Malonic acid (H2C3H2O4) is a diprotic acid. In the titration of malonic acid with NaOH, stoichiometric (aka endpoint) points occur at pH = 3.9 and 8.8. A 25.00-mL sample of malonic acid of unknown concentration is titrated with 0.0984M NaOH, requiring 31.50 mL of the NaOH solution to reach the phenolphthalein end point.
Calculate the concentration of malonic acid in the unknown solution.
The answer is 0.0620 M Malonic Acid but I don't know how to arrive to that answer.
This is what I've figured out so far.
Ka1 = 1.5 x 10^-3
Ka2 = 2.0 x 10^-6
H2C3H2O4 + OH- ↔ H2O + HC3H2O4- ==> Ka1=[HC3H2O4-]/[H2C3H2O4][OH-]
HC3H2O4- + OH- ↔ H2O + C3H2O4-- ==> Ka2=[C3H2O4--]/[HC3H2O4-][OH-]
I tried setting up rice tables but I still don't know how to figure out the initial concentration of malonic acid.