Question

A sample of carbonic acid (0.125 L, 0.145 M, pKa1 = 6.35, pKa2 = 10.33) was titrated with 1.42 M NaOH. Calculate the pH at the following points:

1. Before the titration.

2. At the 1st midpoint.

3. At the 1st stoichiometric point.

4. At the 2nd midpoint.

5. At the 2nd stoichiometric point.

Answer 1

1. Before the titration.

pH = 1/2 [pKa - logC]

pH = 1/2 [6.35 -log 0.145]

pH = 3.59

2. At the 1st midpoint.

here pH = pKa1

pH = 6.35

3. At the 1st stoichiometric point.

here pH = 1/2 [pKa1 + pKa2]

pH = 1/2 [6.35 + 10.33]

pH = 8.34

4. At the 2nd midpoint.

here pH = pKa2

pH = 10.33

5) At the 2nd stoichiometric point.

volume of NaOH needed = 0.125 x 0.145 x 2 / 1.42

                                       = 0.0255 L

A-2 formed = 0.125 x 0.145 / (0.125 + 0.0255) = 0.120 M

A-2 + H2O --------------> HA- + OH-

0.120 -x                              x       x

Kb1 = x^2 / 0.120 - x

2.14 x 10^-4 = x^2 / 0.120 - x

x^2 + 2.14 x 10^-4 x - 2.57 x 10^-5 = 0

x = [OH-] = 4.96 x 10^-3 M

pOH = 2.30

pH + pOH = 14

pH = 11.70