An equilibrium mixture of O2, SO2, and SO3 contains equal concentrations of SO2 and SO3. Calculate the concentration of O2 if Kc = 2.7 * 10^2 for the reaction 2 SO2(g) + O2(g) ⇌ 2 SO3(g).

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Identify the balanced chemical equation: 2 SO2(g) + O2(g) ⇌ 2 SO3(g).

Write the expression for the equilibrium constant Kc: Kc = \frac{[SO3]^2}{[SO2]^2[O2]}.

Since the concentrations of SO2 and SO3 are equal, let [SO2] = [SO3] = x.

Substitute the concentrations into the Kc expression: Kc = \frac{x^2}{x^2[O2]}.

Solve for [O2] by rearranging the equation: [O2] = \frac{x^2}{Kc}.

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 equilibrium is crucial for analyzing reactions and calculating concentrations using 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 2 SO2(g) + O2(g) ⇌ 2 SO3(g), Kc is expressed as [SO3]^2 / ([SO2]^2[O2]). A higher Kc value indicates a greater concentration of products at equilibrium, which is essential for solving equilibrium problems.

Stoichiometry

Stoichiometry involves the quantitative relationships between the amounts of reactants and products in a chemical reaction, based on the balanced chemical equation. It allows for the calculation of concentrations and moles of substances involved in the reaction. In this case, stoichiometry is used to relate the concentrations of SO2, SO3, and O2 to find the unknown concentration of O2 using the given Kc value.

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