At some high temperature, $K_w$ of water is ${10}^{–13}$. Then the pH of the water at the same temperature is ________.

 It is given to find out the pH of the water at the same temperature.

$K_w=\left[H^{+}\right]\left[O{H}^{-}\right]$

Explanation: $K_w=\left[H^{+}\right]\left[O{H}^{-}\right]$

Since $\left[H^{+}\right]=\left[O{H}^{-}\right]$

 therefore, $K_w=[H^{+}{]}^2$

$\sqrt{{10}^{–13}}$ = $\left[H^{+}\right]$

$\left[H^{+}\right]$ = $3.16\times {10}^{-7}$

pH =$-log\left[H^{+}\right]$ = $-\log$[$3.16\times {10}^{-7}$] = 6.5

Hence, the answer is 6.5.