Calculate the pH?

Question

Calculate the pH of a mixture containing equal volumes of
0.520 M NH4Cl ( use Ka = 5.60 x 10 -10 ) and 0.520 M NH3.

Answer 1

Much easier to use Henderson-Hassselbach.

pH = pKa + log [base]/[acid]

Since [base]=[acid], pH = pKa = 9.25

Answer 2

It is a buffer solution.
NH4Cl is a strong electrolyte
NH4Cl >> NH4+ + Cl-
NH3 + H2O <> NH4+ + OH-
initial concentration
0.520 ................0.520......0
at equilibrium
0.520-x.............0.520+x.....x

Kb = Kw /Ka = 1 10^-14 /5.6 10^-10 = 1.79 10^-5

1.79 10^-5 = (0.520+x)(x) / 0.520-x

x= 1.79 10^-5=concentration OH-

pOH =4.75

pH=9.25