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QUESTION

# What does pH measure?

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

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.