(b) If Ksp = 1.1 * 10-12 for Ag2CrO4, what are the molar concentrations of Ag+ and CrO4 2-in solution?

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Identify the dissolution equation for Ag2CrO4: Ag2CrO4(s) \(\rightleftharpoons\) 2Ag^+(aq) + CrO_4^{2-}(aq).

Write the expression for the solubility product constant (K_{sp}): K_{sp} = [Ag^+]^2[CrO_4^{2-}].

Let the solubility of Ag2CrO4 be 's'. Then, [Ag^+] = 2s and [CrO_4^{2-}] = s.

Substitute the expressions for [Ag^+] and [CrO_4^{2-}] into the K_{sp} expression: K_{sp} = (2s)^2(s) = 4s^3.

Set the K_{sp} expression equal to the given K_{sp} value and solve for 's': 4s^3 = 1.1 \(\times\) 10^{-12}.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solubility Product Constant (Ksp)

The solubility product constant (Ksp) is an equilibrium constant that applies to the solubility of sparingly soluble ionic compounds. It represents the product of the molar concentrations of the ions in a saturated solution, each raised to the power of their coefficients in the balanced dissolution equation. For Ag2CrO4, Ksp = [Ag+]^2[CrO4^2-], which allows us to relate the concentrations of the ions to the Ksp value.

Dissociation of Ionic Compounds

Ionic compounds dissociate into their constituent ions when they dissolve in water. For Ag2CrO4, the dissociation can be represented as Ag2CrO4(s) ⇌ 2Ag+(aq) + CrO4^2-(aq). This means that for every mole of Ag2CrO4 that dissolves, two moles of Ag+ and one mole of CrO4^2- are produced, which is essential for calculating their concentrations in solution.

Stoichiometry in Solutions

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction. In the context of this question, it helps us determine the molar concentrations of Ag+ and CrO4^2- based on the Ksp value and the stoichiometric ratios from the dissociation equation. By setting up the relationship between the concentrations and Ksp, we can solve for the unknown concentrations.

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