At a temperature of 430 °C, the reaction H2(g) + I2(g) ⇌ 2 HI(g) has an equilibrium constant Kc = 54.3. Suppose that a mixture of 0.500 mol of H2(g) and 0.500 mol of I2(g) is placed into a 1.00-L stainless-steel flask at 430 °C. Calculate the concentration of HI(g) when equilibrium is reached. (LO 15.10) (a) 0.393 M (b) 0.107 M (c) 0.500 M (d) 0.786 M

Verified step by step guidance

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. Since the volume of the flask is 1.00 L, the initial concentrations are \([\text{H}_2] = 0.500 \text{ M}\) and \([\text{I}_2] = 0.500 \text{ M}\).

Step 4: Assume that \( x \) moles of \( \text{HI} \) are formed at equilibrium. The change in concentration for \( \text{H}_2 \) and \( \text{I}_2 \) will be \(-x\), and for \( \text{HI} \) it will be \(+2x\).

Step 5: Substitute the equilibrium concentrations into the \( K_c \) expression: \( K_c = \frac{(2x)^2}{(0.500 - x)(0.500 - x)} = 54.3 \). Solve this equation for \( x \) to find the equilibrium concentration of \( \text{HI} \).

Key Concepts

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

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. In this state, the system is dynamic, meaning that reactions continue to occur, but there is no net change in concentration. Understanding this concept is crucial for analyzing how concentrations change in response to initial conditions and how they relate to the equilibrium constant.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium, each raised to the power of their coefficients in the balanced equation. For the reaction H2(g) + I2(g) ⇌ 2 HI(g), Kc = [HI]^2 / ([H2][I2]). This constant provides insight into the extent of the reaction and is essential for calculating equilibrium concentrations from initial amounts.

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 given reaction, one can systematically determine how the concentrations of H2, I2, and HI change from their initial values to equilibrium, facilitating the calculation of unknown concentrations using the equilibrium constant.

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Textbook Question

The reaction A21g2 + B21g2 ∆ 2 AB1g2 has an equilib- rium constant Kc = 9. The following figure represents areaction mixture that contains A2 molecules (red), B2 mol- ecules (blue), and AB molecules. What statement about the mixture is true? (LO 15.5)

(a) The mixture is at equilibrium, and there will be no net shift in reaction direction.(b) The reaction will shift toward the reactants to reach equilibrium.(c) The reaction will shift toward the products to reach equilibrium.(d) More information is needed to answer this question.

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Textbook Question

For the general, single-step reaction A1g2 + B1g2 ∆ AB1g2, Kc = 4.5 * 10-6, which of the following statements is true? (LO 15.16) (a) Ea 1forward2 6 Ea 1reverse2 (b) The equilibrium mixture contains mostly products. (c) kr 7 kf (d) The reaction is exothermic.

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