Final answer:
To determine the grams of Zn(CN)₂(s) soluble in 100 mL of H₂O, we can use the balanced reaction and Ksp expression. However, the concentration of CN⁻ in the solution is needed to complete the calculation.
Step-by-step explanation:
To determine the number of grams of Zn(CN)₂(s) that would be soluble in 100 mL of H₂O, we can use the balanced reaction and the expression for Ksp.
The balanced reaction for the dissolution of Zn(CN)₂(s) in water is:
Zn(CN)₂(s) → Zn²⁺(aq) + 2CN⁻(aq)
The expression for Ksp is:
Ksp = [Zn²⁺][CN⁻]²
Given that the Ksp value for Zn(CN)₂(s) is 3.0 × 10⁻¹⁶, we can calculate the number of moles of Zn²⁺ and CN⁻ ions in 100 mL (0.1 L) of water:
Moles of Zn²⁺ = Ksp / [CN⁻]² = (3.0 × 10⁻¹⁶) / ([CN⁻]²)
Since Zn(CN)₂ is a 1:2 electrolyte, the moles of CN⁻ is twice the moles of Zn(CN)₂. Therefore, moles of Zn(CN)₂ = 0.5 * Moles of Zn²⁺.
Finally, we can calculate the number of grams of Zn(CN)₂(s) using the molar mass of Zn(CN)₂:
Grams of Zn(CN)₂ = Moles of Zn(CN)₂ * Molar mass of Zn(CN)₂
Plugging in the values, we get:
Grams of Zn(CN)₂ = 0.5 * (3.0 × 10⁻¹⁶) / ([CN⁻]²) * 117.44 g/mol
To solve for [CN⁻]², we need to know the concentration of CN⁻ in the solution. Without that information, we cannot calculate the grams of Zn(CN)₂ that would be soluble in 100 mL of H₂O.