Question

The unit of ionic product of water $\left(K_w\right)$ is:

• A. $mol{L}^{-1}$
• B. $mo{l}^2{L}^{-2}$
• C. $Lmo{l}^{-1}$
• D. $mo{l}^{-2}{L}^2$

Answer 1

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

Ionic Product of water:
$H_{2}O\left(l\right)+H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}(aq.)+O{H}^{-}(aq.)$ or $H_{2}O\left(l\right)\rightleftharpoons H_3{O}^{+}\left(aq\right)+O{H}^{-}\left(aq\right)$.
As per laws of mass action : $K_c=\frac{\left[H^{+}\right]\left[O{H}^{-}\right]}{\left[H_{2}O\right]}{K}_c\times \left[H_{2}O\right]=K_w=\left[H^{+}\right]\left[O{H}^{-}\right]$
We can see that units of $K_w$ are equal to units of $\left[H^{+}\right]\times \left[O{H}^{-}\right]$
Units of $\left[H^{+}\right]=\left[O{H}^{-}\right]=mol{L}^{-1}\therefore K_w=(mol{L}^{-1}{)}^2=mo{l}^2{L}^{-2}$