[Jinal613]

The solubility of silver sulfate, Ag2SO4, in water has been determined to be 8.0 g/L. What is the solubility in 0.27 M sodium sulfate, Na2SO4?


Well, I know that you have to find the Ksp from the 8.0 g/L (by changing it in Molarity first) and then use that Ksp to find the answer from 0.27 M. But when I do it, I keep the getting the wrong answer, or that's what Webassign keeps telling me. I get 4.9 g/L and apparently it's wrong.

Can you guys PLEASE show me the exact steps??

[Borek]

Looks like you forgot that [Ag⁺] is not the same as concentration of dissolved silver sulfate. Think dissolution stoichiometry.

[lancenti]

The solubility of silver sulfate, Ag₂SO₄, in water has been determined to be 8.0 g/L. What is the solubility in 0.27 M sodium sulfate, Na₂SO₄?

M_r of Ag₂SO₄ = 2(108) + 32.1 + 4(16.0) = 312.1

Then Solubility = 0.0256 M
Ag₂SO₄ (s)  <-> 2 Ag⁺ (aq) + SO₄^2- (aq)

[Ag⁺] = 0.0512 M
[SO₄^2-] = 0.0256 M

Then
K_sp = [Ag⁺]²[SO₄^2-]
K_sp = [0.0512]²[0.0256]
K_sp = 6.71 x 10^-5 mol³dm^-9

Solid <-> Silver + Sulphate
  -             -         0.27          - Initial
  -            2x        0.27 + x     - Equilibrium

K_sp = 4x²(0.27 + x)
... from here on out it's just math.

[Jinal613]

Ahh. So I was getting the wrong answer because I rounded off the molar masses wrong, which pretty much threw off all the answers following it.
Also, dont forget that the -x from 0.27-x would be neglected because the Ksp value is not close to the initial concentration.

Therefore, it would be:
Ksp = (4x^2)(0.27), giving me x=7.9x10^(-3) moles/L = [Ag+] = 2.5 g/L as the final answer

Webassign finally said it was correct. Thanks!

[Borek]

Ahh. So I was getting the wrong answer because I rounded off the molar masses wrong

Judging from numbers you forgot that solubility of the silver sulfate is half that of silver concentration in the saturated solution, that has nothing to do with rounding errors.

However, I think there are rounding errors in lancenti post - one should not round down intermediate results, seems to me that's what lancenti did.

[lancenti]

Typically, we should be working with more than 3 significant figures in intermediates (usually 4 or 5 for A-Levels) but since you were going to do it again, I figured giving everything to 3 SF would be fine.

[Jinal613]

I think you are right Borek. I looked over my previous work and realized that the problem was in the second ICE table. I was writing the Ksp equation as x²(0.27-x), instead of (2x)²(027-x).

I also realized that rounding wasn't a problem. It came out to be the same numbers even with the molar mass I originally determined.