Question

So my teacher justifies an answer this way. Could someone explain the logic?

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For the metal carbonate, MCO₃, the value of the solubility-product constant, K_sp, is 7.4 x 10^–14 at 25°C. M(OH)₂ has a Ksp of7.0 × 10⁻⁶M. Therefor which compound M(OH)₂ or MCO₃, has the greater molar solubility in water at 25°C? Justify your answer with a calculation.

For M(OH)2 : [M2+] and molar solubility = 7.0 × 10−6M For MCO3 : Ksp = 7.4 × 10−14 = [M2+][CO32−] [M2+] and molar solubility = 2.7 × 10−7M Because 7.0 × 10−6M > 2.7 × 10−7M, M(OH)2 has the greater molar solubility.

1 pt is earned for the molar solubility of MCO3. 1 pt is earned for an answer consistent with the calculated molar solubility.

Answer 1

M(OH)2 ---------------> M+2 + 2 OH-

                                       S          2S

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

7 x 10^-6 = S x (2S)^2

S = 0.012 M

MCO3   ----------------> M+2 + CO32-

                                       S           S

Ksp = S^2

7.4 x 10^-14 = S^2

S = 2.7 x 10^-7 M

from the above solubilities , M(OH)2 has the higher molar solubility