Question

A) The generic metal hydroxide M(OH)2 has Ksp = 6.85×10^?12. (NOTE: In this particular problem, because of the magnitude of the Ksp and the stoichiometry of the compound, the contribution ofOH? from water can be ignored. However, this may not always be the case.)

B) What is the solubility of M(OH)2 in a 0.202 Msolution of M(NO3)2?

Express your answer with the appropriate units.

Answer 1

Part a

In pure water the dissociation reaction

M(OH)2 ? M2+ + 2OH-

Solubility product constant

Ksp = [M2+][OH-]^2

Let the molar solubility of M(OH)2 = x M

Molar solubility of [M2+] = x

Molar solubility of [OH-] = 2x

Ksp = [M2+][OH-]^2

6.85*10^-12 = x(2x)^2

4x^3 = 6.85*10^-12

x^3 = 1.7125 * 10^-12

x = 1.196 * 10^-4 M

molar solubility of M(OH)2 in pure water = 1.196 * 10^-4 M

Part b

M(NO3)2 = M2+ + 2NO3-

Concentration of M2+ = 0.202 M

Concentration of [M2+] = 0.202 + x

Concentration of [OH-] = 2x

x << 0.202 + x

0.202*[2x]^2 = 6.85*10^-12

4x^2 = 3.39 * 10^-11

x^2 = 8.47 * 10^-12

x = 2.91 x 10^-6

Molar solubility of M(OH2) = 2.91 x 10^-6