Question

At certain temperature the $H^{+}$ ion concentration of $H_{2}O$ is $4\times {10}^{-7}M$, then the value of $K_w$ at the same temperature will be:

• A. ${10}^{-14}M$
• B. $4\times {10}^{-14}M$
• C. $1.6\times {10}^{-13}M$
• D. $4\times {10}^{-7}M$

Answer 1

The correct option is C $1.6\times {10}^{-13}M$

Solution:- (C) $1.6\times {10}^{-13}$

As we know that,

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

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

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

Therefore,

$K_w={(4\times {10}^{-7})}^2=16\times {10}^{-14}=1.6\times {10}^{-13}$

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