Question

If calcium sulfate and barium sulfate do not form mixed crystals (i.e. they only form 1:1 species), what is the maximum fraction of the barium ion that can be precipitated as the sulfate from a solution that is initially 0.080 M in Ba2+ and 0.100 M in Ca2+, before the precipitation of calcium sulfate starts? For BaSO4, Ksp = 1.1 x 10-10, for CaSO4, Ksp = 2.4 x 10-5

Answer 1

First note that since the (K_SP) of BaSO₄ is very less as compared to that of CaSO₄ ; it means that BaSO₄ is less likely to dissolve or will form precipitate first as compared to CaSO₄ . Therefore, the first precipitate of CaSO₄ will only be formed after some BaSO₄ has already been precipitated. This is what is being asked in the question.

At the instant when first CaSO₄ precipitate is formed ;

Concentration of Ca²⁺ = 0.1 M

From definition of K_{SP ,} we have

[Ca²⁺][SO₄^2-] = 2.4 * 10^-5

0.1M * [SO₄^2-] = 2.4 * 10^-5

=> [SO₄^2-] = 2.4 * 10^-4 M

Thus, concentration of [SO₄^2-] when CaSO₄^2- begins to precipitate is 2.4 * 10^-4 M .

Using K_SP for BaSO₄^2- as [Ba²⁺][SO₄^2-] = 1.1* 10^-10

Since, [SO₄^2-] = 2.4 * 10^-4 M

=> [Ba²⁺] = 1.1* 10^-10/ 2.4 * 10^-4

[Ba²⁺] = 4.6 * 10^-7 M

Fraction of [Ba²⁺] that is now present in the solution = 4.6 * 10^-7 M / 0.8 M = 5.75 * 10 ^-7 (Apparently all Ba²⁺precipitated)

The fraction thus that can be precipitated will be (0.80 - 4.6 * 10^-7 )/0.8 = 1

Required Ans = 1