How to solve for Ksp?

Question

This is an example of the problems we have to do:
The ionic substance T3U2 ionizes to form T2+ and U3- ions. The solubility of T3U2 is 3.77x10^-20 mol/L. What is the value of the solubility-product constant?
Can someone explain to me how to get the answer?
I understand Keq but not this.

Answer 1

OK...

You're OK with writing the expression for Ksp, right? So, for this compound, the equation for Ksp will be:

Ksp = [T2+]^3 [U3-]^2

Now, when you dissolve this compound, you are told that its solubility is 3.77 X 10^-20 mol/L. That means that 3.77 X 10^-20 moles of the compound dissolves in 1 L of solution.

Because of the formula of this compound, the concentration of T2+ ions will be 3(3.77 X 10^-20 mol/L) or 1.132X10-19. Likewise, the concentration of U3- ions will be 2(3.77X10^-20) or 7.54 X 10^-20.

Now, just put those values into the equation for Ksp and solve it. You will need to raise each one of these to their respective powers in the equation for Ksp in order to calculate Ksp.

Hope this helps. Message me if it doesn't.

Answer 2

You know that the generic Ksp equation for this compound would be:
Ksp = [T2+]^3[U3-]^2

now the only problem is that the problem doesnt DIRECTLY give you the values fo [T2+] and [U3-], but they do tell you that 3.77*10-20 moles of T3U2 will dissolve in 1 L water. If 3.77*10-20 moles of T3U2 dissolve in 1L of water you get 3*(3.77*10-20) moles of [T2+] (stoichiometric ratio) and 2*(3.77*10-20) moles of U3- that will be present in the 1 L of water. you can directly convert the moles of the ions to Molarity, since you assume 1L, and then you just plug those values into the Ksp equation.

i hope this helped!