Question

The acidic strength of two monobasic acids may be compared by comparing the hydronium ion concentrations of their aqueous solution of same molar concentration. The dissociation constants of acids HA and HB are $4\times {10}^{-6}\text{and}2.5\times {10}^9$, respectively. How many times HA is stronger than HB? Assume that for both the acids, the degree of dissociation at the concentration taken, is negligible.

Answer 1

$\left(Ka{)}_1\right(forHA)=4\times {10}^{-6}$

$\left(Ka{)}_2\right(forHB)=2.5\times {10}^9$

Let $m$ is the same concentration of both

$[H^{+}{]}_1=\sqrt{k{a}_1\times m}$

$=\sqrt{m\times 4\times {10}^{-6}}$

$[H^{+}{]}_2=\sqrt{m\times 2.5\times {10}^9}$

$\frac{[H^{+}{]}_1}{[H^{+}{]}_2}=\frac{\sqrt{m\times 4\times {10}^{-6}}}{m\times 2.5\times {10}^9}$

$\Rightarrow \frac{4\times {10}^{-3}}{{10}^3}=4\times {10}^{-8}$