Question

Hydrolysis constants of two salts KA and KB of weak acids HA and HB are \[{10^{ - 8}}\] and \[{10^{ - 6}}\]. If the dissociation constant of third acid HC is \[{10^{ - 2}}\]. The order of acidic strengths of three acids will be:
A. HA > HB > HC
B. HB > HA > HC
C. HC > HA > HB
D. HA = HB = HC

Answer 1

Hint: The dissociation constant is a measure of acid strength in which an acid with higher \[{K_a}\] value, will liberate greater number of hydrogen ions per mole of acid in solution and hence acid will be called stronger. It is also known as acidity constant, or acid-ionization constant. It is the equilibrium constant for a chemical reaction \[HA \rightleftharpoons {A^ - } + {H^ + }\] known as dissociation in the context of acid–base reactions. The chemical species HA is an acid that dissociates into \[{A^ - }\]. The system is said to be in equilibrium when the concentrations of its components will not change with the passing of time, because both forward and backward reactions are occurring at the same rate.
The relation between \[{K_a}\], \[{K_W}\] and \[{K_h}\] is given by \[{K_h} =
\dfrac{{{K_W}}}{{{K_a}}}\]
Apply relationship between ionic product of water and hydrolysis constant to get \[{K_a}\]

Complete step by step answer:
The acid dissociation constant \[{K_a}\] is the ratio of the ionic product of water \[{K_W}\] to the hydrolysis constant \[{K_h}\].
Dissociation of acid \[{K_a} = \dfrac{{Ionic{\text{ }}product{\text{ }}of{\text{ }}water{\text{ }}}}{{Hydrolysis{\text{ }}constant}}\;\;\]
Ionic product of water, \[{K_w} = {10^{ - 14}}\] (a constant)
For acid HA, \[{K_a} = \dfrac{{{K_w}}}{{{K_h}}} = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 8}}}} = {10^{ - 6}}\]
For acid HB, \[{K_a} = \dfrac{{{K_w}}}{{{K_h}}} = \dfrac{{{{10}^{ - 14}}}}{{{{10}^{ - 6}}}} = {10^{ - 8}}\]
For acid HC, \[{K_a} = {10^{ - 2}}\]
Comparing \[{K_a}\]values, it is found that \[{K_a}\]of HC is greatest and \[{K_a}\] of HB is least and \[{K_a}\] of HA lies in between
 Now, as mentioned above, the acid strength is directly proportional to \[{K_a}\] values.
Therefore, the order of acid strengths is:
\[HC > HA > HB\]

That is, option C. is the correct one.

Note: \[{K_w}\] and \[{K_h}\] values should be used to calculate \[{K_a}\] and directly find the acidic strength by using the relationship that higher the \[{K_a}\] value, higher the acidic strength.