Calculate Kc for each reaction. b. N2(g) + O2(g) ⇌ 2 NO(g) Kp = 4.10×10^–31 (at 298 K)

Verified step by step guidance

1. Identify the relationship between Kc and Kp using the equation: Kc = Kp(RT)^-Δn, where R is the ideal gas constant (0.0821 L·atm/mol·K), T is the temperature in Kelvin, and Δn is the change in moles of gas.
2. Calculate Δn for the reaction: Δn = moles of gaseous products - moles of gaseous reactants. For the reaction N2(g) + O2(g) ⇌ 2 NO(g), Δn = 2 - (1 + 1) = 0.
3. Substitute the values into the equation: Kc = Kp(RT)^-Δn. Since Δn = 0, the equation simplifies to Kc = Kp, because (RT)^0 = 1.
4. Use the given value of Kp = 4.10×10^–31 and the fact that Kc = Kp to determine Kc.
5. Conclude that for this reaction at 298 K, Kc is equal to the given Kp value, 4.10×10^–31.

Key Concepts

Equilibrium Constant (Kc and Kp)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. Kc refers to concentrations in molarity, while Kp refers to partial pressures. The relationship between Kc and Kp is given by the equation Kp = Kc(RT)^(Δn), where Δn is the change in moles of gas. Understanding this relationship is crucial for converting between Kc and Kp.

Reaction Quotient (Q)

The reaction quotient (Q) is a measure of the relative amounts of products and reactants at any point in a reaction, not just at equilibrium. It is calculated using the same formula as K, but with the current concentrations or pressures. Comparing Q to K helps predict the direction in which a reaction will proceed to reach equilibrium, which is essential for understanding dynamic chemical processes.

Temperature Dependence of K

The value of the equilibrium constant (K) is temperature-dependent, meaning it can change with variations in temperature. For exothermic reactions, increasing temperature typically decreases K, while for endothermic reactions, it increases K. This concept is vital when calculating Kc or Kp at different temperatures, as it influences the position of equilibrium and the concentrations of reactants and products.