Question

The pKb values for the dibasic base B are:
pKb1= 2.10
pKb2= 7.70
Calculate the pH at each of the following points in the titration of 50.0 mL of a 0.75 M B(aq) with a 0.75 M HCl(aq).
a. before addition of any HCl
b. after addition of 25.0 mL of HCl
c. after addition of 50.0 mL of HCl
d. after addition of 75.0 mL of HCl
e. after addition of 100.0 mL of HCl

please show your work as I really do want to understand the process. thank you so much :)

Answer 1

pKb1 = 2.10

Kb1 = 10^-pKb1 =7.94 x 10^-3

pKb2 = 7.70

B molarity = 0.75 M

(a) before addition of any HCl

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

0.75 0             0   ------------------> initial

0.75 -x                                      x              x ------------------------> equilibrium

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

7.94 x 10^-3 = x^2 / 0.75 -x

x^2 + 7.94 x 10^-3 x - 5.96 x 10^-3 = 0

x = 0.0733

[OH-] = 0.0733 M

pOH = -log (0.0733)

pOH = 1.14

pH + pOH = 14

pH = 12.86

(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 + 7.70) / 2

pOH = 4.90

pH = 9.10

(d) after additon of 75 mL HCl

it is second half equivalence point

pOH = pKb2

pOH = 7.70

pH = 6.30

e) after additon of 100 mL HCl

B millimoles = 50 x 0.75 = 37.5

BH2+ salt is here only remains

BH2+2 concentration = millimoles / total volume

                                   = 37.5 / (50 +100)

                                  = 0.25 M

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

0.25 0 0

0.25 -x    x x

Ka2 = x^2 / 0.25 -x

pKa2 = 14 - 7.70 = 6.30

Ka2 = 10^-pKa2

Ka2 = 5.01 x 10^-7

5.01 x 10^-7     = x^2 / 0.25 –x

x^2 +5.01 x 10^-7 x - 1.25 x 10^-7 = 0

x = 3.53 x 10^-4

x = [H+] = 3.53 x 10^-4 M

pH = -log [H+]

pH = 3.45