
+ 0.2 x 2' (for BaZ+) + 0.2 x 2 (for NO;)) = 0.5 (1.4) = 0.7
It can be shown on the basis of the Debye-Hückel theory that for aqueous
solutions at room temperature:
0.505zi2. Io.'
log yi = -
1 + 3.3 x 107 a. IO.'
where y, is the activity coefficient of the ion, zi is the charge number of the ion
concerned, I is the ionic strength of the solution, and a is the average 'effective
diameter' of al1 the ions in the solution. For very dilute solutions (Io.' < 0.1)
the second term of the denominator is negligible and the equation reduces to:

For more concentrated solutions (Io.' > 0.3) an additional term BI is added to
the equation; B is an empirical constant. For a more detailed treatment of the
Debye-Hückel theory a textbook of physical chemistry should be consulted.'

2.6 SOLUBlLlTY PRODUCT
For sparingly soluble salts (i.e. those of which the solubility is less than
0.01 mol per L) it is an experimental fact that the mass action product of the
concentrations of the ions is a constant at constant temperature. This product
K, is termed the 'solubility product'. For a binary electrolyte:

K~(AB) CA+] x CB-1
=
In general, for an electrolyte ApBq, which ionises into pAq+ and qBP- ions:

A plausible deduction of the solubility product relation is the following. When
excess of a sparingly soluble electrolyte, Say silver chloride, is shaken up with