# How do you find pOH given pH?

May 9, 2016

$p O H = 14 - p H$

#### Explanation:

To find the $p O H$ from the given $p H$ you can simply use the following relationship:

$p O H = 14 - p H$

This relationship is derived from the expression of the water dissociation constant ${K}_{w}$, where,

${K}_{w} = \left[{H}^{+}\right] \left[O {H}^{-}\right] = 1.0 \times {10}^{- 14}$

Taking the $- \log$ of both parties we get:

$- \log {K}_{w} = - \log \left[{H}^{+}\right] - \log \left[O {H}^{-}\right] = 14$

Therefore, $p H + p O H = 14 \implies p O H = 14 - p H$

remember, $p H = - \log \left[{H}^{+}\right]$ and $p O H = - \log \left[O {H}^{-}\right]$