What is the concentration of the phosphoric acid solution?

Question

A student measures that it takes 7.21mL of 0.326 M NaOH (aq) solution to reach the first equivalence point of a titration of 100.0 mL of phosphoric acid solution. He also notes that it takes a total of 14.40 mL of 0.326 M NaOH (aq) solution to reach the second equivalence point. What is the concentration of the phosphoric acid solution?

Answer 1

Equation for the first equivalence point:

H3PO4 + NaOH ==> NaH2PO4 + H2O .. note it takes 1 mol NaOH per 1 mol H3PO4

Equation for the second equivalence point:

NaH2PO4 + NaOH ==> Na2HPO4 + H2O . note it takes 1 mol NaOH per 1 mol H3PO4

moles NaOH used = 7.21 ml x 1 L / 1000 ml x 0.326 mol / L = 0.00235 mols NaOH

moles H3PO4 present = 0.00235 mols NaOH x 1 mol H3PO4 / mol NaOH = 0.00235 mols H3PO4

Concentration of H3PO4 = 0.00235 mols / 100.0 ml x 1000 ml / L = 0.0235 mol / L = 0.0235 M

You could repeat the calculation for the 2nd equivalence point and will come out with the same answer because each equivalence point requires a 1:1 mole ratio of NaOH, i.e. 1st eq. point requires 7.21 mls; 2nd eq.point should require a total of 14.4 mls and 3rd should requires a total of 21.6 mls.