Ch.14 - Chemical Kinetics

Problem 139

Previous problem

Next problem

Chapter 14, Problem 139

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?

Verified step by step guidance

Convert the initial pressure of NO2 from mm Hg to atm using the conversion factor 1 atm = 760 mm Hg.

Use the ideal gas law, PV = nRT, to calculate the initial moles of NO2 in the reaction vessel. Remember to use the appropriate units for R (0.0821 L atm / mol K) and convert the temperature to Kelvin.

Determine the change in moles of NO2 over the reaction time using the rate constant and the integrated rate law for a first-order reaction: ln([NO2]0/[NO2]t) = kt.

Calculate the moles of O2 produced using the stoichiometry of the balanced chemical equation: 2 NO2 -> 2 NO + O2.

Convert the moles of O2 to mass using the molar mass of O2 (32.00 g/mol).

Verified Solution

Video duration:

10m

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

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

Rate Constant and Reaction Order

The rate constant (k) is a proportionality factor in the rate law of a chemical reaction, indicating how the rate of reaction depends on the concentration of reactants. The units of k vary with the order of the reaction; for a second-order reaction, the units are typically M^-1 s^-1. Understanding the reaction order helps in determining how the concentration of reactants affects the rate of product formation over time.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of a gas. This law is essential for converting between pressure and moles, especially when calculating the amount of gas produced or consumed in a reaction. In this context, it will help determine the moles of O2 produced from the decomposition of NO2.

Stoichiometry of the Reaction

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. For the decomposition of NO2 into NO and O2, the balanced equation shows that 2 moles of NO2 produce 1 mole of O2. This relationship is crucial for calculating the mass of O2 produced after a specific reaction time, as it allows for the conversion of moles of NO2 reacted to moles of O2 formed.

Recommended video:

Guided course

01:16

Stoichiometry Concept

Previous problem

Next problem

Related Practice

Textbook Question

Values of E_a = 6.3 kJ/mol and A = 6.0⨉10⁸/(M s) have been measured for the bimolecular reaction: NO(g) + F₂(g) → NOF(g) + F(g) (a) Calculate the rate constant at 25 °C.

533

views

Textbook Question

Values of E_a = 6.3 kJ/mol and A = 6.0⨉10⁸/(M s) have been measured for the bimolecular reaction: NO(g) + F₂(g) → NOF(g) + F(g) (d) Why does the reaction have such a low activation energy?

266

views

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?

403

views

Textbook Question

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?

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.

502

views

Textbook Question

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.

866

views