The molar solubility of ZnS is 1.6 × 10-10 M in pure water at a certain temperature. Calculate the Ksp for ZnS at this temperature.
The solubility product constant, Ksp, is defined as the product of the concentrations of the ions in a saturated solution of a compound. In the case of ZnS, it can be represented as:
ZnS (s) ⇌ Zn²⁺ (aq) + S²⁻ (aq)
The molar solubility of ZnS in pure water is given as 1.6 × 10^-10 M. This means that at equilibrium, the concentration of Zn²⁺ and S²⁻ ions in the solution is 1.6 × 10^-10 M.
Therefore, the Ksp for ZnS can be calculated as follows:
Ksp = [Zn²⁺] × [S²⁻]
Since the molar solubility of ZnS is 1.6 × 10^-10 M, the concentration of Zn²⁺ and S²⁻ ions is also 1.6 × 10^-10 M.
Ksp = (1.6 × 10^-10 M) × (1.6 × 10^-10 M)
Ksp = 2.56 × 10^-20 M²
Therefore, the Ksp for ZnS at this temperature is 2.56 × 10^-20 M².
To calculate the Ksp (solubility product constant), you need to determine the concentrations of the ions in the saturated solution. From the molar solubility of ZnS, which is 1.6 × 10^-10 M, we can assume that the equilibrium expression is:
ZnS(s) ⇌ Zn2+(aq) + S2-(aq)
Let's assume that 'x' represents the molar solubility of ZnS in moles per liter.
⇒ [Zn2+] = x M
⇒ [S2-] = x M
The Ksp expression for ZnS is:
Ksp = [Zn2+][S2-]
Since the stoichiometry of ZnS is 1:1, the equilibrium expression can be simplified to:
Ksp = (x)(x) = x^2
Substituting the value of the molar solubility (x = 1.6 × 10^-10 M) into the Ksp expression:
Ksp = (1.6 × 10^-10)^2
Calculating this expression:
Ksp = 2.56 × 10^-20
Therefore, the solubility product constant (Ksp) for ZnS at this temperature is 2.56 × 10^-20.