Chemistry: Finding volume for a buffer question

Question

What is the volume (in mL) of glacial acetic acid (15.4 M) that would have to be added to 500 mL of a solution of 0.20 M sodium acetate in order to achieve a pH of 5.00? (Ka = 1.74 x10-5)

Answer 1

For this type of problem, you can generally use the Henderson Hasselbalch equation:

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

pH = 5.00

pKa = -log Ka = -log 1.74x10^-5 = 4.76

log [salt]/[acid] = ?

0.2 mol/L x 0.5 L = 0.1 moles of salt (NaAc) present, so we need to solve for log (0.1/x)

5.00 = 4.76 + log (0.1/x)

log (0.1/x) = 0.24

0.1/x = 1.74

x = 0.057 moles acid need to be added

To find the volume of 15.4 M acetic acid...

15.4 mole/L (x L) = 0.057 moles

x = 0.00370 L = 3.7 mls of acetic acid need to be added (this assumes we neglect the small change in volume from 500 mls to 503.7 mls)