# Why will a strong acid neutralize as much base as a weak acid?

This is a simple concept that I can't seem to understand. Why will a strong acid neutralize as much base as a weak acid, if the acids are of the same volume and concentration? A strong acid will dissociate more in solution and thus have a greater number of $\ce{H^+}$ ions, as far as my understanding goes. The opposite if true for the weak base. So wouldn't the strong acid neutralize more base than the weak acid, because it has more $\ce{H^+}$ ions to neutralize the $\ce{OH^-}$ ions of the base with?

Strong acid is dissociated all but completely: you have a certain amount of $\ce H^+$ and start neutralizing them, one drop at a time. As you do so, their numbers steadily decrease. It feels like sawing a huge log with a hand saw: you see the amount of job, and you do it until it is all done.
Weak acid is dissociated only partially. You see a relatively small amount of $\ce H^+$, but as you start neutralizing them, more molecules of acid get dissociated and their $\ce H^+$ ions stand in place of those you've neutralized. It feels like sawing a thin log, but a peculiar one: it seems to regenerate under the saw.
So at the end of the day, it is the sheer amount of acid that matters, rather than immediate concentration of $\ce H^+$.