Question

Determine the molar solubility of Y for XY2 if Ksp is 2.2x10^-4

The answer is 0.038, but I'm not sure how

Answer 1

.........XY2 ==> X^2+ + 2Y^-
I........solid...0.......0
C........solid...z.......2z
E........solid...z.......2z

Ksp = 2.2E-4 = (X^2+)(Y^-)^2
2.2E-4 = (z)(2z)^2
Solve for z.

Answer 2

I did and I got 0.015 as my answer:

2.2x10^-4 = 4z^3
3√2.2x10^-4 = 4z^3
0.060368107 = 4z
0.015 = z

Answer 3

No. The answer is 0.038 as you first stated. The error you are making is that you are taking the cube root BEFORE dividing by 4. It's the other way around. Thanks for showing your work; it makes it easy to spot the problem.
Ksp = 2.2E-4 = 4z^3
z^3 = 2.2E-4/4 = 5.5E-5
z = cube root 5.5E-5 = 0.038 M

I also want to point out an error you are making in equalities; i.e.,
2.2x10^-4 = 4z^3
<b>That first line is correct.</b>
<b>The next line is not right.</b>
3√2.2x10^-4 = 4z^3
<b>4z^3 = 2.2E-4 and not cube root 2.2E-4.</b>

0.060368107 = 4z
0.015 = z