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Ch.15 - Chemical Equilibrium
All textbooksMcMurry 8th EditionCh.15 - Chemical EquilibriumProblem 101
Chapter 15, Problem 101

A 5.00-L reaction vessel is filled with 1.00 mol of H2, 1.00 mol of I2, and 2.50 mol of HI. Calculate the equilibrium concentrations of H2, I2, and HI at 500 K. The equilibrium constant Kc at 500 K for the reaction H2(g) + I2(g) ⇌ 2 HI(g) is 129.

Verified step by step guidance
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Step 1: Write the balanced chemical equation for the reaction: \( \text{H}_2(g) + \text{I}_2(g) \rightleftharpoons 2 \text{HI}(g) \).
Step 2: Set up the expression for the equilibrium constant \( K_c \) for the reaction: \( K_c = \frac{[\text{HI}]^2}{[\text{H}_2][\text{I}_2]} \).
Step 3: Define the initial concentrations of the reactants and products. Since the volume of the vessel is 5.00 L, calculate the initial concentrations: \([\text{H}_2]_0 = \frac{1.00 \text{ mol}}{5.00 \text{ L}}\), \([\text{I}_2]_0 = \frac{1.00 \text{ mol}}{5.00 \text{ L}}\), \([\text{HI}]_0 = \frac{2.50 \text{ mol}}{5.00 \text{ L}}\).
Step 4: Assume a change in concentration \( x \) for the reactants and products as the system reaches equilibrium. Express the equilibrium concentrations in terms of \( x \): \([\text{H}_2] = [\text{H}_2]_0 - x\), \([\text{I}_2] = [\text{I}_2]_0 - x\), \([\text{HI}] = [\text{HI}]_0 + 2x\).
Step 5: Substitute the equilibrium concentrations into the \( K_c \) expression and solve for \( x \): \( 129 = \frac{([\text{HI}]_0 + 2x)^2}{([\text{H}_2]_0 - x)([\text{I}_2]_0 - x)} \). Solve this equation to find the value of \( x \), and then calculate the equilibrium concentrations of \( \text{H}_2 \), \( \text{I}_2 \), and \( \text{HI} \).

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 H2(g) + I2(g) ⇌ 2 HI(g), Kc is calculated using the formula Kc = [HI]^2 / ([H2][I2]). A higher Kc value indicates that the products are favored at equilibrium.
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Initial Concentrations

Initial concentrations refer to the amounts of reactants and products present in a reaction mixture before any reaction occurs. In this case, the initial concentrations of H2, I2, and HI can be calculated by dividing the number of moles by the volume of the reaction vessel (5.00 L). These initial values are crucial for determining how the system will shift to reach equilibrium.
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ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations, the changes in concentrations as the reaction proceeds, and the equilibrium concentrations of reactants and products. By setting up an ICE table for the reaction, one can systematically calculate the changes in concentration based on the stoichiometry of the reaction and the equilibrium constant, leading to the final equilibrium concentrations.
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Related Practice
Textbook Question
At 1000 K, the value of Kc for the reaction C1s2 + H2O1g2 ∆ CO1g2 + H21g2 is 3.0 * 10-2. Calculate the equilibrium concentrations of H2O, CO2, and H2 in a reac- tion mixture obtained by heating 6.00 mol of steam and an excess of solid carbon in a 5.00-L container. What is the molar composition of the equilibrium mixture?
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