You want to make 1000 ml of an 0.1 M HA buffer so that the pH=pKa of HA. To make this buffer you need to add ____ HA and ____ mL of 1M NaOH and then add enough water to give 1000 mL. HA is a weak acid.

Answer 1

pH = pKa + log{[A-]/[HA]}
or
pH = pKa + log{[NaA]/[HA]}
if pH = pKa, then {[log{[NaA]/[HA]} = 0
or [NaA] = [HA]
The reaction between NaOH and HA is:
NaOH + HA --> NaA + H2O
Since we start with no NaA, we must add enough NaOH so that [NaA] = [HA]
That happens when we neutralize HALF of the HA by using NaOH. The mole ratio of NaOH added to HA is 1 to 2 or 1/2.
I gave you most of the solution of the problem. You should be able to finish it on your own.