By what factor should you dilute the 1.00M NaOH stock solution so that you will reach the first equivalence point in about 10mL?

Question

It takes 2.1 mL of 1.00M NaOH (aq) stock solution to reach the second equivalence point in a titration of 50.0mL of phosphoric acid solution. By what factor should you dilute the 1.00M NaOH stock solution so that you will reach the first equivalence point in about 10mL?

Answer 1

Phosphoric acid is H3PO4. It has 3 titratable hydrogens.

H₃PO₄ + OH- ==> H2O + H₂PO₄^- .. 1st equivalence

H₂PO₄^- + OH- ==> H2O + HPO₄^2- .. 2nd equivalence

HPO₄^2- + OH- ==> H2O + PO₄^3- .. 3rd equivalence

It will take the same number of moles of NaOH for each equivalence point. So, if it took 2.1 ml to titrate 50.0 ml to reach the 2nd equivalence point, that means it took 1.05 mls to reach the first equivalence point (and it would take about 3.15 mls to reach the 3rd equivalence point). To increase this to about 10 mls, we'd need to dilute the original 1 M NaOH by about a factor of 10. That way, instead of requiring 1.05 mls to reach the 1st equivalence point, it would require about 10.5 mls. Hope this makes sense. (You could go through the calculations, but this is easier).