Why does the pH drop rapidly when an acid-base titration reaches equivalence point?
The weaker the acid or base is the more gradual the titration curve will look. You can see this if you compare the titration curve of acetic acid to that for hydrochloric acid. Acetic acid has a much more gradual curve. When you are at the equivalence point the pH is about 7 (depending on the acid/base), which means the hydronium ion concentration is 10^-7. If you add an acid or base it will move away from that concentration by orders of magnitude, which causes the sharp up or down (depending what is being tritrated). After a few drops have been added in the titration the curve levels out because you are only doubling or adding to the ion concentration at the same magnitude instead of changing the order of magnitude. In other words, after the equivalence point is reached, when you add a drop the pH would change from 10^-7 to 10^-6 (if titrating with an acid) or 10^-8 (if titrating with a base. This is a factor of 10 change, and the curve is steep. But later on if you add another few dr