Question

What does pH measure?

Answer 1

`pH` is a quantitative measure of the concentration of hydronium ion, `H_3O^+` in aqueous solution.

Explanation:

Water is known to undergo autoprotolysis according to the following reaction:

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

This equilibrium has been exhaustively studied and we write the equilibrium in the normal way,

`K_"eq"=([H_3O^+][HO^-])/([H_2O])`

Because `[H_2O]` is LARGE, it can be assumed to be constant, and removed from the expression to give:

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

A temperature is specified, because the extent of reaction depends upon temperature, especially for a bond-breaking reaction. Now this is a mathematical expression, the which we can divide, multiply etc., provided that we do it to BOTH sides of the expression. One think we can do is to take `log_10` of both sides for reasons that will become apparent later:

`log_10K_w=log_10{[H_3O^+][HO^-]}=log_10{10^-14}`

And thus, `log_10[H_3O^+]+log_10[HO^-]=log_10{10^-14}`

But `log_10{10^-14}=-14` by definition, and we can rearrange the given expression to give:

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

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

So for water at `298K`, `pH+pOH=14`. This is the defining expression for acid base behaviour in water, and it is one with which you will get very familiar.

So to answer your question (finally!), `pH` is a quantitative measure of the concentration of `H_3O^+` (in water).

I apologize for going on so long, but you will need the given background if you don't know it already.