Use the following solubility data to calculate a value of K_sp for each compound. (c) MgC₂O₄: 0.094 g/L (d) Zn(CN)₂; 4.95 x 10^-4 g/L

Verified step by step guidance

1. Step 1: Convert the solubility from grams per liter to moles per liter (molarity, M) for Zn(CN)2. Use the molar mass of Zn(CN)2 to do this conversion. The molar mass of Zn(CN)2 can be calculated by adding the atomic masses of Zinc (Zn) and twice that of Cyanide (CN).
2. Step 2: Write the dissolution equation for Zn(CN)2. When Zn(CN)2 dissolves in water, it dissociates into Zinc ions (Zn2+) and Cyanide ions (CN-). The balanced chemical equation is: Zn(CN)2(s) \rightarrow Zn^{2+}(aq) + 2CN^{-}(aq).
3. Step 3: Express the solubility product constant (Ksp) for Zn(CN)2. Based on the stoichiometry of the dissolution equation, if 's' is the solubility of Zn(CN)2 in moles per liter, then the concentration of Zn2+ is 's' and the concentration of CN- is '2s'.
4. Step 4: Substitute the concentrations into the expression for Ksp. The Ksp expression for Zn(CN)2 is Ksp = [Zn^{2+}][CN^{-}]^2. Replace [Zn^{2+}] with 's' and [CN^{-}] with '2s'.
5. Step 5: Calculate the Ksp using the values obtained from the previous steps. Simplify the expression to find the Ksp in terms of 's', which is the molarity of Zn(CN)2.

Key Concepts

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that quantifies the solubility of a sparingly soluble ionic compound. It is defined as the product of the molar concentrations of the ions, each raised to the power of their coefficients in the balanced dissolution equation. For example, for Zn(CN)2 dissolving into Zn²⁺ and 2CN⁻, Ksp = [Zn²⁺][CN⁻]².

Molarity and Concentration

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. To calculate Ksp from solubility data, it is essential to convert the given solubility (in g/L) into molarity by dividing the mass of the solute by its molar mass and then adjusting for the volume of the solution. This conversion allows for accurate representation of ion concentrations in the Ksp expression.

Dissociation of Ionic Compounds

When ionic compounds dissolve in water, they dissociate into their constituent ions. For Zn(CN)2, the dissociation can be represented as Zn(CN)2(s) ⇌ Zn²⁺(aq) + 2CN⁻(aq). Understanding this dissociation is crucial for determining the concentrations of the ions involved, which are necessary for calculating the Ksp value accurately.