The equilibrium constant for the reaction SO₂(g) + NO₂(g) ⇌ SO₃(g) + NO(g) is K_c = 3.0. Find the amount of NO₂ that must be added to 2.4 mol of SO₂ in order to form 1.2 mol of SO₃ at equilibrium.

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Identify the balanced chemical equation: \( \text{SO}_2(g) + \text{NO}_2(g) \rightleftharpoons \text{SO}_3(g) + \text{NO}(g) \).

Write the expression for the equilibrium constant \( K_c \): \( K_c = \frac{[\text{SO}_3][\text{NO}]}{[\text{SO}_2][\text{NO}_2]} \).

Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of each species. Initially, you have 2.4 mol of \( \text{SO}_2 \) and 0 mol of \( \text{SO}_3 \). Let \( x \) be the amount of \( \text{NO}_2 \) added.

At equilibrium, the concentration of \( \text{SO}_3 \) is 1.2 mol. Use the stoichiometry of the reaction to express the changes in concentrations of all species in terms of \( x \).

Substitute the equilibrium concentrations into the \( K_c \) expression and solve for \( x \), the amount of \( \text{NO}_2 \) needed.

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주요 개념

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Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. The equilibrium constant (Kc) quantifies this balance, indicating the ratio of product concentrations to reactant concentrations at equilibrium. Understanding this concept is crucial for predicting how changes in concentration affect the system.

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 SO2(g) + NO2(g) ⇌ SO3(g) + NO(g), Kc = 3.0 means that at equilibrium, the concentration of SO3 and NO is three times that of SO2 and NO2. This constant helps in calculating the necessary concentrations to achieve equilibrium.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions based on the balanced equation. It allows us to determine the amounts of substances consumed and produced. In this question, stoichiometry is essential for calculating how much NO2 must be added to achieve the desired amount of SO3 at equilibrium, using the initial amounts and the equilibrium constant.

The equilibrium constant for the reaction SO2(g) + NO2(g) ⇌ SO3(g) + NO(g) is Kc = 3.0. Find the amount of NO2 that must be added to 2.4 mol of SO2 in order to form 1.2 mol of SO3 at equilibrium.