What is the solubility of RaSO4 in 0.1381M Na2SO4? Ksp = 4.3x10^-11?

RaSO4 ==> Ra^+2 + SO4^-2

Ksp = (Ra^+2)(SO4^-2).
If you let S = solubility RaSO4, then
Ra^+2 = S
SO4^-2 = S from RaSO4 and 0.1381 M in Na2SO4 so a total of (S + 0.1381)
Substitute those values into Ksp expression and solve for S.

Ksp = [Ra^+2][SO4^-2]

4.3x10^-11 = [x][x]
x=6.56x10^-6

6.56x10^-6 + .1381??

is that how im suppose to do it?

No.

4.3 x 10^-11 = (x)(x+0.1381)
solve for x.
NOTE:
If you solve the equation as I wrote it you will need to solve a quadratic. Those are usually easy to do with modern calculators; however, you CAN make a simplifying assumption. You make the assumption that x + 0.1381 = 0.1381 (that is, that x is so small in comparison to 0.1381 that when added it isn't different than 0.1381). The equation then would look like this.
4.3 x 10^-11 = (x)(0.1381) and solve for x. When you finish, then look at x+0.1381 and see how far it is from 0.1381. If x is so small that x+0.1381 is just 0.1381, then the assumption is ok. If not, the assumption is not ok and you must solve the quadratic. I ALWAYS make the assumption first and solve the easy equation, then check at the end and see if the assumption is ok.

thanks a bunch!

To determine the solubility of RaSO4 in 0.1381M Na2SO4, we need to use the concept of the solubility product constant (Ksp). The Ksp value represents the equilibrium constant for the dissolution of a sparingly soluble compound.

1. Write the balanced equation for the dissolution of RaSO4:
RaSO4 (s) ⇌ Ra2+ (aq) + SO4^2- (aq)

2. Write the expression for the solubility product constant (Ksp):
Ksp = [Ra2+][SO4^2-]

3. Determine the molar solubility of RaSO4. Let's assume it to be "x" mol/L.
[Ra2+] = x
[SO4^2-] = x

4. Since the stoichiometry of RaSO4 is 1:1, the concentrations of Ra2+ and SO4^2- are the same.

5. Substitute the concentrations into the Ksp expression:
Ksp = x * x
Ksp = x^2

6. Plug in the value of Ksp (4.3x10^-11) into the equation and solve for x:
4.3x10^-11 = x^2

7. Take the square root of both sides to solve for x:
x = √(4.3x10^-11)

8. Calculate the solubility (x) using a calculator:
x ≈ 6.56x10^-6 mol/L

Therefore, the solubility of RaSO4 in 0.1381M Na2SO4 is approximately 6.56x10^-6 mol/L.