If the solubility product of CuS is 6 × 10–16, calculate the maximum molarity of CuS in aqueous solution.

To determine the maximum molarity of copper(II) sulfide (CuS) in an aqueous solution using its solubility product (Ksp), we can follow a systematic approach. The solubility product constant is a measure of the extent to which a compound can dissolve in water, and it is defined for the equilibrium between a solid and its ions in solution.

Understanding the Dissolution of CuS

When CuS dissolves in water, it dissociates into its constituent ions:

• CuS (s) ⇌ Cu²⁺ (aq) + S^2- (aq)

For this equilibrium, the solubility product expression (Ksp) can be written as:

• Ksp = [Cu²⁺][S^2-]

Setting Up the Calculation

Let’s denote the solubility of CuS in moles per liter (M) as 's'. When CuS dissolves, it produces 's' moles of Cu²⁺ and 's' moles of S^2-. Therefore, we can express the concentrations of the ions at equilibrium as:

• [Cu²⁺] = s
• [S^2-] = s

Substituting these values into the Ksp expression gives us:

• Ksp = s × s = s²

Calculating Maximum Molarity

Given that the solubility product (Ksp) of CuS is 6 × 10^-16, we can set up the equation:

• s² = 6 × 10^-16

To find 's', we take the square root of both sides:

• s = √(6 × 10^-16)

Performing the Calculation

Calculating the square root:

• s = √(6) × 10^-8
• s ≈ 2.45 × 10^-8 M

Final Result

Thus, the maximum molarity of CuS in an aqueous solution, based on its solubility product, is approximately:

• 2.45 × 10^-8 M

This means that in a saturated solution of CuS, the concentration of Cu²⁺ and S^2- ions will each be around 2.45 × 10^-8 moles per liter. This low solubility reflects the strong ionic bond in CuS, which limits its dissolution in water.