I got a different value for the initial pH. Here's what I got:
Benzoic acid is a weak acid and dissociates:
I will assume that the no. of moles given refers to equilibrium moles. Since the volume is 1L we can write:
Now a small amount of HCl is added. We have a buffer solution here with a large reserve of benzoate ions which can absorb the addition of small amounts of
If we add 0.05 moles of
So we can say:
There may be a volume change on mixing but this does not matter as the volume is common to acid and co - base so cancels.
We can now put these values into our original expression for
You can see that the buffer has worked since the pH has fallen only very slightly.