D39.2 Titration Curves

Titration is effective in quantitatively analyzing a solution’s acid (or base) concentration because pH changes rapidly near the equivalence point. In other words, there is a large observable change accompanying a small addition of titrant, which minimizes experimental uncertainty. For example, an acid-base indicator generally changes color over a range of about 2 pH units, so if pH increases (or decreases) by 2 or more pH units when 0.01 mL of titrant is added at the equivalence point, the color change would effectively signal the end point of the titration.

The figure below shows a titration curve, a graph of pH as a function of volume of titrant, for the titration of a 50.00-mL sample of 0.100-M hydrochloric acid with 0.100-M sodium hydroxide.

Now consider the titration of 50.00 mL of 0.100-M acetic acid (a weak acid) with 0.100-M sodium hydroxide (Figure: Titration curve (acetic acid and NaOH)). Comparing this titration curve to that of Figure: Titration curve (HCl and NaOH), we see that although the initial volumes and concentrations of the acids (acetic acid vs. HCl) are the same, the pH for acetic acid begins at a higher value and the titration curve maintains higher pH values up to the equivalence point. This is because, unlike HCl, acetic acid is only partially ionized.

The pH at the equivalence point is also higher (8.72 rather than 7.00) due to the presence of acetate anion, a weak base that raises the pH via the reaction:

After the equivalence point, the two titration curves are identical because the pH depends on the excess hydroxide ion from NaOH added in both cases.

The midpoint of a titration is when half the volume of titrant needed to reach the equivalence point has been added. As part (b) in the above exercise shows, when titrating a weak acid with a strong base, the pH of the solution equals the pK_a of the weak acid at the midpoint because we have added half the amount of strong base needed to react with all the weak acid. Therefore, the solution is a buffer and according to the Henderson-Hasselbalch equation: