Answer:
The solubility product constant, Ksp, for the reaction of copper(I) cyanide (CuCN) in water is given as 4x10^−20. The balanced chemical equation for this reaction is:
CuCN (s) ↔ Cu+ (aq) + CN− (aq)
The Ksp expression for this reaction is:
Ksp = [Cu+][CN−]
At equilibrium, the solution is saturated with CuCN, which means that the concentration of CuCN is equal to its solubility (S), and the concentrations of Cu+ and CN− are equal to x (the amount that dissolves). Thus, we can write:
CuCN (s) ↔ Cu+ (aq) + CN− (aq)
I S x x
The solubility of CuCN is equal to the amount that dissolves, which is equal to the initial concentration of Cu+ and CN− in the solution. Therefore:
[S] = [Cu+] = [CN−] = x
Substituting these values into the Ksp expression, we get:
Ksp = [Cu+][CN−] = x^2
Solving for x, we get:
x = sqrt(Ksp) = sqrt(4x10^-20) = 2x10^-10
Therefore, the concentrations of Cu+ and CN− in a saturated CuCN solution are both 2x10^-10 mol/L.