Two salts A₂X and MX have the same value of solubility product of 4.0 × 10⁻¹². The ratio of their molar solubilities i.e. S(A₂X)/S(MX) = __________. (Round off to the Nearest Integer)

Solution

Chemistry ma’am · 3 steps

Same Ksp does not mean same solubility: write each salt's Ksp in terms of S, then solve separately.

1. Salt A2X. A₂X ⇌ 2A⁺ + X²⁻ gives [A⁺] = 2S and [X²⁻] = S. So Kₛₚ = (2S)² × S = 4S³.

   4S³ = 4.0 × 10⁻¹² ⇒ S³ = 1.0 × 10⁻¹² ⇒ S(A₂X) = 1.0 × 10⁻⁴ mol L⁻¹

2. Salt MX. MX ⇌ M⁺ + X⁻ gives Kₛₚ = S². So S² = 4.0 × 10⁻¹² and S(MX) = 2.0 × 10⁻⁶ mol L⁻¹.
3. So. The ratio is (1.0 × 10⁻⁴)/(2.0 × 10⁻⁶) = 50, so the answer is 50.

The common slip: 79. Writing Kₛₚ = S³ for A₂X forgets that [A⁺] = 2S is squared. That gives S = 1.59 × 10⁻⁴ and a ratio of about 79, not 50.

The idea to keep. Never compare solubilities by comparing Kₛₚ values when the salts give different numbers of ions. Write Kₛₚ in terms of S for each salt, including the coefficient raised to its power.

Answer from the NTA final answer key. Solution by PrepWiser.