Question

We have seen from our study of acid/base chemistry that the presence of a weak base such as ammonia (Kb = 1.8 X 10-5) can affect the pH of an aqueous solution. This pH can in turn affect the solubility of a metal hydroxide salt as a result of the common ion effect. The Ksp for gallium hydroxide = 7.28 X 10-36. What is the molar solubility of gallium hydroxide in a 3.00M solution of ammonia?

Answer 1

       NH₃ + H₂O NH₄⁺ + OH^-

I     3 M                   0          0

C    -x                      +x         +x

E    3-x                   x              x

Kb = [NH₄⁺][OH^-]/ [NH₃]
1.8 x 10^-5 = x(x)/(3.0 – x)
one can neglect the x in (3.0 –x) since it is very small compared to 3.0
x² = 3(1.8 x 10^-5)
x² = 5.4 x 10^-5
x = 7.3 x 10^-3

[OH^-] = 7.3 x 10^-3

        Ga(OH)₃ Ga⁺³ + 3OH^-

Let Y = molar solubility of Ga(OH)3

[Ga⁺³] = Y ; [OH^-] = 7.3 x 10^-3 + 3Y

Ksp = [Ga⁺³][OH^-]³
7.28 x 10^-36 = Y(7.3 x 10^-3 + 3Y)³
One can neglect the 3Y since it is very, very small compare to 7.3 x 10^-3

Y(7.3 x 10^-3)³ = 7.28 x 10^-36
Y( 3.89 x 10^-7) = 7.28 x 10^-36
Y = 1.87 x 10^-29 Your answer