# What are the pH and pOH scales?

May 13, 2016

These are logarithmic scales which measure the concentrations of the acidium ions, $\left[{H}_{3} {O}^{+}\right]$, and hydroxide ions $\left[H {O}^{-}\right]$ in water.

#### Explanation:

Water is known to undergo an autoprotolysis reaction as shown, and this has been accurately measured under standard conditions.

$2 {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + H {O}^{-}$

As for any equilibrium, we can write the equilibrium expression:

$K {'}_{w} = \frac{\left[{H}_{3} {O}^{+}\right] \left[H {O}^{-}\right]}{\left[{H}_{2} O \left(l\right)\right]}$

Now because $\left[{H}_{2} O\right]$ is effectively a constant, so this can be included on the left had side of the equation,

${K}_{w} = \left[{H}_{3} {O}^{+}\right] \left[H {O}^{-}\right]$ $=$ ${10}^{-} 14$ at $298 \cdot K$

We can take ${\log}_{10}$ of both sides to get:

${\log}_{10} {K}_{w} = {\log}_{10} \left[{H}_{3} {O}^{+}\right] + {\log}_{10} \left[H {O}^{-}\right]$

OR,

$- {\log}_{10} {K}_{w} = - {\log}_{10} \left[{H}_{3} {O}^{+}\right] - {\log}_{10} \left[H {O}^{-}\right]$

But by definition, $- {\log}_{10} \left[H {O}^{-}\right] = p O H$, and $- {\log}_{10} \left[{H}_{3} {O}^{+}\right] = p H$, and $- {\log}_{10} {K}_{w} = - {\log}_{10} \left({10}^{-} 14\right) = 14$.

Thus $p H + p O H = 14$

This equation tells us that in acid solutions, $p H$ is low, and in alkaline solutions, $p O H$ is low, but the equilibrium relationship between ${H}_{3} {O}^{+}$ and $H {O}^{-}$ is maintained.