Question

The solubility of a salt of weak acid $\left(AB\right)$ at $pH$ $=3$ is $Y$$\times {10}^{-3}$ $mol$ $L^{-1}$. The value of $Y$ is _________.
(Given that the value of solubility product of $AB$ $\left(K_{sp}\right)=2\times {10}^{-10}$ and the value of ionization constant of $HB$ $\left(K_a\right)=1\times {10}^{-8})$

Answer 1

Given that,

$pH=3\Rightarrow \left[H^{+}\right]={10}^{-3}M$

Now,

Solubility, $S=\sqrt{K_{sp}\left(\frac{\left[H^{+}\right]}{K_a}+1\right)}$

$S=\sqrt{2\times {10}^{-10}\left(\frac{{10}^{-3}}{{10}^{-8}}+1\right)}$

$S=\sqrt{2\times {10}^{-5}}$

$S=4.47\times {10}^{-3}$ M.