If a saturated solution prepared by dissolving Ag2CO3 in water has [Ag+] = 2.56 x 10^-4 M, what is the value of Ksp for Ag2CO3?

Verified step by step guidance

1. Step 1: Write the balanced dissolution equation for Ag2CO3 in water: Ag2CO3(s) \rightleftharpoons 2Ag^+(aq) + CO3^{2-}(aq).
2. Step 2: Express the solubility product constant (Ksp) expression for the dissolution of Ag2CO3: K_{sp} = [Ag^+]^2[CO3^{2-}].
3. Step 3: Use the given concentration of [Ag^+] = 2.56 \times 10^{-4} \text{ M} to determine the concentration of CO3^{2-}. Since 2 moles of Ag^+ are produced for every mole of CO3^{2-}, [CO3^{2-}] = \frac{[Ag^+]}{2}.
4. Step 4: Substitute the values of [Ag^+] and [CO3^{2-}] into the Ksp expression: K_{sp} = (2.56 \times 10^{-4})^2 \times \left(\frac{2.56 \times 10^{-4}}{2}\right).
5. Step 5: Simplify the expression to find the value of Ksp.

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 Ag2CO3, Ksp can be calculated using the concentrations of Ag+ and CO3^2- ions at equilibrium.

Dissociation of Ionic Compounds

Ionic compounds dissociate into their constituent ions when dissolved in water. For silver carbonate (Ag2CO3), the dissociation can be represented as Ag2CO3(s) ⇌ 2Ag+(aq) + CO3^2-(aq). Understanding this dissociation is crucial for determining the concentrations of the ions in a saturated solution, which are necessary for calculating Ksp.

Saturation and Equilibrium

A saturated solution is one in which the maximum amount of solute has been dissolved at a given temperature, leading to a dynamic equilibrium between the dissolved ions and the undissolved solid. In this state, the rates of dissolution and precipitation are equal, allowing for the calculation of Ksp based on the concentrations of the ions present in the solution.