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?

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

검증된 단계별 안내

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.

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.