Page 73 - Vogel's TEXTBOOK OF QUANTITATIVE CHEMICAL ANALYSIS

HYDROLYSIS CONSTANT AND DECREE OF HYDROLYSIS 2.19
Applying the Law of Mass Action and taking the activity of un-ionised water
ai unity, we have:
~MOH HA - [MOHI. CHAI YMOLYHA
x
K, = -
a,+ x a,- [M']. [A-] y,+.y,-
By the usual approximations, i.e. by assuming that the activity coefficients of
the un-ionised molecules and, less justifiably, of the ions are unity, the following
approximate equation is obtained:
[MOH] x [HA] [Base] x [Acid]
-
K, = -
[M'] x [A-] [Unhydrolysed saltI2
If x is the degree of hydrolysis of 1 mole of the Salt dissolved in Vlitres of
solution, then the individual concentrations are:

[MOH] = [HA] = x/V; [M'] = [A-] = (1 -x)/V
leading to the result

The degree of hydrolysis and consequently the pH is independent of the
concentration of the solution.*
It may be readily shown that:

or pK, = pKw - pKa - pKb
This expression enables us to calculate the value of the degree of hydrolysis
from the dissociation constants of the acid and the base.
The hydrogen ion concentration of the hydrolysed solution is calculated in
the following manner:

C HA1 xl v X
[H'] = Ka x - x = Ka x ---
Ka
=
CA - 1 (1 -x)/V (1-X)
But x/(l - x) = fi
Hence [H'] = K,& =

If the ionisation constants of the acid and the base are equal, that is Ka = Kb,
pH = f pKw = 7.0 and the solution is neutral, although hydrolysis may be
considerable. If Ka > K,, pH < 7 and the solution is acid, but when Kb >Ka,
pH > 7 and the solution reacts alkaline.
The pH of a solution of ammonium acetate is given by:

i.e. the solution is approximately neutral. On the other hand, for a dilute

*This applies only if the original assumptions as to activity coefficients are justified. In solutions
of appreciable ionic strength, the activity coefficients of the ions will Vary with the total ionic strength.