At 25°C, the reaction CaCrO₄(𝑠) ⇌ Ca²⁺(𝑎𝑞) + CrO₄²⁻(𝑎𝑞) has an equilibrium constant 𝐾_𝑐= 7.1×10⁻⁴. What are the equilibrium concentrations of Ca²⁺ and CrO₄²⁻ in a saturated solution of CaCrO₄?

검증된 단계별 안내

Identify the reaction and write the equilibrium expression. For the dissolution of CaCrO4, the reaction is: CaCrO4(s) ⇌ Ca2+(aq) + CrO42−(aq). The equilibrium expression is Kc = [Ca2+][CrO42−].

Set up an ICE table (Initial, Change, Equilibrium) to track the concentrations of the ions. Initially, the concentrations of Ca2+ and CrO42− are 0. Let x be the change in concentration of Ca2+ and CrO42− as CaCrO4 dissolves.

At equilibrium, the concentrations of Ca2+ and CrO42− will both be x. Substitute these values into the equilibrium expression: Kc = x * x = x^2.

Solve for x by taking the square root of both sides of the equation Kc = x^2. This gives x = sqrt(Kc).

Substitute the value of Kc (7.1×10−4) into the equation for x to find the equilibrium concentrations of Ca2+ and CrO42−.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction CaCrO₄(s) ⇌ Ca²⁺(aq) + CrO₄²⁻(aq), Kc indicates how far the reaction favors the formation of products. A small Kc value, like 7.1×10⁻⁴, suggests that at equilibrium, the concentration of reactants is much higher than that of products.

Saturated Solution

A saturated solution is a solution that contains the maximum concentration of a solute that can dissolve at a given temperature and pressure. In the context of the reaction, a saturated solution of CaCrO₄ means that the solution has reached a point where no more CaCrO₄ can dissolve, and the concentrations of Ca²⁺ and CrO₄²⁻ ions are at their equilibrium values, determined by the Kc of the reaction.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations, changes in concentrations, and equilibrium concentrations of reactants and products in a chemical reaction. For the given reaction, the ICE table helps to set up the relationship between the initial concentration of CaCrO₄, the changes in concentrations of Ca²⁺ and CrO₄²⁻ as the system reaches equilibrium, and ultimately allows for the calculation of their equilibrium concentrations using the Kc value.

At 25°C, the reaction CaCrO4(𝑠) ⇌ Ca2+(𝑎𝑞) + CrO42−(𝑎𝑞) has an equilibrium constant 𝐾𝑐 = 7.1×10−4. What are the equilibrium concentrations of Ca2+ and CrO42− in a saturated solution of CaCrO4?