Question

lculate the pH for each of the following cases in the titration of 25.0 mL of 0.200 M pyridine, C5HsN(aq) with 0.200 M HBr(aq): Number (a) before addition of any HBr Number (b) after addition of 12.5 mL of HBr Number (c) after addition of 22.0 mL of HBr Number (d) after addition of 25.0 mL of HBr Number (e) after addition of 36.0 mL of HBr

Answer 1

HBr and C₅H₅N react in a 1:1 mole ratio: C₅H₅N + HBr $\rightarrow$ C₅H₅NH+Br-
Since the molarities of both reactants is 0.200 M, then it will take 25.0 mL of HBr to titrate the 25.0 mL of C₅H₅N.
The Kb for C₅H₅N is 1.7 x 10^-9.

Ka C₅H₅NH⁺ = (1 x 10^-14) / Kb = (1 x 10^-14) / (1.7 x 10^-9) = 5.9 x 10^-6
pKa = -log Ka = -log (5.9 x 10^-6) = 5.23

a)

[OH-] = sqrt (Kb x [B]₀) = sqrt ((1.7 x 10^-9)(0.200)) = 2.0 x 10^-5
pOH = -log [OH-] = -log (2.0 x 10^-5) = 4.70
pH = 14.00 - pOH = 14.00 - 4.70 = 9.30

b)
(b) 12.5 mL represents the halfway point of the titration (i.e. the equivalence point is at 25.0 mL HBr) where [C₅H₅N] = [C₅H₅NH⁺]. Using the Henderson-Hasselbalch equation for buffers,

pH = pKa + log ([buffer base] / [buffer acid]) = 5.23 + log ([C₅H₅N] / [C₅H₅NH⁺])
pH = 5.23 + log 1 = 5.23 + 0 = 5.23

(c) Since the equivalence point is at 25.0 mL HBr, at 22.0 mL HBr you have converted 22.0 / 25.0 of the C₅H₅N to C₅H₅NH⁺. So there are 22.0 parts C₅H₅NH⁺ and 3.0 parts C₅H₅N. So pH can be calculated by using Henderson-Hasselbalch equation .

pH = 5.23 + log (3.0 / 22.0) = 5.23 - 0.865 = 4.365

(d) We are now at the equivalence point. The only thing present is the salt C₅H₅NH⁺Br^-. It acts as a weak acid like so: C₅H₅NH⁺ + H₂O $\rightleftharpoons$ H₃O⁺ + C₅H₅N

The pH of a weak acid solution may be calculated using

[H₃O⁺] = sqrt ([HA] x Ka)

initial mmoles C₅H₅N = M C₅H₅N x mL C₅H₅N = (0.200)(25.0) = 5.00 mmoles C₅H₅N. Since all of it was converted to C₅H₅NH⁺ in the titration, then at the equivalence point there are 5.00 mmoles of C₅H₅NH⁺.
[C₅H₅NH⁺] = 5.00 mmoles / 50.0 mL = 0.1 M

[H₃O⁺] = sqrt ((0.10)(5.9 x 10^-6)) = 7.6 x 10^-4
pH = -log [H₃O⁺] = -log (7.6 x 10^-4) = 1.88