Ch.14 - Chemical Kinetics

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.14 - Chemical Kinetics

Problem 140b

Chapter 14, Problem 140b

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

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).

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.

Use the rate constant: The rate constant k is given as 1.7 \times 10^{-3} \text{s}^{-1}.

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.

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.

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Key Concepts

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

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.

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Textbook Question

A 1.50 L sample of gaseous HI having a density of 0.0101 g>cm3 is heated at 410 °C. As time passes, the HI decomposes to gaseous H2 and I2. The rate law is -Δ3HI4>Δt = k3HI42, where k = 0.031>1M ~ min2 at 410 °C. (b) What is the partial pressure of H2 after a reaction time of 8.00 h?

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Textbook Question

The rate constant for the decomposition of gaseous NO2 to NO and O2 is 4.7>1M ~ s2 at 383 °C. Consider the decomposition of a sample of pure NO2 having an initial pressure of 746 mm Hg in a 5.00 L reaction vessel at 383 °C. (c) What is the mass of O2 in the vessel after a reaction time of 1.00 min?

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. (a) If 2.70 g of gaseous N₂O₅ is introduced into an evacuated 2.00 L container maintained at a constant temperature of 55 °C, what is the total pressure in the container after a reaction time of 13.0 minutes?

For the thermal decomposition of nitrous oxide, 2 N2O1g2S 2 N21g2 + O21g2, values of the parameters in the Arrhenius equation are A = 4.2 * 109 s-1 and Ea = 222 kJ>mol. If a stream of N2O is passed through a tube 25 mm in diameter and 20 cm long at a flow rate of 0.75 L/min at what temperature should the tube be maintained to have a partial pressure of 1.0 mm of O2 in the exit gas? Assume that the total pressure of the gas in the tube is 1.50 atm.

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Textbook Question

A 0.500 L reaction vessel equipped with a movable piston is filled completely with a 3.00% aqueous solution of hydrogen peroxide. The H2O2 decomposes to water and O2 gas in a first-order reaction that has a half-life of 10.7 h. As the reaction proceeds, the gas formed pushes the piston against a constant external atmospheric pressure of 738 mm Hg. Calculate the PV work done (in joules) after a reaction time of 4.02 h. (You may assume that the density of the solution is 1.00 g/mL and that the temperature of the system is maintained at 20 °C.)

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