Consider the dissolution of AB(s): AB(s)⇌A+(aq)+B−(aq) Le Châtelier's principle tells us that an increase in either [A+] or [B−] will shift this equilibrium to the left, reducing the solubility of AB. In other words, AB is more soluble in pure water than in a solution that already contains A+ or B− ions. This is an example of the common-ion effect. The generic metal hydroxide M(OH)2 has Ksp = 8.45×10−12. (NOTE: In this particular problem, because of the magnitude of the Ksp and the stoichiometry of the compound, the contribution of OH− from water can be ignored. However, this may not always be the case.) Part A What is the solubility of M(OH)2 in pure water? Express your answer with the appropriate units. View Available Hint(s) nothing nothing Part B What is the solubility of M(OH)2 in a 0.202 M solution of M(NO3)2? Express your answer with the appropriate units. View Available Hint(s) nothing nothing

Respuesta :

Answer:

A. 0.000128 M is the solubility of M(OH)2 in pure water.

B. [tex]3.23\times 10^{-6} M[/tex] is the solubility of [tex]M(OH)_2[/tex] in a 0.202 M solution of [tex]M(NO_3)_2[/tex].

Explanation:

A

Solubility product of generic metal hydroxide = [tex]K_{sp}=8.45\times 10^{-12}[/tex]

[tex]M(OH)_2\rightleftharpoons M^{2+}+2OH^-[/tex]

                      S         2S

The expression of a solubility product is given by :

[tex]K_{sp}=[M^{2+}][OH^-]^2[/tex]

[tex]K_{sp}=S\times (2S)^2=4S^3[/tex]

[tex]8.45\times 10^{-12}=4S^3[/tex]

Solving for S:

[tex]S=0.000128 M[/tex]

0.000128 M is the solubility of M(OH)2 in pure water

B

Concentration of [tex]M(NO_3)_2[/tex] = 0.202 M

Solubility product of generic metal hydroxide = [tex]K_{sp}=8.45\times 10^{-12}[/tex]

[tex]M(OH)_2\rightleftharpoons M^{2+}+2OH^-[/tex]

                   S          2S

So, [tex][M^{2+}]=0.202 M+S[/tex]

The expression of a solubility product is given by :

[tex]K_{sp}=[M^{2+}][OH^-]^2[/tex]

[tex]8.45\times 10^{-12}=(0.202 M+S)(2S)^2[/tex]

Solving for S:

[tex]S=3.23\times 10^{-6} M[/tex]

[tex]3.23\times 10^{-6} M[/tex] is the solubility of [tex]M(OH)_2[/tex] in a 0.202 M solution of [tex]M(NO_3)_2[/tex].