Question

What are the pH and pOH scales?

Answer 1

These are logarithmic scales which measure the concentrations of the acidium ions, `[H_3O^+]`, and hydroxide ions `[HO^-]` in water.

Explanation:

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

`2H_2O(l) rightleftharpoons H_3O^+ + HO^-`

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

`K'_w=([H_3O^+][HO^-])/([H_2O(l)])`

Now because `[H_2O]` is effectively a constant, so this can be included on the left had side of the equation,

`K_w=[H_3O^+][HO^-]` `=` `10^-14` at `298*K`

We can take `log_(10)` of both sides to get:

`log_(10)K_w=log_(10)[H_3O^+] + log_(10)[HO^-]`

OR,

`-log_(10)K_w=-log_(10)[H_3O^+] - log_(10)[HO^-]`

But by definition, `- log_(10)[HO^-]=pOH`, and `- log_(10)[H_3O^+]=pH`, and `-log_(10)K_w=-log_10(10^-14)=14`.

Thus `pH + pOH =14`

This equation tells us that in acid solutions, `pH` is low, and in alkaline solutions, `pOH` is low, but the equilibrium relationship between `H_3O^+` and `HO^-` is maintained.