The generic metal hydroxide M(OH)2 has Ksp = 6. 65x10-16. (NOTE: In this particu

Question

The generic metal hydroxide M(OH)2 has Ksp = 6. 65x10-16. (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. ) What is the solubility of M(OH)2 in pure water? Express your answer with the appropriate units. What is the solubility of M(OH)2 in a 0. 202 M solution of M(N03)2? Express your answer with the appropriate units.

Explanation / Answer

The equilibrium will be : M(OH)2 M2+ + 2OH- and the requirement for equilibrium is that Ksp = [M2+] [ OH-]^2 Let x = mole/L M(OH)2 that dissolve in water We would get x mol/L M2+ and 2x mol/L OH- Substitute these in the Ksp expression 6.65 x 10^-18 = x ( 2x)^2 = 4x^3 x = 1.185 x 10^-6 M M(NO3)2 is a strong electrolyte: M(NO3)2 >> M2+ + 2NO3- [M2+] = 0.202 M At equilibrium [M2+] = x+0.202 [OH-] = 2x 6.65 x 10^-18 = ( x+0.202) (2x)^2 Since x has to be small compared to 0.202 we can assume: x+ 0.202 = 0.202 6.65 x 10^-18 = 0.202 (4x^2) x = 2.86 x 10^-9 M

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