Calculating the effect of a common ion on concentrations, pH and percent dissociation

In 0.15 M NH₃, the pH is 11.21 and the percent dissociation is 1.1%. Calculate the concentrations of all species present, the pH, and the percent dissociation of ammonia in a solution that is 0.15 M in NH₃ and 0.45 in NH₄Cl. Kb = 1.8 x 10^-5

Solution

The principal reaction is proton transfer to NH₃ from H₂O:

NH_3(aq) + H₂O_(l) ↔ NH⁺_(aq) + OH^-_(aq)

Since NH⁺ ions come both from the NH₄Cl present initially (0.45M) and from the reaction of NH₃ with H₂O, the concentrations of the species involved in the principal reaction are as follows:

Principal reaction                           NH3(aq) + H2O(l) ↔ NH4+(aq) + OH-(aq)

Initial concentration (M)                 0.15                         0.45

Change (M)                                      -x                              +x               +x

Equilibrium concentration (M)     0.15 – x                  0.45 + x             x

The equilibrium equation for the principal reaction is

We assume x is negligible compared to 0.45 and 0.15 because:

1.     The equilibrium constant K_b is small

2.     The equilibrium is shifted to the left by the common – ion effect

Thus, the assumption concerning the size x is justified

The H₃O⁺ concentration and the pH are