A saturated aqueous solution of Ag2SO3 contains 3.2x10-5 M Ag+. What is the solubility-product equilibrium constant for Ag2SO3? A) 2.0x10-2 B) 1.6x10-2 C) 1.3x10-13 D) 1.6x10-14 E) 4.1x10-15

D) 1.6 x 10⁻¹⁴

Explanation:

The solubility-product equilibrium constant for Ag₂SO₃ is given by the expression

Ksp = [Ag⁺]² [SO₃²⁻]

where [Ag⁺] and [SO₃²⁻] are the concentration of the species dissolved in solution for the equlibrium

Ag₂SO₃ (s) ⇄ 2 Ag⁺ + SO₃²⁻

we are given the concentration of Ag⁺ and from the stoichiometry of the equilibrium, the concentration of SO₃²⁻ is half that value, so

[Ag⁺]² = 3.2 x 10⁻⁵ M

[SO₃²⁻] = 3.2 x 10⁻⁵ M / 2 = 1.6 x 10⁻⁵ M

plugging these values into the solubility product constant equation we have

Ksp = (3.2 x 10⁻⁵) ² x (1.6 x 10⁻⁵) = 1.6 x 10¹⁴

Therefore D is the correct answer.