Question

Are pH and pOH related to each other?

Answer 1

Absolutely! In water:

`pH + pOH = 14`

Explanation:

We know that water undergoes autoprotolysis:

`2H_2O rightleftharpoons H_3O^+ + HO^-`

This is an equilibrium reaction, measured precisely over a range of temperatures. It is a fact that at `298K`,

`[H_3O^+][HO^-]` `=` `10^(-14)` (`[H_2O]` is treated as a constant!). Now this is a mathematical equation, which I can manipulate, as long as I do the same thing to both sides.

Taking `log_10` of both sides:

`log_10[H_3O^+] + log_10[HO^-]` `=` `-14`

On rearrangement,

`14` `=` `-log_10[H_3O^+] - log_10[HO^-]`

But by definition, `-log_10[H_3O^+] = pH`, and `log_10[HO^-] =pOH`.

So `pH + pOH = 14`