Topic 8.5 Acid-Base Titrations: interpret titration curves to find the equivalence point and pH at key points, and use the half-equivalence point to find pKa for a weak acid.

What this topic is asking

The College Board (Topic 8.5) wants you to interpret titration curves to find the equivalence point and the pH at key points, and to use the half-equivalence point to find the pKa of a weak acid. This builds on the basic titration of Unit 4 with the pH detail that the acids-and-bases unit demands.

Reading the titration curve

The equivalence point is found from the volume at the midpoint of the steep jump. The shape of the curve depends on the strengths of the acid and base: strong-strong titrations have a long, sharp jump centered at pH 7; titrations involving a weak species have a shorter jump centered above or below 7.

pH at the equivalence point

So the equivalence point is not always at pH 7; only the strong-strong case is neutral. For a weak acid titrated with strong base, the solution at equivalence is a solution of the conjugate base $\text{A}^-$, which makes it basic. This is a frequent exam discriminator.

The buffer region and the half-equivalence point

Before the equivalence point in a weak-acid titration, both the weak acid and its conjugate base are present, so the solution is a buffer and the curve rises only gently (the buffer region). At the half-equivalence point, exactly half the weak acid has been converted to conjugate base, so $[\text{HA}] = [\text{A}^-]$. By the Henderson-Hasselbalch equation (Topic 8.7), $\text{pH} = \text{p}K_a$ when these are equal, so the pH at the half-equivalence point directly gives the $\text{p}K_a$ of the acid. Reading $\text{p}K_a$ off the curve this way is a classic AP task.

Choosing an indicator

An indicator is a weak acid or base whose two forms have different colors; it changes color over a small pH range near its own $\text{p}K_a$. You choose an indicator whose color-change range brackets the pH at the equivalence point of the titration, so the endpoint (the observed color change) closely matches the equivalence point.

Try this

Q1. A strong acid is titrated with a strong base. State the pH at the equivalence point. [1 point]

• Cue. pH $= 7$ (the salt is neutral).

Q2. At the half-equivalence point of a weak-acid titration the pH is 5.0. State the $\text{p}K_a$ of the acid. [1 point]

• Cue. $\text{p}K_a = 5.0$, because $[\text{HA}] = [\text{A}^-]$ there.