Titration of a Weak Acid with a Late Endpoint
A student titrates 25.0 mL of an unknown weak monoprotic acid with 0.100 M sodium hydroxide. The burette reads 0.50 mL initially. Phenolphthalein turns faint pink at 24.10 mL, but the student continues adding base to 24.90 mL because the pink 'looked too faint to count.' The student uses the final reading to calculate the acid concentration. A second student uses bromothymol blue, sees a color change near pH 7, and reports a different concentration. The teacher confirms that the true equivalence point is at the first persistent pink, where the pH is about 8.8, and that the pH at half-equivalence is 4.2. The class must decide which volume and indicator choice are defensible and how to calculate Ka.
1. Calculate the acid concentration using the correct equivalence volume. Then explain why the student's use of 24.90 mL gives a concentration that is too high or too low, and by what approximate percent.
Read the worked answer
The correct volume of NaOH delivered at the first persistent pink is 24.10 mL - 0.50 mL = 23.60 mL, or 0.02360 L. Moles NaOH = 0.02360 L x 0.100 mol/L = 0.002360 mol. Because the acid is monoprotic and reacts 1:1 with NaOH, moles acid = 0.002360 mol. Concentration = 0.002360 mol / 0.0250 L = 0.0944 M.
Using the final reading gives 24.90 mL - 0.50 mL = 24.40 mL, or 0.02440 L. Moles NaOH = 0.002440 mol, so the reported concentration would be 0.002440 / 0.0250 = 0.0976 M. This is too high. The percent error relative to the correct value is (0.0976 - 0.0944)/0.0944 x 100 = about 3.4 percent. The extra base was added past the equivalence point, so it did not react with additional acid; it only changed the indicator and pH. The calculation must use the volume at the stoichiometric point, not the volume at which the student decided the color was dark enough.
2. Explain the difference between endpoint and equivalence point, and evaluate phenolphthalein versus bromothymol blue for this titration.
Read the worked answer
The equivalence point is the stoichiometric point at which moles of added base equal moles of acid. The endpoint is the observed signal, usually a color change, that the chemist uses to estimate the equivalence point. A good indicator changes color over a pH range that closely brackets the pH at the equivalence point.
For a weak monoprotic acid titrated with strong base, the equivalence point is basic because the conjugate base hydrolyzes. Here the teacher gives pH about 8.8 at equivalence. Phenolphthalein changes from colorless to pink over roughly pH 8.2 to 10.0, so its first persistent pink is a reasonable endpoint. Bromothymol blue changes over roughly pH 6.0 to 7.6, which is in the buffer region before equivalence. A color change there would be early, giving a smaller NaOH volume and a lower calculated acid concentration. That explains the second student's different result. The indicator choice should be justified by the equivalence-point pH, not by convenience or by how intense the color looks.
3. Use the half-equivalence pH to calculate Ka for the acid. Explain why the half-equivalence point is useful and what assumption is required.
Read the worked answer
At half-equivalence, half of the weak acid has been converted to its conjugate base, so [HA] is approximately equal to [A-]. The Henderson-Hasselbalch equation gives pH = pKa + log([A-]/[HA]). When the ratio is about 1, log(1) = 0, so pH = pKa. The given half-equivalence pH is 4.2, so pKa = 4.2 and Ka = 10^-4.2 = 6.3 x 10^-5.
The half-equivalence point is useful because it gives pKa directly from a pH measurement without knowing the acid concentration. The main assumption is that the equilibrium concentrations of HA and A- are approximately equal at that point. This requires the acid to be weak enough that its own dissociation is small compared with the amount converted by added base, and it requires activity effects to be negligible. The volume increase from added NaOH dilutes both species, but because both are diluted in the same solution, their ratio remains approximately 1 at half-equivalence.