Textbook Question
At 100 °C, Kc = 4.72 for the reaction 2 NO21g2 ∆ N2O41g2. An empty 10.0-L flask is filled with 4.60 g of NO2 at 100 °C. What is the total pressure in the flask at equilibrium?
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Ch.15 - Chemical Equilibrium
Chapter 15, Problem 107
At 25 °C, Kc = 216 for the reaction 2 NO2(g) ⇌ N2O4(g). A 1.00-L flask containing a mixture of NO2 and N2O4 at 25 °C has a total pressure of 1.50 atm. What is the partial pressure of each gas?
Verified step by step guidance1
Step 1: Use the ideal gas law to relate the total pressure to the concentrations of NO2 and N2O4. Since the volume and temperature are constant, the partial pressures can be related to the concentrations by P = nRT/V.
Step 2: Express the equilibrium constant Kc in terms of partial pressures. For the reaction 2 NO2(g) ⇌ N2O4(g), Kc = [N2O4]/[NO2]^2. Convert this to Kp using the relation Kp = Kc(RT)^Δn, where Δn is the change in moles of gas.
Step 3: Set up the expression for the total pressure in terms of the partial pressures: P_total = P_NO2 + P_N2O4. Use the stoichiometry of the reaction to express the partial pressures in terms of a single variable, such as the change in moles of NO2.
Step 4: Substitute the expressions for the partial pressures into the equilibrium expression for Kp. Solve the resulting equation for the variable representing the change in moles of NO2.
Step 5: Calculate the partial pressures of NO2 and N2O4 using the solved value from Step 4 and the total pressure equation.
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 2 NO2(g) ⇌ N2O4(g), Kc = [N2O4]/[NO2]^2. A higher Kc value indicates that, at equilibrium, the products are favored over the reactants.
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Equilibrium Constant Expressions
Partial Pressure
Partial pressure is the pressure exerted by a single component of a gas mixture. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. In this case, the total pressure of 1.50 atm can be used to find the partial pressures of NO2 and N2O4 based on their mole fractions.
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Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law can be used to calculate the number of moles of each gas in the mixture, which is essential for determining their partial pressures. In this scenario, knowing the total pressure and the equilibrium constant allows for the calculation of the individual gas pressures.
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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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