Show the equilibrium expression for the above equilibrium and state the unit of the equilibrium constant in terms of mol dm-3

Question

Barium sulfate (BaSO₄) is widely used as a contrast agent in the body for diagnoses

of certain disorders in the digestive system. Barium sulfate can barely dissolve in

water following the chemical equilibrium below.

BaSO₄(s) ⇌ Ba²⁺(aq) + SO₄^2-(aq)

Given the solubility product (K_sp) of BaSO₄ is 1.0842x10^-10 at 25^oC with appropriate units.

a) Show the equilibrium expression for the above equilibrium and state the unit of the equilibrium constant in terms of mol dm^-3

(b) A technician wants to evaluate the solubility of barium sulfate (BaSO4) in aqueous solution. He accidentally added 0.0152M potassium sulfate (K2SO4) into the solution before the addition of 3.52g barium sulfate (BaSO4) solids into the solution. Given the total volume of the solution is 80.00mL, please evaluate the molarity of barium ions (Ba2+) in the resulting solution.

Answer 1

BaSO₄(s) ⇌ Ba²⁺(aq) + SO₄^2-(aq) ... Ksp = 1.0842x10^-10

(a) K = [Ba²⁺][SO₄^2-]

units are M² = (mol dm^-3)²

(b) Common ion effect:

[Ba2+] = 3.52 g BaSO4 x 1 mol / 233.4 g = 0.0151 mols / 0.08 L = 0.189 M

[SO42-] = 0.0152 M + 0.189 M = 0.204 M

Q = (0.189)(0.204) = 0.0385 which is greater than Ksp so a ppt will form

1.0842x10^-10 = [Ba²⁺][SO₄^2-] = (x)(0.204]

x = 5.31x10^-10 M = [Ba²⁺]