!! LONG ANSWER !!
The pH of the solution will be 4.77.
So, you know that you're dealing with citric acid, a triprotic acid that ionizes in three steps, each with its own acid dissociation constant -
The key to this problem is actually the relationship that exists between how much citric acid you have, 0.001 moles, and how many moles of strong base you add.
The balanced chemical equation for the neutralization of citric acid is
Notice that you have a
Since you have less moles of sodium hydroxide than you would need for a complete neutralization, you can predict that the pH will be acidic, i.e. some citric acid will be left in solution.
So, start by writing the first reaction between citric acid and sodium hydroxide (net ionic equation, so I didn't include the sodium cation)
Once again, notice the
As a result, you'll produce some sodium citrate,
Since you still have strong base left in solution, a second reaction will take place
This time, the strong base will be consumed, and disodium citrate will be produced, so you'll be left with
At this point, this should look familiar. Equal number of moles, i.e. concentrations, since the volume is the same for both, for a weak acid,
Use the Henderson-Hasselbalch equation to calculate the pH
Since citric acid is tri - protic I'll call it
Sodium hydroxide is a strong base so will strip all the protons from the citric acid:
We can work out the number of moles of NaOH:
Because you need 3 moles of NaOH for every mole of
So no. moles left after neutralisation =
This means the no. moles
So we are left with a solution effectively consisting of