Question

The solubility of Mg₃(AsO₄)₂ in water is 0.685 g in 0.935 L of water at a given temperature. What is the value of K_sp for Mg₃(AsO₄)₂? (The molar mass of Mg₃(AsO₄)₂ is 350.7 g/mol)

Answer 1

Mg3(AsO4)2 --- >              3 Mg²⁺ + 2 AsO4^3-

I                                                         0                  0

C     (molar solubility ) -x               +3x                 +2x

E                                                              3x                2x

Ksp = [ Mg²⁺ ]³ [ AsO4^3-]²

= (3x)³ (2x)²

Ksp = (9 x³ ) (4x²)

Ksp = 36 x⁵

We need to calculate x

x is molar solubility. That is moles / L

moles of Mg3(AsO4)2 = 0.685 g / 350.7 g per mol

       (mol = mass / molar mass

Moles of Mg3(AsO4)2 = 0.001953

[Mg3(AsO4)2]= 0.001953 mol / 0.935 L …. (molarity = mol /L )

= 0.002089 M

So x = 0.002089 M

Lets plug this value to get ksp ‘

Ksp = 36 x⁵ = 36 x (0.002089)⁵

=1.42 E-12

Ksp of Mg3(AsO4)2 = 1.42 E-12