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?

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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).

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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.

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