[ch3mical]

Hi,

I have attempted the question below.

Q) The solubility of barium sulphate after adding 1mL of 10M H₂SO₄ is 1.6E-8M. The volume of your solution is 1000mL. Calculate the solubility of barium sulphate in a saturated solution before the addition of H₂SO₄.

My attempt
BaSO₄ Ba²⁺ + SO₄^2-

We are told that [BaSO₄] = 1.6E-8M. The concentration of sulphate ions from the H₂SO₄ is 10M×1mL/1000mL=0.01M

I know that K_sp = [Ba²⁺][SO₄^2-], so I can say that
K_sp = (x)(0.01 + x)

I don't know how to proceed. Please advise.

Thanks.

[Orcio_87]

1. Aproximate that all SO₄^2- comes from dissociation of H₂SO₄, not BaSO₄.
2. Calculate K_sp.
3. Calculate solubility of the BaSO₄.

[ch3mical]

1. Aproximate that all SO₄^2- comes from dissociation of H₂SO₄, not BaSO₄.
2. Calculate K_sp.
3. Calculate solubility of the BaSO₄.

Many thanks for the pointers! I will try to apply it as follows...

1. We have 0.01M of H₂SO₄, so I will assume the total [SO₄^2-] = 0.01M

2. K_sp = [Ba²⁺][SO₄^2-] = 1.6E-8 × 0.01 = 1.6E-9

3. I am not sure how to perform this step. Is it [BaSO₄] = (1.6E-9)^0.5 = 4E-5M ?

My approach in step 3 feels wrong as I haven't taken into account the absence of H₂SO₄. Could you please clarify how to do this, and why it's correct?

[Orcio_87]

Absence of H₂SO₄ in don't important. For me it is the correct solution.

[Borek]

There is no such thing as

the absence of H₂SO₄

if the solution is said to be saturated with respect to BaSO₄ - that means there is a solid BaSO₄ present and the dissolution produces SO₄^2-.

But there is another problem with this question and your solution.

1. We have 0.01M of H₂SO₄, so I will assume the total [SO₄^2-] = 0.01M

While this is a common approximation, it is wrong in general. pK_a2 for sulfuric acid equals 2, that means is 0.01 M solution (which has pH close to 2 - compare that with pK_a2) not all HSO₄^- is dissociated, and the concentration of SO₄^2- is substantially lower (actually below 0.005 M).

No idea if you are expected to take that into account, but if you ignore you are making an over 100% error in the final answer, hardly negligible.

[mjc123]

Also 1.6E-8 * 0.01 is not 1.6E-9.

[ch3mical]

Thank you all.