Question

The $p{{K}_{a}}$ of a weak acid, HA, is 4.80 and the $p{{K}_{b}}$ of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be:
(A) 8.58
(B) 4.79
(C) 7.01
(D) 9.22

Answer 1

The salt of weak acid and weak base is generally given as;
$BOH+HA\to {{B}^{+}}{{A}^{-}}+{{H}_{2}}O$ where, BA is the salt for which we need to find the required pH.
- To analyse the pH of the corresponding salt, we need to have basic knowledge of relevant acidity and basicity constants i.e. $p{{K}_{a}}$ and $p{{K}_{b}}$.

Complete Solution :
Let us learn the concepts pH of acids, bases and salts;
The pH of salts depends upon the type of salt and its formation. Generally, salts are formed by the neutralisation reaction between acid and base. Thus, the pH of salt must be generally equal to 7 i.e. neutral. But this statement has exceptions i.e. salts can be acidic or basic too.
Case I-
The salt of a strong acid and a strong base will be neutral in nature i.e. the pH will be 7.
Case II-
The salt of a strong acid and a weak base will be acidic in nature i.e. the pH will be less than 7.
Case III-
The salt of a weak acid and a strong base will be basic in nature i.e. the pH will be more than 7.
Case IV-
The nature of salt of a weak acid and a weak base will depend upon the value of dissociation constant of acid and base.
Illustration-
In the given problem, we have case IV as discussed above:
The pH of the formed salt will be hence, given as,
$pH = \dfrac{1}{2}\left[ p{{K}_{w}}+p{{K}_{a}}-p{{K}_{b}} \right]$
So, putting the values we get;
$pH = \dfrac{1}{2}\left( 14 + 4.80 - 4.78 \right) = 7.01$

So, the correct answer is “Option C”.

Note: Do note that in general the pH of a salt will be equal to 7 or if any exception will be near to the value of 7. The value will not differ away with high rates from 7.