Question 37 of 50intermediate🔧 ApplyNumerical2 marks

If the solubility product of CuS is 6×6 \times 10^{-16}$$, calculate the maximum molarity of CuS in aqueous solution.

Correct Answer

The maximum molarity of CuS in aqueous solution is 2.45×102.45 \times 10⁻⁸ mol L⁻¹.

Exercise: EXERCISES | Q: 1.27 | (Page 29)
For More Understanding

Explanation

This question tests the concept of solubility product (Ksp) and its relationship with solubility. For a sparingly soluble salt like CuS, the solubility product is the product of molar concentrations of ions at equilibrium. Since CuS dissociates into Cu²⁺ and S²⁻ in a 1:1 ratio, the concentration of each ion equals the solubility 's'. Thus, Ksp = s², and solubility can be found by taking the square root of Ksp.

Solution Steps

  1. Step 1: Write the dissociation equilibrium for CuS: CuS(s) ⇌ Cu²⁺(aq) + S²⁻(aq)

  2. Step 2: Express Ksp in terms of solubility 's': If solubility of CuS is s mol L⁻¹, then [Cu²⁺] = s and [S²⁻] = s. Therefore, Ksp = [Cu²⁺][S²⁻] = s × s = s²

  3. Step 3: Substitute the given value: s² = 6×106 \times 10⁻¹⁶

  4. Step 4: Calculate solubility: s = \sqrt{$$6 \times 10$$⁻¹⁶} = √6×106 \times 10⁻⁸ = 2.45×102.45 \times 10⁻⁸ mol L⁻¹

  5. Step 5: The maximum molarity of CuS equals its solubility = 2.45×102.45 \times 10⁻⁸ M

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