What happens when you mix a strong acid with a strong base?

When a strong acid and a strong base mix, all acidic protons will react with every basic molecule until one or the other runs out. The curve for a titration of a strong acid with a strong base will change slowly at first, and dramatically when the equivalence point (where the number of moles of acid is equal to the number of moles of base) is reached. The reaction, like all acid-base reactions, is fast.