Calculate the equilibrium concentrations of SO2, Cl2, and SO2Cl2 at 298 K if the initial concentrations are [SO2] = 1.50 M and [Cl2] = 0.85 M. The equilibrium constant Kc for the reaction SO2(g) + Cl2(g) ⇌ SO2Cl2(g) is 8.40 × 10^-3 at 298 K.

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Write the balanced chemical equation for the reaction: \( \text{SO}_2(g) + \text{Cl}_2(g) \rightleftharpoons \text{SO}_2\text{Cl}_2(g) \).

Define the initial concentrations: \([\text{SO}_2] = 1.50 \text{ M}\), \([\text{Cl}_2] = 0.85 \text{ M}\), and \([\text{SO}_2\text{Cl}_2] = 0 \text{ M}\).

Set up an ICE (Initial, Change, Equilibrium) table to track the changes in concentrations as the system reaches equilibrium.

Express the changes in concentration in terms of \(x\), where \(x\) is the amount of \(\text{SO}_2\text{Cl}_2\) formed at equilibrium. The changes will be: \([-x]\) for \(\text{SO}_2\) and \(\text{Cl}_2\), and \([+x]\) for \(\text{SO}_2\text{Cl}_2\).

Write the expression for the equilibrium constant \(K_c = \frac{[\text{SO}_2\text{Cl}_2]}{[\text{SO}_2][\text{Cl}_2]}\) and substitute the equilibrium concentrations from the ICE table into this expression to solve for \(x\).

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 equilibrium constants.

Equilibrium Constant (Kc)

The equilibrium constant (Kc) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction SO2(g) + Cl2(g) ⇌ SO2Cl2(g), Kc = [SO2Cl2] / ([SO2][Cl2]). A small Kc value, like 8.40 × 10^-3, indicates that at equilibrium, the concentration of reactants is much greater than that of the product, suggesting the reaction favors the reactants.

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, one can systematically determine how the initial concentrations of SO2 and Cl2 will change to reach equilibrium, allowing for the calculation of the final concentrations based on the equilibrium constant.

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