MCQ
Assuming complete ionisation, the $pH$  of $0.1\,M\,HCl,$ is $1$. The molarity of ${H_2}S{O_4}$ with the same $pH$ is
  • $0.05$
  • B
    $0.2$
  • C
    $0.1$
  • D
    $2.0$

Answer

Correct option: A.
$0.05$
a
The correct option is $\mathbf{C} 0.05$ $\mathrm{pH}$ of $0.1 \mathrm{M} \mathrm{HCl}$ is 1 .

$\therefore\left[\mathrm{H}^{+}\right]=0.1 \mathrm{M}$

The acid dissociation reaction of $\mathrm{H}_2 \mathrm{SO}_4$ is :

$\mathrm{H}_2 \mathrm{SO}_4 \rightleftharpoons \mathrm{H}^{+}+\mathrm{HSO}_4^{-} $

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

$\therefore 1 \mathrm{H}_2 \mathrm{SO}_4$ ionizes to give $2 \mathrm{H}^{+}$ions.

$2 \mathrm{MH}^{+} \text {ions }=1 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4 $

$1 \mathrm{MH}^{+} \text {ions }=\frac{1}{2} \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4 $

$0.1 \mathrm{MH}^{+} \text {ions }=\frac{0.1}{2} \mathrm{M} \mathrm{H}_2 \mathrm{SO}$$_4=0.05 \mathrm{M} \mathrm{H}_2 \mathrm{SO}_4$

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