ADDED INFO. Consider a weak acid,
The acid dissociation constant for
So, you're dealing with a buffer, which is a solution that contains a weak acid and its conjugate base (or a weak base and its conjugate acid).
The great thing about dealing with buffers is that you can use the Henderson-Hasselbalch equation to determine the pH of the solution.
When you have equal concentrations of weak acid and conjugate base, the pH of the solution will be equal to the
Now you go ahead and add sodium hydroxide, a strong base. The sodium hydroxide will react with the weak acid
Since you didn't provide the volumes of the two solutions, I'll assume that you have 1 L of each.
The number of moles of weak acid would be
For the sodium hydroxide, you have
The sodium hydroxide will react with the weak acid and get consumed. The number of moles of weak acid will decrease by how many moles of sodium hydroxide it reacted with, so
At the same time, you'll produce 0.1 moles of conjugate base,
The total volume of the solution will now be
The concentrations of the weak acid and of its conjugate base will be
Therefore, the pH of the solution will be
SIDE NOTE If you have other volumes for the solution, just use this answer as a model to guide you through the calculations.
I didn't take into account sig figs either.