What is the volume of base added at second equivalence point?

[PinguNinjitsu]

Homework Statement

You have a solution that is buffered at pH =2.0 using H3PO4 and H2PO−4 (pKa1 = 2.12;
pKa2 = 7.21; pKa3 = 12.68). You decide to titrate this buffer with a strong base. 15.0 mL are needed to reach the first equivalence point. What is the total volume of base that will have been added when the second equivalence point is reached?

I know that the answer is >30ml but I don't know how to get to that point.

Homework Equations

PH=(PKa1+PKa2)/2 First equivalence point
PH=(PKa2+PKa3)/2 Second equivalence point

The Attempt at a Solution

I honest don't know what to do, I did try finding the concentrations of OH at the equivalence points using the pH formulas above, but that didn't seem to get me anywhere since those values were tiny and I didn't know how to get mL from it..

Any help would be much appreciated! Thanks!

 

[Borek]

Use information about pH to find initial concentrations of H₃PO₄ and H₂PO₄^-. First end point means you have neutralized all H₃PO₄. Now you have solution containing initial H₂PO₄^- and H₂PO₄^- from H₃PO₄ neutralization.

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