What is the total amount of heat absorbed (in kilojoules) after a reaction time of 10.0 min for the first-order decomposition of gaseous N2O5 to NO2 and O2 at 55 °C, given that the rate constant is 1.7 * 10^-3 s^-1?

Verified step by step guidance

1. Identify the reaction: The decomposition of N2O5 is a first-order reaction, which means the rate of reaction depends on the concentration of N2O5.
2. Use the first-order rate equation: The integrated rate law for a first-order reaction is \( [A] = [A]_0 e^{-kt} \), where \([A]\) is the concentration at time \(t\), \([A]_0\) is the initial concentration, \(k\) is the rate constant, and \(t\) is the time.
3. Calculate the fraction of N2O5 decomposed: Rearrange the integrated rate law to find the fraction decomposed: \( 1 - \frac{[A]}{[A]_0} = 1 - e^{-kt} \). Substitute \(k = 1.7 \times 10^{-3} \text{s}^{-1}\) and \(t = 10.0 \text{ min} \times 60 \text{ s/min} \) to find the fraction decomposed.
4. Determine the moles of N2O5 decomposed: If the initial moles of N2O5 are known, multiply by the fraction decomposed to find the moles of N2O5 that have decomposed.
5. Calculate the heat absorbed: Use the stoichiometry of the reaction and the enthalpy change (if given or known) to calculate the total heat absorbed. The heat absorbed can be calculated using \( q = n \Delta H \), where \(n\) is the moles of N2O5 decomposed and \(\Delta H\) is the enthalpy change per mole of N2O5 decomposed.

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 the rate constant (k) is used to determine how quickly the reactant is consumed over time. The integrated rate law for a first-order reaction can be used to calculate the concentration of reactants at any given time.

Rate Constant (k)

The rate constant (k) is a proportionality factor in the rate equation that is specific to a particular reaction at a given temperature. For first-order reactions, k has units of s^-1, indicating how fast the reaction proceeds. In this question, the rate constant of 1.7 * 10^-3 s^-1 is crucial for calculating the amount of N2O5 decomposed over the specified reaction time of 10.0 minutes.

Heat Absorption in Reactions

The total amount of heat absorbed or released during a chemical reaction is related to the enthalpy change (ΔH) of the reaction. In this context, the heat absorbed can be calculated using the stoichiometry of the reaction and the amount of reactant consumed. Understanding how to relate the change in concentration of N2O5 to the heat absorbed is essential for solving the problem presented.