Question

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

Answer 1

$\begin{array}{cccc}HA\rightleftharpoons & H^{+}+& A^{-}& \\ C_1(1-{\alpha }_1)& C_1{\alpha }_1& C_1{\alpha }_1& \end{array}$

$K_{a_1}=\frac{(C_1{\alpha }_1{)}^2}{C_1(1-\alpha )}$

Since the degree of dissociation is negligible, $\alpha <<<1,1-\alpha \approx 1$
$\therefore K_{a_1}=C_1{\alpha }_1^2$

Again,
$\begin{array}{cccc}HB\rightleftharpoons & H^{+}+& B^{-}& \\ C_2(1-{\alpha }_2)& C_2{\alpha }_2& C_2{\alpha }_2& \end{array}$

Here, $K_{a_2}=C_2{\alpha }_2^2$
$\therefore \frac{{\alpha }_1}{{\alpha }_2}=\sqrt{\frac{K_{a_1}}{C_1}\times \frac{C_2}{K_{a_2}}}=\sqrt{\frac{K_{a_1}}{K_{a_2}}}$
{as $C_1=C_2$ }
$=\sqrt{\frac{4\times {10}^{-6}}{2.5\times {10}^{-9}}}=\sqrt{1600}=40$
$\therefore \frac{{\alpha }_1}{{\alpha }_2}=40$

Hence, HA is $40$ times stronger than $HB$.