Answer:
38.4%
Explanation:
Step 1 Obtain the concentration of Ca^2+ and SO4^2-
[Ca^2+] = 0.05 L (0.0125 mol/L) (1/0.1 L) = 6.25 * 10^-3 M
[SO4^2-] = 0.05 L (0.0152mol/L) (1/0.1L) = 7.60 * 10^-3 M
Step 2 Obtain the concentration of [SO4^2-] left
Ca^2+(aq) + SO4^2-(aq)------> CaSO4(s)
initial 6.25 * 10^-3 M 7.60 * 10^-3 M
final 0 1.35 * 10^-3 M
Step 3 Determine the amount of Ca^2+ left from the common ion problem
CaSO4(s) --------> Ca^2+(aq) + SO4^2-(aq)
initial 0 1.35 * 10^-3 M
equilibrium x (1.35 * 10^-3 + x) M
But Ksp of CaSO4 = 9.1 * 10^-6
Ksp = [Ca^2+] [SO4^2-]
9.1 * 10^-6= [x] [1.35 * 10^-3 + x]
9.1 * 10^-6= 1.35 * 10^-3 x + x^2
Rearranging:
x^2 + 1.35 * 10^-3 x + 9.1 * 10^-6 = 0
solving the quadratic yields x = 2.4 * 10^-3
Step 4 Calculate the amount of Ca^2+ remaining;
% Ca^2+ remaining = 2.4 * 10^-3/ 6.25 * 10^-3 M * 100
% Ca^2+ remaining = 38.4%
