Question

Selenious acid $\left(H_{2}Se{O}_3\right)$, a diprotic acid has $K_{a_1}=3.0\times {10}^{-3}$ and $K_{a_2}=5.0\times {10}^{-8}$. What is the $\left[O{H}^{-}\right]$ of a $0.30M$ solution of a seleniuos acid?

• A. $2.85\times {10}^{-3}$
• B. $5.0\times {10}^{-6}$
• C. $3.5\times {10}^{-12}$
• D. $3.5\times {10}^{-13}$

Answer 1

Answer: (D)

$3.5\times {10}^{-13}$

Here also, ${Ka}_2<<<{Ka}_1$ so second ionisation can be neglected

$\therefore H_2{SeO}_3\rightleftharpoons HSe{O}_3^{-}+H^{+}$

initial $(0.03\times 10)$ $-$ $-$

at eqbm $(10\times 0.03)-x$

or Since $(10\times 0.03)-x\approx (0.03\times 10)$ since $x$ is very small

$\therefore {Ka}_1=3\times {10}^{-3}=\frac{x^2}{(0.03\times 10)}$

or $x=\sqrt{9\times {10}^{-4}}=3\times {10}^{-2}$

$\therefore \left[{OH}^{-}\right]=\frac{{10}^{-14}}{\left[H^{+}\right]}=3.3\times {10}^{-13}\approx 3.5\times {10}^{-13}$