Question

The solubility products of CaCO₃ and FeCO₃ are 4.5×10⁻⁹ and 2.1×10⁻¹¹, respectively.

Calculate the ratio of [Ca²⁺] to [Fe²⁺] in a lake in which the water is in equilibrium with deposits of both CaCO₃ and FeCO₃. Assume that the water is slightly basic and that the hydrolysis of the carbonate ion can therefore be ignored.

Answer 1

CaCO₃        Ca²⁺   + CO₃^2-

FeCO₃         Fe²⁺  + CO₃^2-

Writing the Ksp equations,

Ksp = 4.5 x 10^-9 = [ Ca²⁺ ] [CO₃^2-]

Ksp = 2.1 *10^-11= [ Fe²⁺] [CO₃^2-]

Taking the ratio,

4.5 x 10^-9 /2.1 x 10^-11 = ([Ca²⁺ ][CO₃^2-])/([ Fe²⁺][CO₃^2-])

4.5 x 10^-9 /2.1 x 10^-11 = [Ca²⁺]/[Fe²⁺]

[Ca²⁺]/[Fe²⁺] = 2.1 x 10²