Question

The unit of ionic product of water $K_w$ is:

• A. $Mo{l}^{-1}{L}^{-1}$
• B. $Mo{l}^2{L}^{-2}$
• C. $Mo{l}^{-2}{L}^{-1}$
• D. $Mo{l}^2{L}^2$

Answer 1

The correct option is B $Mo{l}^2{L}^{-2}$

$H_{2}O\rightleftharpoons H^{\oplus }+O{H}^{⊝}$

$K_{eq}=\frac{\left[H^{+}\right]\left[O{H}^{-}\right]}{\left[H_{2}O\right]}=\left[H^{+}\right]\left[O{H}^{-}\right];[\because [H_{2}O]=1]$

$\Rightarrow (1.0\times {10}^{-16}M)\left(55.5M\right)=1.0\times {10}^{-14}{M}^2$

This $M$ is concentration so it is in $M/L$ so, $1.0\times {10}^{-14}(M/L{)}^2\Rightarrow 1.0\times {10}^{-14}{M}^2/L^2$