Question

The pKb values for the dibasic base B are pKb1 = 2.10 and pKb2 = 7.65. Calculate the pH at each of the following points in the titration of 50.0 mL of a 0.85 M B(aq) with 0.85 M HCl(aq).

a) before addition of any HCl

b)after addition of 25.0mL of HCl

c)after addition of 50.0mL of HCl

d) after addition of 75.0mL of HCl

e) after addition of 100.0 mL of HCl

Answer 1

pKb1 = 2.10

pKb2 = 7.65

B molarity = 0.85 M

(a) before addition of any HCl

B   +   H2O <----------------------> BH+   + OH-

0.85    0             0   ------------------> initial

0.85 -x                                      x              x ------------------------> equilibrium

Kb1 = [BH+][OH-]/[B]

7.94 x 10^-3 = x^2 / 0.85 -x

x^2 + 7.94 x 10^-3 x - 6.749 x 10^-3 = 0

x = 0.0783

[OH-] = 0.0783M

pOH = -log (0.0783)

pOH = 1.106

pH + pOH = 14

pH = 12.89

(b) after additon of 25 mL HCl

it is first half equilivalence point .

at this point . pOH = pKa1

pOH = 2.10

pH + pOH = 14

pH = 11.90

c) after additon of 50 mL HCl

it is first equivalence point

here : pOH = (pKb1 + pKb2)/2

pOH = (2.10 + 7.65) / 2

pOH = 4.875

pH = 9.12

(d) after additon of 75 mL HCl

it is second half equivalence point

pOH = pKb2

pOH = 7.65

pH = 6.35

e) after additon of 100 mL HCl

B millimoles = 50 x 0.85 = 42.5

BH2+ salt is here only remains

BH2+2 concentration = millimoles / total volume

                                   = 42.5 / (50 +100)

                                  = 0.283 M

BH2+2 ----------------------------> BH+ + H+

0.283 0 0

0.283 -x    x x

Ka2 = x^2 / 0.283 -x

pKa2 = 14 - 7.65 = 6.35

Ka2 = 10^-pKa2

Ka2 = 4.47 x 10^-7

4.47 x 10^-7     = x^2 / 0.283 -x

x = 3.35 x 10^-4

x = [H+] =3.35 x 10^-4 M

pH = -log [H+]

pH = 3.47