Question

A solution of Na₂CO₃ is added dropwise to a solution that contains 1.05×10-2 M Fe₂⁺ and 1.45×10-2 M Cd₂⁺. What concentration of CO₃²⁻ is needed to initiate precipitation? Neglect any volume changes during the addition. Express your answer with the appropriate units.

Answer 1

To determine the concentration of CO₃²⁻ needed to initiate precipitation, set up the equilibrium expression for the reaction and solve for CO₃²⁻. The concentration of CO₃²⁻ needed will be less than or equal to the solubility of FeCO₃.

Step-by-step explanation:

To determine the concentration of CO₃²⁻ needed to initiate precipitation, we need to find the solubility product constant (Ksp) of FeCO₃ and CdCO₃. The Ksp values are not provided, but we can assume that they are sufficiently small so that the concentrations of Fe²⁺ and Cd²⁺ remain constant during the precipitation. Let's assume the solubility of FeCO₃ is s, then the concentration of Fe²⁺ will be s since one mole of FeCO₃ dissociates to one mole of Fe²⁺. Similarly, the concentration of Cd²⁺ will be (0.0105 - s) since the initial concentration of Cd²⁺ is 0.0105 M and one mole of CdCO₃ dissociates to one mole of Cd²⁺. The concentration of CO₃²⁻ will be s.

Now, let's set up the equilibrium expression for the precipitation of FeCO₃ and CdCO₃:

FeCO₃ → Fe²⁺ + CO₃²⁻

The expression is:

Ksp = [Fe²⁺][CO₃²⁻]

Substituting the values:

Ksp = s * s = s²

Since the Ksp for FeCO₃ is not known, we cannot determine the exact concentration of CO₃²⁻ that is needed to initiate precipitation. However, we know that the concentration of CO₃²⁻ needed to initiate precipitation will be less than or equal to the solubility of FeCO₃.