Calculate the pKa of HA

Question

A buffer is prepared by adding 25 mL of 0.10 M HA ( a weak acid) to 15 mL of 0.10 M NaA (the salt of its conjugate base). The measured pH of the buffer is 3.48. Calculate the pK_a of HA. (Hint: Use the volumes of the buffer components in place of concentrations.)

Answer 1

For many buffer problems, we can use the Henderson Hasselbalch equation:

pH = pKa + log [salt] / [acid]

pH = 3.48

pKa = ?

[salt] / [acid] = [A^-] / [ HA]

The "hint" in the problem tells us to use volumes of the components in place of concentrations, in which case the ratio of [A^-] / [ HA] will be 15 ml / 25 ml (please note that this will only work when the concentrations of the two are the same, i.e. 0.10 M).

Solving the HH equation for pKa, we have ...

3.48 = pKa + log (15 / 25)

3.48 = pKa + log 0.6

3.48 = pKa + (-0.22)

pKa = 3.70