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

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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 \( \text{HI} \).
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