JEE Main 2025 · 24 January · morning · Single correct · +4 / −1

Kₛₚ for Cr(OH)₃ is 1.6 × 10⁻³⁰. What is the molar solubility of this salt in water?

  1. (a) ⁵√(1.8 × 10⁻³⁰)
  2. (b) (1.8 × 10⁻³⁰)/27
  3. (c) ∜((1.6 × 10⁻³⁰)/27)
  4. (d) √(1.6 × 10⁻³⁰)
Answer and solution

Answer (c) ∜((1.6 × 10⁻³⁰)/27)

Solution

Chemistry ma’am · 3 steps

Write the ions first: one Cr³⁺ and three OH⁻, and that 3 gets cubed.

  1. Set up the dissolution. If s mol of Cr(OH)₃ dissolves per litre, Cr(OH)₃ ⇌ Cr³⁺ + 3OH⁻ gives [Cr³⁺] = s and [OH⁻] = 3s.
  2. Write Ksp. Each concentration is raised to the power of its coefficient, so the hydroxide term is (3s)³ = 27s³.

    Kₛₚ = s (3s)³ = 27s⁴ ⇒ s = ∜(Kₛₚ/27)

  3. So. s = ∜((1.6 × 10⁻³⁰)/27) ≈ 1.56 × 10⁻⁸ mol L⁻¹, which is option (c).

The idea to keep. For a salt that gives x cations and y anions, Kₛₚ = xˣ yʸ sˣ⁺ʸ. Count the ions, and that total sets the root you take.

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

Study Ionic Equilibrium

Asked about 100 times in JEE Main since 2020. This question is from 2025.