What will be pH of a 100 mL buffer solution containing 0.064 M of acetic acid and 0.036 M of sodium acetate, after addition of 1 millimole of the hydrochloric acid? pKa=4.75.
Simplest approach to such a question is to assume added acid reacts with acetate ions protonating them - qualitatively - to the acetic acid. Thsi is quite safe assumption, that works OK for most typical buffer solutions (although in some cases, when the solution is diluted, or pKa is very low or very high, it will not work).
100 mL of the buffer contains 6.4 millimoles of acetic acid (n=CV) and 3.6 millimoles of acetate. As the protonation goes to the end, from a stochiometry we can easily calculate that after reaction we have 6.4+1 millimoles of acetic acid and 3.6-1 millimoles of acetate. We can convert these numbers to concentrations, or - as volumes of acid and conjugate base solutions in the Henderson-Hasselbalch equation are identical and cancel out - put them directly into the equation:
pH=4.75+log(2.6/7.4)=4.30.