When 0.500 mol of N2O4 is placed in a 4.00-L reaction vessel and heated at 400 K, 79.3% of the N2O4 decomposes to NO2. (a) Calculate Kc and Kp at 400 K for the reaction N2O4(g) ↔ 2 NO2(g).

Verified step by step guidance

Step 1: Determine the initial concentration of N_2O_4. Use the formula \( \text{Concentration} = \frac{\text{moles}}{\text{volume}} \) to find the initial concentration of N_2O_4 in the 4.00 L vessel.

Step 2: Calculate the change in concentration of N_2O_4 due to decomposition. Since 79.3% of N_2O_4 decomposes, multiply the initial concentration by 0.793 to find the amount decomposed.

Step 3: Determine the equilibrium concentrations. Subtract the decomposed concentration from the initial concentration of N_2O_4 to find its equilibrium concentration. For NO_2, use the stoichiometry of the reaction to find its equilibrium concentration, knowing that 2 moles of NO_2 are produced for every mole of N_2O_4 decomposed.

Step 4: Calculate the equilibrium constant \( K_c \). Use the expression \( K_c = \frac{[\text{NO}_2]^2}{[\text{N}_2O_4]} \) and substitute the equilibrium concentrations to find \( K_c \).

Step 5: Calculate the equilibrium constant \( K_p \). Use the relation \( K_p = K_c(RT)^{\Delta n} \), where \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( \Delta n \) is the change in moles of gas (2 - 1 = 1 for this reaction).

Key Concepts

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

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies 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 is calculated using the formula Kc = [NO2]^2 / [N2O4], where the brackets denote molarity. Understanding Kc is essential for predicting the extent of the reaction and the concentrations of species at equilibrium.

Partial Pressure and Kp

Kp is the equilibrium constant expressed in terms of partial pressures of the gases involved in the reaction. It is related to Kc through the equation Kp = Kc(RT)^(Δn), where Δn is the change in moles of gas. For the reaction N2O4(g) ↔ 2 NO2(g), Δn = 2 - 1 = 1, making it necessary to convert Kc to Kp if required, especially when dealing with gaseous reactions.

Stoichiometry and Reaction Extent

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. In this case, knowing that 79.3% of N2O4 decomposes allows us to calculate the moles of NO2 produced and the remaining N2O4. This information is crucial for determining the concentrations needed to calculate Kc and Kp, as it directly influences the equilibrium state of the system.

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Textbook Question

The F-F bond in F₂ is relatively weak because the lone pairs of electrons on one F atom repel the lone pairs on the other F atom; K_p = 7.83 at 1500 K for the reaction F₂(g) ⇌ 2 F(g). (a) If the equilibrium partial pressure of F₂ molecules at 1500 K is 0.200 atm, what is the equilibrium partial pressure of F atoms in atm?

Textbook Question

The F-F bond in F₂ is relatively weak because the lone pairs of electrons on one F atom repel the lone pairs on the other F atom; K_p = 7.83 at 1500 K for the reaction F₂(g) ⇌ 2 F(g). (b) What fraction of the F₂ molecules dissociate at 1500 K?

Textbook Question

The F-F bond in F₂ is relatively weak because the lone pairs of electrons on one F atom repel the lone pairs on the other F atom; K_p = 7.83 at 1500 K for the reaction F₂(g) ⇌ 2 F(g). (c) Why is the F-F bond in F₂ weaker than the Cl-Cl bond in Cl₂?

Textbook Question

The equilibrium constant K_c for the gas-phase thermal decomposition of cyclopropane to propene is 1.0 ⨉10⁵ at 500 K:

(a) What is the value of K_p at 500 K?

Textbook Question

The equilibrium constant Kc for the gas-phase thermal decomposition of cyclopropane to propene is 1.0 * 105 at 500 K:

(c) Can you alter the ratio of the two concentrations at equilibrium by adding cyclopropane or by decreasing the volume of the container? Explain.