Ch.15 - Chemical Equilibrium

Problem 41

Chapter 15, Problem 41

Consider the interconversion of A molecules (red spheres) and B molecules (blue spheres) according to the reaction A ∆ B. Each of the series of pictures at the right represents a separate experiment in which time increases from left to right:(b) What is the value of the equilibrium constant Kc for the reaction A ∆ B?

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Count the number of A molecules (red spheres) and B molecules (blue spheres) in each image at equilibrium.

Calculate the concentration of A and B molecules for each experiment by dividing the number of molecules by the total number of molecules in the system.

Use the equilibrium concentrations to determine the equilibrium constant Kc for each experiment using the formula Kc = [B]/[A].

Average the Kc values obtained from each experiment to find the overall equilibrium constant for the reaction.

Verify the consistency of the calculated Kc values across different experiments to ensure accuracy.

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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 chemical reaction. For the reaction A ⇌ B, Kc is calculated as [B]/[A], where [B] and [A] are the molar concentrations of B and A, respectively. A larger Kc indicates a greater concentration of products at equilibrium, while a smaller Kc suggests a higher concentration of reactants.

Dynamic Equilibrium

Dynamic equilibrium occurs in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction, resulting in constant concentrations of reactants and products over time. In the context of the reaction A ⇌ B, this means that the interconversion between A and B continues, but the overall concentrations remain unchanged. Understanding this concept is crucial for determining the equilibrium constant.

Concentration Changes Over Time

In the series of images, the changes in the number of red (A) and blue (B) molecules over time illustrate how the concentrations of reactants and products evolve as the reaction progresses. By analyzing these changes, one can determine the point at which the system reaches equilibrium, which is essential for calculating Kc. Observing the relative amounts of A and B at equilibrium allows for the accurate determination of the equilibrium constant.

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Related Practice

Textbook Question

The reaction

2 PH31g2 + As21g2 ∆ 2 AsH31g2 + P21g2

has Kp = 2.9 * 10-5 at 873 K. At the same temperature,

what is Kp for each of the following reactions?

(a) 2 AsH31g2 + P21g2 ∆ 2 PH31g2 + As21g2

Textbook Question

Calculate the value of the equilibrium constant at 427 °C for the reaction

Na O1s2 + 1>2 O 1g2 ∆ Na O 1s2

given the following equilibrium constants at 427 °C.

Na2O1s2 ∆ 2 Na1l2 + 1>2 O21g2 Kc = 2 * 10-25 Na O 1s2 ∆ 2 Na1l2 + O 1g2 K = 5 * 10-29

Textbook Question

Calculate the value of the equilibrium constant for the reaction 4 NH31g2 + 3 O21g2 ∆ 2 N21g2 + 6 H2O1g2

given the following equilibrium constants at a certain temperature.

2 H21g2 + O21g2 ∆ 2 H2O1g2 Kc = 3.2 * 1081

N21g2 + 3 H21g2 ∆ 2 NH31g2 Kc = 3.5 * 108

Textbook Question

The reaction A2 + B ∆ A + AB has an equilibrium con-stant Kc = 2. The following pictures represent reaction mix- tures that contain A atoms (red), B atoms (blue), and A2 and AB molecules.

(a) Which reaction mixture is at equilibrium?

Textbook Question

The following pictures represent the initial state and the equilibrium state for the reaction of A₂ molecules (red) with B atoms (blue) to give AB molecules. (a) Write a balanced chemical equation for the reaction.

Textbook Question

Consider the reaction A + B ∆ AB. The vessel on the right contains an equilibrium mixture of A molecules (red spheres), B molecules (blue spheres), and AB molecules. If the stopcock is opened and the contents of the two vessels are allowed to mix, will the reaction go in the forward or reverse direction? Explain.