Investigation 14: Acid-Base Titration Curves
A titration curve plots pH against volume of titrant added, and it holds more information than any color-change indicator: the acid's concentration from the equivalence point, and its identity (Ka) from the half-equivalence point.
An indicator only tells you when a reaction is roughly done. A pH probe records the whole story as you add base to acid, drop by drop, giving you a continuous curve instead of one color flip. That curve has two landmarks worth memorizing. The equivalence point is where moles of acid equal moles of base added; it is the steepest part of the curve, where pH rises fastest for the smallest addition of titrant. The half-equivalence point is halfway to that volume, where only half the original acid has been neutralized, leaving equal concentrations of the acid and its conjugate base.
At half-equivalence, [HA] = [A-], so the Henderson-Hasselbalch equation collapses to pH = pKa. Read the pH at that point straight off the curve, and Ka = 10−pH. That single number identifies the acid, since every weak acid has its own characteristic Ka. The equivalence point itself tells you concentration: moles of acid originally present equal moles of base delivered by that volume, so starting molarity falls out from volume and known base concentration.
Finding the equivalence point precisely means finding the steepest slope, and the cleanest way to do that is to graph the first derivative, dpH/dVolume, against volume. The derivative curve peaks sharply right at the equivalence point, because that is where pH is changing fastest per drop of titrant. This connects titration directly to the error-analysis and graphing practices used across the lab units: derivative peaks are sensitive to data spacing, so smooth, closely spaced data points near equivalence matter for locating that peak accurately.
Key terms
- Equivalence point
- The volume of titrant where moles of added base exactly equal moles of acid originally present.
- Half-equivalence point
- The point where half the acid has reacted, so [HA] equals [A-] and pH equals pKa.
- Ka
- The acid dissociation constant, a measure of how strongly a weak acid ionizes in water.
- Hydrolysis of conjugate base
- The reaction of the leftover conjugate base with water, which raises pH above 7 at equivalence for weak acids.
- First derivative curve
- A plot of dpH/dVolume versus volume, whose sharp peak marks the equivalence point precisely.
Watch it explained
- How it worksHow do you extract both the concentration and the identity of an unknown acid from one curve?
- Worked exampleFind the Ka of an unknown acid from a curve whose half-equivalence point sits at pH 4.76.
- Worked exampleGraph the first derivative of a titration curve and explain why the peak locates the equivalence point.
- Common mistakeWhy isn't the steepest point of the curve at the same pH for every acid?
Check yourself
End of topic.