To a saturated aqueous solution of barium carbonate is added just enough sodium sulfate to achieve a maximum sulfate concentration without precipitation of barium sulfate.If no complexes form and the "salt effect" is negligible,what is the concentration of the sulfate ion in this solution? [K_sp for barium carbonate is 1.6 × 10^-9;K_sp for barium sulfate is 7.9 × 10^-11]

Question

Quizplus · Accepted Answer

The chemical equation for the reaction between barium carbonate and sodium sulfate is:

BaCO3(s) + Na2SO4(aq) → BaSO4(s) + Na2CO3(aq)

The solubility product constant, Ksp, for barium carbonate is given as:

Ksp for BaCO3 = [Ba2+][CO32-] = 1.6 × 10-9

Since it is a saturated solution, the concentration of [Ba2+] can be considered equal to the solubility of barium carbonate, which is the square root of its Ksp:

[Ba2+] = [CO32-] = (Ksp for BaCO3)1/2
[Ba2+] = [CO32-] = (1.6 × 10-9)1/2 = 1.26 × 10-5 M

Now, the reaction between Ba2+ and SO42- is:

Ba2+(aq) + SO42-(aq) → BaSO4(s)

The solubility product constant, Ksp, for barium sulfate is given as:

Ksp for BaSO4 = [Ba2+][SO42-] = 7.9 × 10-11

If no precipitation of barium sulfate occurs, the concentration of Ba2+ and SO42- would be in equilibrium, and their product would be equal to the Ksp for barium sulfate:

[Ba2+][SO42-] = Ksp for BaSO4 
(1.26 × 10-5 M)(x) = 7.9 × 10-11 
x = 6.27 × 10-6 M

Therefore, the concentration of the sulfate ion in the solution is 6.27 × 10-6 M, which is closest to choice C, 2.0 × 10-6 M.

To a Saturated Aqueous Solution of Barium Carbonate Is Added