In a titration of a weak acid, the end point was reached after adding 16.2 mL of base. Calculations showed that the equivalence point was reached after adding 15.6 mL of base.

How many mL of base was required to reach the point at which pH = pKa?

Question

In a titration of a weak acid, the end point was reached after adding 16.2 mL of base. Calculations showed that the equivalence point was reached after adding 15.6 mL of base.

How many mL of base was required to reach the point at which pH = pKa?

BlackTom AI · Accepted Answer

To locate the pH = pKa point in a titration of a weak acid with strong base, recall the half-equivalence principle: at the half-neutralization point, the amount of base added equals half of the amount needed to reach the equivalence point, and the pH equals the pKa of the weak acid.

Option 1: 16.2 mL. This volume corresponds to the endpoint and, for a weak acid–strong base titration, is not the half-equivalence point. Therefore, it does not give pH = pKa.

Option 2: 7.80 mL. Since the equivalence point occurs at 15.6 mL of base, half of that volume is 15.6 ÷ 2 = 7.8 mL. This is exactly the volume where the solution has equal moles of acid and its conjugate base, yielding pH = pKa by the Henderson–Hasselbalch framework.

Option 3: 8.10 mL. This value is slightly more than the half-equivalence volume. At any volume greater than half the equivalence volume, the pH would be higher than pKa, so this option does not satisfy pH = pKa.

Option 4: 15.6 mL. This is the equivalence point volume, where stoichiometric amounts have been mixed. At equivalence for a weak acid, the pH is typically > 7 and not equal to pKa. Hence this is not the pH = pKa point.

In summary, the only choice that aligns with pH = pKa for a weak acid titrated with a strong base is the half-equivalence volume, which is 7.80 mL. The other options correspond to the endpoint, a point slightly past half-equivalence, or the equivalence point, none of which satisfies pH = pKa.

CHEM 110 Lecture Quiz Week 10

In a titration of a weak acid, the end point was reached after adding 16.2 mL of base. Calculations showed that the equivalence point was reached after adding 15.6 mL of base. How many mL of base was required to reach the point at which pH = pKa?

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