The purpose of Titrations
Acids and bases are two substances, which, when mixed in aqueous solution, react to produce water and a salt. When you titrate a strong acid, such as hydrochloric, HCL, with a strong base such as sodium hydroxide, NaOH, the H+ and the OH- form H2O and the Na+ and the Cl- remain in solution as aqueous NaCl. A titration involves mixing an equal number of moles of acid with base. Generally in a titration, you'll have an acid in a flask, an indicator that changes pH somewhere around the neutral point for that particular acid and base (for a strong acid and a strong base, you'll need an indicator that changes somewhere around pH 7). Then you start adding the base to the acid. At the equivalence point, defined as the point where the moles of base are equal to the moles of acid, the indicator changes color. The place where the color changes is called the end point, and that is usually very close to the equivalence point. From this titration, you can tell the molarity of the base or the molarity of the acid if you know one or the other. This is the purpose of a titration.
What Happens - Strong Acid, Strong Base
In a titration, when you begin adding the base to the acid, the pH doesn't rise very much. It might start out around 1 if you're working with .1 molar HCl. As you titrate it, the pH will rise just slightly. Near the equivalence point, the pH will begin to rise more rapidly, lets say from 1 to 2 to 3. As you go through the equivalence point, the pH will change dramatically, say from 2 up to 12. With a very small difference in the amount of added base, the pH changes and causes the indicator to change color. After you go through the equivalence point, the pH levels off then again, at 11 or 12 or 13 depending on the concentration of the base that you're adding.
Weak Acid, Strong Base
When you titrate a weak acid, such as acetic acid, CH3COOH, with a strong base, the pH starts off a little higher, as the weak acid doesn't dissociate as much as the strong acid. The pH rises gradually, starting at 2 or 3, and then might rise to 5. When you get near the equivalence point, the pH changes rapidly from 5 up to 11 or 12 or 13 depending on how strong the base is that you're using. Thus the pH break at the endpoint, rather than being from 2 to 12, is from 5 to 12, and there's less of a dramatic change in the pH. It's still a significant change, but it's not as drastic as with the strong acid. These differences can be seen on titration curves.
Interesting things happen in the titration of a weak acid with a strong base. The Ka expression for the titration of weak acetic acid would be
Ka = ( [H3O+] [CH3COO-] ) / ( [CH3COOH] )
At the midpoint of the titration, half of the acid has been titrated and turned into A-. Therefore, in the Ka expression, the acid concentration which is in the denominator of Ka, and the acetate concentration which is in the numerator, cancel each other out and you're left with Ka = [H+]. Another way to say that would be pK = pH at the midpoint of the titration. pK is defined as the opposite of the log of the equilibrium constant for that acid. So at the midpoint of the titration, the pK = pH.
pK = _ log [Ka]
Strong Acid, Weak Base
Now, for the titration of a weak base with a strong acid, the case is just reversed. Your pH, if you add a weak base and you're titrating a strong acid, will drop gradually, say from 11 down to 8 or 9. At the endpoint, the pH would be around 4 or 5 rather than 7, because the endpoint is going to be on the acid side of the scale, considering the fact that the acid is stronger than the base.