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Ch.15 - Chemical Equilibrium
All textbooksMcMurry 8th EditionCh.15 - Chemical EquilibriumProblem 112
Chapter 15, Problem 112

At 45 °C, Kc = 0.619 for the reaction N2O4(g) ⇌ 2 NO2(g). If 46.0 g of N2O4 is introduced into an empty 2.00-L container, what are the partial pressures of NO2 and N2O4 after equilibrium has been achieved at 45 °C?

Verified step by step guidance
1
Calculate the initial concentration of N2O4 by dividing the mass of N2O4 by its molar mass to find moles, then divide by the volume of the container to find molarity.
Set up an ICE (Initial, Change, Equilibrium) table to track the concentrations of N2O4 and NO2. Initially, the concentration of NO2 is zero, and the concentration of N2O4 is the initial concentration calculated.
Define the change in concentration for the reaction as x, where N2O4 decreases by x and NO2 increases by 2x, according to the stoichiometry of the reaction.
Write the expression for the equilibrium constant Kc in terms of the equilibrium concentrations: Kc = [NO2]^2 / [N2O4]. Substitute the expressions from the ICE table into this equation.
Solve the quadratic equation for x to find the equilibrium concentrations of N2O4 and NO2. Use these concentrations to calculate the partial pressures using the ideal gas law: P = (n/V)RT, where n is the number of moles, V is the volume, R is the ideal gas constant, and T is the temperature in Kelvin.

Key Concepts

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

Equilibrium Constant (Kc)

The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction N2O4(g) ⇌ 2 NO2(g), Kc = [NO2]^2 / [N2O4]. A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 indicates that reactants are favored.
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Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. It can be calculated using the ideal gas law, where the partial pressure of a gas is equal to its mole fraction multiplied by the total pressure of the system. In this context, the partial pressures of N2O4 and NO2 will be determined after the system reaches equilibrium, reflecting their respective concentrations in the container.
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Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. For the reaction N2O4(g) ⇌ 2 NO2(g), the stoichiometry indicates that one mole of N2O4 produces two moles of NO2. This relationship is crucial for calculating the changes in concentrations and partial pressures as the system shifts towards equilibrium after the introduction of N2O4 into the container.
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Related Practice
Textbook Question
The equilibrium constant Kc for the reaction N21g2 + 3 H21g2 ∆ 2 NH31g2 is 4.20 at 600 K. When a quantity of gaseous NH3 was placed in a 1.00-L reaction vessel at 600 K and the reaction was allowed to reach equilibrium, the vessel was found to contain 0.200 mol of N2. How many moles of NH3 were placed in the vessel?
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Textbook Question
The reaction of fumarate with water to form L-malate is catalyzed by the enzyme fumarase; Kc = 3.3 at 37°C. When a reaction mixture with [fumarate] = 1.56 * 10-3 M and [l -malate] = 2.27 * 10-3 M comes to equilibrium in the presence of fumarase at 37 °C, what are the equilibrium concentrations of fumarate and L-malate? (Water can be omit- ted from the equilibrium equation because its concentration in dilute solutions is essentially the same as that in pure water.)
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