Which Ion Precipitates Last as Na2SO4 Is Added?

[Macroer]

Homework Statement

1. A 1L solution contains 0.1M of each Pb⁺²,Ca⁺², and Sr⁺². Which ion precipitates last as Na₂SO₄ is slowly added with no change in volume?
2. What is the concentration of the ion that precipitates first when the second ion precipitates?

Given:
Ksp PbSO₄=1.8x10^-8
Ksp CaSO₄=7.1x10^-5
Ksp SrSO₄=3.4x10^-7

Homework Equations

The Attempt at a Solution

1. Pb2+ precipitates first as it has the lowest Ksp value.
2. This is where i get stuck. I know SrSO4 is the second ion to precipitate. I get:
ksp=[Sr²⁺][SO₄^2-]
4x10^-7=[Sr²⁺][SO₄^2-]

Don't know where to go from here. Help is appreciated.

 

[Borek]

Not sure what your problem is - so far you are right, Pb will precipitate first, Sr second. Not many possibilities left at this stage.

Think about it this way - calculate (knowing cation concentrations) at what concentration of SO₄^2- they will precipitate. Obviously when you add sulfate concentration of SO₄^2- can only go up starting from zero, so when you sort cations according to concentration of sulfate at which they start to precipitate, you have your answer. Not surprisingly, as concentrations of cations are identical, list you are looking for will not differ from just the sorted list of Ksp values.

--
methods

 

[Macroer]

So...
ksp=[Sr²⁺][SO₄^2-]
3.4x10^-7=[Sr²⁺][SO₄^2-]
3.4x10^-7=[0.1M][SO₄^2-]
[SO₄^2-]=3.4x10^-6M

Now in Pb²⁺
1.8x10^-8=[Pb²⁺][SO₄^2-]
1.8x10^-8=[Pb²⁺][3.4x10^-6M]
[Pb²⁺]=5.29x10^-3M

Is this how i do it, or do i have to set up an ICE table?

 

[Borek]

No, you got it wrong. Strontium sulfate starts to precipitate when sulfate concentration is as you have calculated, that's OK. At this moment nothing else can precipitate. But then, when you add more sodium sulfate, strontium is removed from the solution and concentration of free SO₄^2- goes up - till it is high enough to precipitate next cation.

--
methods

 

[DeeNos]

The concentration of the ion that precipitates first when the second ion precipitates depends on the relative solubility product (Ksp) values of the two ions. In this case, PbSO4 has a lower Ksp value than SrSO4, which means it is less soluble and will precipitate first. However, the concentration of the first ion to precipitate will also depend on the initial concentrations of all three ions in solution. Without this information, it is not possible to determine the exact concentration of the first ion to precipitate.