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Question: A monoprotic acid in a \[0.1M\] solution ionises to \[0.001\% \]. Its ionization constant is: A. \...

A monoprotic acid in a 0.1M0.1M solution ionises to 0.001%0.001\% . Its ionization constant is:
A. 1×10−111 \times {10^{ - 11}}
B. 1×10−31 \times {10^{ - 3}}
C. 1×10−61 \times {10^{ - 6}}
D. 1×10−81 \times {10^{ - 8}}

Explanation

Solution

Monoprotic acid is an acid which can donate only one proton. For example, HClHCl, HBrHBr, HNO3HN{O_3}, CH3COOHC{H_3}COOH etc are all monoprotic acid. The monoprotic acid undergoes ionization to produce hydrogen ion and a conjugate base.

Complete step by step answer: The ionization of a monoprotic acid can be shown as
HA→H++A−HA \to {H^ + } + {A^ - }
Let the initial concentration of the acid is CC. Let the degree of dissociation for the acid HAHA be α\alpha . Then the progress of the dissociation can be shown as
HA→H++A−HA \to {H^ + } + {A^ - }
CC 00 00 (At the beginning)
C−CαC - C\alpha CαC\alpha CαC\alpha
In this case, the concentration of acid given is0.1M0.1M,i.e. C=0.1MC = 0.1M.
The degree of dissociation is 0.001%0.001\% , i.e. α = 0.001% =0.001100=1×10−5\alpha {\text{ }} = {\text{ }}0.001\% {\text{ }} = \dfrac{{0.001}}{{100}} = 1 \times {10^{ - 5}}.
Thus the ionization constant for the acid will be written as
Ka=[H+][A−][HA]{K_a} = \dfrac{{[{H^ + }][{A^ - }]}}{{[HA]}}
Inserting the values of [H+][{H^ + }], [A−][{A^ - }] and [HA][HA] in the equation,
Ka=Cα×CαC−Cα{K_a} = \dfrac{{C\alpha \times C\alpha }}{{C - C\alpha }}
Ka=[1×10−5]×[1×10−5]0.1−[0.1×1×10−5]{K_a} = \dfrac{{[1 \times {{10}^{ - 5}}] \times [1 \times {{10}^{ - 5}}]}}{{0.1 - [0.1 \times 1 \times {{10}^{ - 5}}]}}
Ka=1×10−11{K_a} = 1 \times {10^{ - 11}}.
So the option A is the correct answer, i.e. the ionization constant of the monoprotic acid is 1×10−111 \times {10^{ - 11}} .

Note: Unlike monoprotic acid the acid which can donate more than one proton during the ionization is called a polyprotic acid, i.e. diprotic for two, triprotic for three. In a similar way the monoprotic base is the base which can accept one proton. Normally diprotic acids are stronger than monoprotic acid, for example H2SO4{H_2}S{O_4} is stronger than HClHCl due to the availability of two protons for donation. This in fact is clearer by comparing the pHpHvalues of the respective acids. The pHpH of H2SO4{H_2}S{O_4} (2.75) is lower than pHpH of HClHCl (3.01) for a 1mM1mMsolution. The acid acts as Brønsted acids.