At certain temperature, the ${\mathrm{H}}^{+}$ion concentration of water is $4\times {10}^{-7}\mathrm{M}$ then the value of ${\mathrm{K}}_{\mathrm{w}}$ at the same temperature is

As we know that,

${\mathrm{K}}_{\mathrm{w}}=\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]$

As the water is neutral, and for a neutral solution-

$\left[{\mathrm{H}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]=4\times {10}^{-7}\mathrm{M}$

Therefore,

${\mathrm{K}}_{\mathrm{W}}={\left(4\times {10}^{-7}\right)}^2=16\times {10}^{-14}=1.6\times {10}^{-13}$

Hence the value of $K_{\mathrm{w}}$ will be $1.6\times {10}^{-13}$.

Hence the correct answer (C) $1.6\times {10}^{-13}{\mathrm{M}}^2$