Lactic acid has a pK_a of 3.08. What is the approximate degree of dissociation of a 0.35 M solution of lactic acid?

Question

Quizplus · Accepted Answer

Using the Henderson-Hasselbalch equation:

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

We can rearrange and solve for [A-]/[HA]:

[A-]/[HA] = 10^(pKa - pH)

At the halfway point of dissociation (when [A-] = [HA]), the ratio [A-]/[HA] = 1, so:

1 = 10^(pKa - pH)

pKa - pH = log(1) = 0

pH = pKa = 3.08

At pH 3.08, half of the lactic acid molecules will dissociate, so the degree of dissociation (alpha) is 0.5 or 50%.

However, the question asks for the approximate degree of dissociation of a 0.35 M solution of lactic acid, not at pH 3.08 specifically. We can use the approximation that when pH is within 1 unit of pKa, the degree of dissociation will be about 10% of the initial concentration.

Our solution is 0.35 M, so if alpha is about 10%, then [H+] = [A-] = 0.035 M and [HA] = 0.315 M. We can check our assumption by calculating the pH using the Henderson-Hasselbalch equation:

pH = pKa + log([A-]/[HA]) = 3.08 + log(0.035/0.315) = 2.52

Since pH is within 1 unit of pKa, our approximation is valid, and the answer is approximately 4.8% (10% of 0.35). Therefore, the best choice is C.

Lactic Acid Has a PKa of 3

Lactic Acid Has a PK_a of 3