The $\mathrm{pH}$ of $0.01\mathrm{M}$ solution of acetic acid is 5.0. What are the values of $\left[{\mathrm{H}}^{+}\right]$ and ${\mathrm{K}}_{\mathrm{a}}$ respectively?

It is given to find the values of $\left[{\mathrm{H}}^{+}\right]$ and ${\mathrm{K}}_{\mathrm{a}}$ respectively.

$PH=-\log \left[H^{+}\right]$

$5·0=-\log \left[H^{+}\right]$

$\left[H^{+}\right]=1\times {10}^{-5}\mathrm{M}$

$PH=-\log \left(\sqrt{K_a\times C}\right)$

$PH=-\log \left(\sqrt{K_a\times 0.01}\right)$

$5.0=-\log \left(\sqrt{K_a\times 0.01}\right)$

$K_a=1\times {10}^{-8}$

Hence the correct answer (C) $1\times {10}^{-5}\mathrm{M},1\times {10}^{-8}$