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.

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