Question

What are the concentrations of $H^{+},HS{O}_4^{-},S{O}_4^{2-}$ and $H_{2}S{O}_4$ in a $0.20$M solution of sulphuric acid?
Given: $H_{2}S{O}_4\to H^{+}+HS{O}_4^{-}$; strong
$HS{O}_4^{-}\rightleftharpoons S{O}_4^{2-};K_2={10}^{-2}$M.

Answer 1

$H_2{SO}_4⟶H^{+}+H{SO}_4^{(-)}$ (Strong dissociation)

${HSO}_4^{-}\rightleftharpoons H^{+}+{SO}_4^{2-}$

$K_a=\frac{\left[H^{+}\right]\left[{SO}_4^{2-}\right]}{\left[{HSO}_4^{-}\right]}=\frac{x^2}{0.2-x}$

$\Rightarrow \frac{x^2}{0.2-x}={10}^{-2}$

$\Rightarrow x^2+{10}^{-2}x-{10}^{-2}\times 0.2=0$

$\therefore$ $x=\frac{-{10}^{-2}+\sqrt{{\left({10}^{-2}\right)}^2+\mathrm{4.1.}{10}^{-2}\times 0.2}}{2}=0.04$

$\therefore$ $\left[H^{+}\right]=\left[{SO}_4^{2-}\right]=0.04M$

$\therefore$ $\left[{HSO}_4^{-}\right]=0.2-0.04=0.16M$