Calculate the molar solubility of MnS in a 0.30 M NH4Cl - 0.50 M NH3 buffer solution that is saturated with H2S ([H2S] ≈ 0.10 M). What is the solubility of MnS (in g/L)? (Ksp for MnS is 3 x 10^-7.)

Verified step by step guidance

1. Identify the relevant chemical equilibria: MnS(s) ⇌ Mn²⁺(aq) + S²⁻(aq) and H₂S(aq) ⇌ H⁺(aq) + HS⁻(aq).
2. Use the given Ksp value for MnS to express the solubility product: Ksp = [Mn²⁺][S²⁻].
3. Recognize that the buffer solution affects the concentration of S²⁻ through the equilibrium of H₂S, which is influenced by the NH₄Cl and NH₃ buffer.
4. Calculate the concentration of S²⁻ using the equilibrium expression for H₂S and the buffer's pH, considering the common ion effect.
5. Substitute the calculated [S²⁻] into the Ksp expression to solve for the molar solubility of MnS, and then convert this to solubility in g/L using the molar mass of MnS.

Key Concepts

Molar Solubility

Molar solubility refers to the maximum amount of a solute that can dissolve in a given volume of solvent at equilibrium, expressed in moles per liter (M). It is crucial for understanding how much of a compound can dissolve in a solution, especially when considering the effects of common ions and pH on solubility.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced equation. For MnS, Ksp = [Mn^2+][S^2-], and knowing Ksp helps in calculating the molar solubility in different conditions.

Buffer Solutions

Buffer solutions are mixtures that resist changes in pH upon the addition of small amounts of acids or bases. In this case, the NH4Cl-NH3 buffer system helps maintain a stable pH, which can influence the solubility of MnS by affecting the concentration of sulfide ions (S^2-) in solution, thereby impacting the equilibrium established by the Ksp.