The reaction NO(g) + NO2(g) ⇌ N2O3(g) takes place in the atmosphere with Kc = 13 at 298 K. A gas mixture is prepared with 2.0 mol NO and 3.0 mol NO2 and an initial total pressure of 1.65 atm. (a) What are the equilibrium partial pressures of NO, NO2, and N2O3 at 298 K?

Verified step by step guidance

1. Step 1: Write the expression for the equilibrium constant Kc for the reaction: \( K_c = \frac{[\text{N}_2\text{O}_3]}{[\text{NO}][\text{NO}_2]} \).
2. Step 2: Convert the initial moles of NO and NO2 to concentrations using the ideal gas law. Use the formula \( P = \frac{nRT}{V} \) to find the initial concentrations, where \( P \) is the pressure, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( V \) is the volume.
3. Step 3: Set up an ICE (Initial, Change, Equilibrium) table to track the changes in concentrations of NO, NO2, and N2O3 as the system reaches equilibrium. Define the change in concentration of NO and NO2 as \( -x \) and the change in concentration of N2O3 as \( +x \).
4. Step 4: Substitute the equilibrium concentrations from the ICE table into the Kc expression. Solve for \( x \) to find the change in concentration at equilibrium.
5. Step 5: Calculate the equilibrium partial pressures of NO, NO2, and N2O3 using the equilibrium concentrations and the ideal gas law.

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction at a given temperature. For the reaction NO(g) + NO2(g) ⇌ N2O3(g), Kc = [N2O3]/([NO][NO2]). A Kc value greater than 1 indicates that products are favored at equilibrium, while a value less than 1 suggests reactants are favored.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. According to Dalton's Law, the total pressure of a gas mixture is the sum of the partial pressures of its individual gases. In this problem, the initial total pressure and the number of moles of each gas will help determine their respective partial pressures at equilibrium.

ICE Table (Initial, Change, Equilibrium)

An ICE table is a tool used to organize the initial concentrations (or pressures), the changes that occur as the system reaches equilibrium, and the equilibrium concentrations (or pressures) of the reactants and products. By setting up an ICE table for the given reaction, one can systematically calculate the equilibrium partial pressures of NO, NO2, and N2O3 based on the initial conditions and the stoichiometry of the reaction.