Question

The maximum amount of silver carbonate that will dissolve in a 0.278 M sodium carbonate solution is: M.

Answer 1

This is a problem of solubility where there is presence of common ion, that is carbonate.

Silver carbonate dissolves according to the reaction equation:
Ag₂CO₃ ⇄ 2 Ag⁺ + CO₃²⁻

Initial 0 0 0.278

Intermediate -x +2x +x

Equilibrium -x +2x 0278+x

So the ionic molarities in a saturated solution satisfy the relation:
Ksp = [Ag⁺]²∙[CO₃²⁻] with Ksp = 8.1×10⁻¹²

Due to the small value of the Ksp we can expect x to be very small compared to 0.278M. Also x value will be small due to common ion effect exerted by carbonate ions. Hence we can approximate: [CO₃²⁻] ≈ 0.278M

The silver ion concentration which is equal to the solubility of silver carbonate is

Ksp = [Ag⁺]²∙[CO₃²⁻]

8.1×10⁻¹² = (2x)² * (0.278)

x = (8.1×10⁻¹² )/ 1.112

x = 2.6 * 10^-6 M