Lactic acid, which is found in milk products, has a pK_a of 3.85. A 50.0 mL solution of 0.05 M lactic acid is titrated with 0.025 M sodium hydroxide. What is the pH of the solution after 64.0 mL of the sodium hydroxide has been added?

Question

Quizplus · Accepted Answer

We can use the Henderson-Hasselbalch equation to calculate the pH at any point of the titration:

pH = pKa + log([A-]/[HA])

Where pKa is the dissociation constant of the acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the acid.

At the start of the titration, only lactic acid is present, so [HA] = 0.05 M and [A-] = 0.

At the equivalence point, all lactic acid has been neutralized, so [HA] = 0 and [A-] = 0.025 M.

At the point where 64.0 mL of 0.025 M NaOH has been added, we know that 32.0 mL of NaOH are required to reach the equivalence point. Therefore, we have added half the amount of NaOH required to neutralize all acid. This means we have converted half of the lactic acid into lactate, so:

[HA] = 0.05/2 = 0.025 M
[A-] = 0.025 M

Plugging in these values into the Henderson-Hasselbalch equation:

pH = 3.85 + log(0.025/0.025) = 3.85

Therefore, the pH of the solution after 64.0 mL of NaOH has been added is 3.85. The closest option to this value is D) 4.10, which is the correct answer.

Lactic Acid, Which Is Found in Milk Products, Has a PKa

Lactic Acid, Which Is Found in Milk Products, Has a PK_a