Question

Butyric acid is responsible for the foul smell of rancid butter. The pK_a of butyric acid is 4.84.

(a) Calculate the pK_b for the butyrate ion.

(b) Calculate the pH of a 0.048 M solution of butyric acid.

(c) Calculate the pH of a 0.048 M solution of sodium butyrate.

Answer 1

Part a)

Here, pKa = 4.84

Therefore,

Ka = 10^-pH = 10^(-4.84) = 1.5 x 10^-5

Kb = Kw / Ka

Kb = (1 x 10^-14) / 1.5 x 10^-5 = 6.92 x 10^-10

pKb = -logKb = 9.15

Part b)

            C₄H₈O₂  + H₂O     C₄H₇O₂^- + H₃O⁺

I           0.048                                                      0           0

C             -x                                                        +x          +x

E         0.048-x                                                   +x           +x

1.5 x 10^-5 = [C₄H₇O₂^-][H₃O+] / [C₄H₈O2]

1.5 x 10^-5 = x² / (0.048-x)   [Here, x can be neglected in comparison with 0.048]

1.5 x 10^-5 = x² / (0.048)  

x = 8.485 x 10^-4

pH = -log[H₃O⁺] = -log(8.485 x 10^-4) = 3.07

Part c)

               C₄H₇O₂^- + H₂O    C₄H₈O₂ + OH^-

I               0.048                                                      0              0

E             0.048-x                                                   +x             +x

Kb = [C₄H₈O₂][OH^-] / [C₄H₇O₂^-]

6.9 x 10^-10 = x² / (0.048-x) [Here, x can be neglected in comparison with 0.048]

6.9 x 10^-10 = x² / (0.048)

x = 5.75 x 10^-6

pOH = -log[5.75 x 10^-6] = 5.24

pH = 14 - 5.24 = 8.76