Ch.15 - Chemical Equilibrium

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.15 - Chemical Equilibrium

Problem 58

Chapter 15, Problem 58

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?

Verified step by step guidance

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−.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

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.

Recommended video:

Guided course

01:14

ICE Charts and Equilibrium Amount

Related Practice

Textbook Question

Consider the following equilibrium, for which Δ𝐻<0

2 SO₂(𝑔) + O₂(𝑔) ⇌ 2 SO₃(𝑔)

(f) How will each of the following changes affect an equilibrium mixture of the three gases: SO₃(𝑔) is removed from the system?

Textbook Question

At 80°C, 𝐾_𝑐= 1.87×10⁻³ for the reaction PH₃BCl₃(𝑠) ⇌ PH₃(𝑔) + BCl₃(𝑔) (a) Calculate the equilibrium concentrations of PH₃ and BCl₃ if a solid sample of PH₃BCl₃ is placed in a closed vessel at 80°C and decomposes until equilibrium is reached. (b) If the flask has a volume of 0.250 L, what is the minimum mass of PH₃BCl₃(𝑠) that must be added to the flask to achieve equilibrium?

Textbook Question

Consider the following equilibrium, for which Δ𝐻<0

2 SO₂(𝑔) + O₂(𝑔) ⇌ 2 SO₃(𝑔)

(e) the total pressure of the system is increased by adding a noble gas

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?

Verified video answer for a similar problem:

Key Concepts

Equilibrium Constant (Kc)

Saturated Solution

ICE Table (Initial, Change, Equilibrium)

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?