What is the value for pH?

Question

What is the pH of a 0.710 M solution of NaCN (Ka of HCN is 4.9 × 10⁻¹⁰)?

Answer 1

CN- + H2O ==> HCN + OH- ... hydrolysis of CN- where CN- acts as a base

Kb for CN- = 1x10^-14 / 4.9x10^-10 = 2.04x10^-5

Kb = 2.04x10^-5 = [HCN][OH-] / [CN-]

2.04x10^-5 = (x)(x) / 0.710 - x (and assume x is small in the denominator and ignore it)

2.04x10-5 = x2 / 0.710

x² = 1.45x10^-5

x = [OH-] = 3.81x10^-3 M (note that this is small relative to 0.710 so assumption was valid)

pOH = -log 3.81x10^-3 = 2.42

pH = 14 - pOH

pH = 11.6