The rate constant for the first-order decomposition of gaseous N₂O₅ to NO₂ and O₂ is 1.7 * 10-3 s-1 at 55 °C. (b) Use the data in Appendix B to calculate the initial rate at which the reaction mixture absorbs heat (in J/s). You may assume that the heat of the reaction is independent of temperature.

Verified step by step guidance

1. Identify the reaction: The decomposition of N_2O_5 is a first-order reaction, which can be represented as 2 N_2O_5 (g) -> 4 NO_2 (g) + O_2 (g).
2. Determine the rate of reaction: For a first-order reaction, the rate is given by the expression rate = k[N_2O_5], where k is the rate constant and [N_2O_5] is the concentration of N_2O_5.
3. Use the rate constant: The rate constant k is given as 1.7 \times 10^{-3} \text{s}^{-1}.
4. Calculate the heat absorbed: Use the enthalpy change (\Delta H) for the reaction from Appendix B. The rate of heat absorption is related to the rate of reaction and \Delta H.
5. Express the initial rate of heat absorption: The initial rate of heat absorption can be calculated as rate \times \Delta H, where rate is the initial rate of reaction.

Key Concepts

First-Order Reactions

First-order reactions are chemical reactions where the rate is directly proportional to the concentration of one reactant. In this case, the decomposition of N2O5 follows first-order kinetics, meaning that as the concentration of N2O5 decreases, the rate of reaction also decreases. The rate constant (k) is a crucial parameter that quantifies this relationship and is given in units of s-1.

Rate of Reaction and Heat Absorption

The rate of a chemical reaction can be related to the heat absorbed or released during the reaction. For exothermic reactions, heat is released, while for endothermic reactions, heat is absorbed. In this question, calculating the initial rate at which the reaction mixture absorbs heat involves understanding the enthalpy change of the reaction and how it correlates with the rate of reaction.

Heat of Reaction

The heat of reaction, or enthalpy change (ΔH), is the amount of heat absorbed or released during a chemical reaction at constant pressure. It is essential for determining how much heat is involved in the decomposition of N2O5. Since the problem states that the heat of the reaction is independent of temperature, this simplifies calculations, allowing the use of standard values from reference tables to find the heat absorbed per mole of reactant.