Forward and reverse rate constants for the reaction CO2(g) + N2(g) ⇌ CO(g) + N2O(g) exhibit the following temperature dependence: Temperature (K), kf (M-1 s-1), kr (M-1 s-1): 1200 K: kf = 9.1 * 10^-11, kr = 1.5 * 10^5; 1300 K: kf = 2.7 * 10^-9, kr = 2.6 * 10^5. Is the reaction endothermic or exothermic? Explain in terms of kinetics.

Verified step by step guidance

1. Step 1: Understand the relationship between temperature and reaction rates. In general, an increase in temperature will increase the rate constants for both the forward and reverse reactions due to increased molecular collisions.
2. Step 2: Calculate the equilibrium constant (K) at each temperature using the formula K = kf / kr, where kf is the forward rate constant and kr is the reverse rate constant.
3. Step 3: Compare the equilibrium constants at the two different temperatures. If the equilibrium constant increases with temperature, the reaction is endothermic. If it decreases, the reaction is exothermic.
4. Step 4: Analyze the change in equilibrium constant with temperature. An endothermic reaction absorbs heat, shifting the equilibrium towards the products as temperature increases, thus increasing K. Conversely, an exothermic reaction releases heat, shifting the equilibrium towards the reactants, thus decreasing K.
5. Step 5: Conclude whether the reaction is endothermic or exothermic based on the trend observed in the equilibrium constants calculated in Step 3.

Key Concepts

Rate Constants and Temperature Dependence

Rate constants (kf for the forward reaction and kr for the reverse reaction) are crucial in determining the speed of a chemical reaction. They are temperature-dependent, often described by the Arrhenius equation, which shows that as temperature increases, the rate constants typically increase. This relationship helps in understanding how reaction rates change with temperature, which is essential for analyzing the given data.

Equilibrium and Reaction Direction

In a reversible reaction, the equilibrium position can shift based on the relative magnitudes of the forward and reverse rate constants. If kf is significantly smaller than kr, the reaction favors the products at equilibrium. Conversely, if kf increases relative to kr with temperature, it suggests that the reaction may favor the formation of products, indicating the nature of the reaction (endothermic or exothermic) based on energy changes.

Endothermic vs. Exothermic Reactions

Endothermic reactions absorb heat from the surroundings, leading to an increase in the rate of the forward reaction with temperature, while exothermic reactions release heat, often resulting in a decrease in the forward rate with increasing temperature. By analyzing the temperature dependence of the rate constants, one can infer the heat exchange associated with the reaction, thus determining whether it is endothermic or exothermic.