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Chapter 13: Problem 69

OBJECTIVE. Describe a chemical reaction as a sequence of elementary processes. Sum the following elementary steps to determine the overall stoichiometry of the gas-phase reaction. $$ \begin{array}{l} \mathrm{NO}_{2}+\mathrm{NO}_{2} \rightarrow \mathrm{NO}_{3}+\mathrm{NO} \\ \mathrm{NO}_{3}+\mathrm{CO} \rightarrow \mathrm{NO}_{2}+\mathrm{CO}_{2} \end{array} $$

Short Answer

Expert verified
\(\mathrm{NO}_{2} + \mathrm{CO} \rightarrow \mathrm{NO} + \mathrm{CO}_{2}\).

Step by step solution

01

Write Down the Given Reactions

We are provided with two elementary steps of a reaction sequence. The first step is \(\mathrm{NO}_{2} + \mathrm{NO}_{2} \rightarrow \mathrm{NO}_{3} + \mathrm{NO}\). The second step is \(\mathrm{NO}_{3} + \mathrm{CO} \rightarrow \mathrm{NO}_{2} + \mathrm{CO}_{2}\).
02

Identify Cancelled Intermediates

Identify any species that appear in the products of one step and the reactants of another. In this case, \(\mathrm{NO}_{3}\) appears as a product in the first step and as a reactant in the second step, and therefore, it cancels out in the overall reaction.
03

Add Up the Remaining Reactants

Combine the reactants from both steps, excluding any intermediates that were cancelled out. This gives us \(2\, \mathrm{NO}_{2} + \mathrm{CO}\) since \(\mathrm{NO}_{3}\) is canceled.
04

Add Up the Remaining Products

Combine the products from both steps, again excluding any intermediates which were cancelled out. This yields \(\mathrm{NO} + \mathrm{NO}_{2} + \mathrm{CO}_{2}\) since \(\mathrm{NO}_{3}\) is canceled.
05

Write the Overall Reaction

By combining the remaining reactants and products, the overall stoichiometry of the reaction is \(2\, \mathrm{NO}_{2} + \mathrm{CO} \rightarrow \mathrm{NO} + \mathrm{NO}_{2} + \mathrm{CO}_{2}\).
06

Simplify the Overall Reaction

Simplify the overall equation by canceling out any species that appear on both sides of the equation. This leaves \(\mathrm{NO}_{2} + \mathrm{CO} \rightarrow \mathrm{NO} + \mathrm{CO}_{2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Elementary Steps
In chemical reactions, understanding elementary steps is crucial. Elementary steps are the simplest stages of a chemical reaction. They represent reactions that occur in a single step and typically involve only a few molecules. These steps can be added together to give an overall chemical reaction. In our example, we have two elementary steps:
  • The first step is \( \mathrm{NO}_{2} + \mathrm{NO}_{2} \rightarrow \mathrm{NO}_{3} + \mathrm{NO} \)
  • The second step is \( \mathrm{NO}_{3} + \mathrm{CO} \rightarrow \mathrm{NO}_{2} + \mathrm{CO}_{2} \)
Each step describes a specific molecular event, and when combined, they yield the overall reaction. Elementary steps are usually fast and reversible, making them essential to grasp for predicting reaction rates.
Reaction Intermediates
Reaction intermediates are species that are produced in one step of a chemical mechanism and consumed in another. They appear in both the reactants and products during different stages of the reaction but do not appear in the overall balanced equation. In the provided example, \( \mathrm{NO}_{3} \) acts as an intermediate.
  • It is created in the first elementary step: \( \mathrm{NO}_{2} + \mathrm{NO}_{2} \rightarrow \mathrm{NO}_{3} + \mathrm{NO} \)
  • It is used up in the second step: \( \mathrm{NO}_{3} + \mathrm{CO} \rightarrow \mathrm{NO}_{2} + \mathrm{CO}_{2} \)
Intermediates are crucial for understanding mechanisms because they provide insight into the stepwise progression of a reaction.
Stoichiometry
Stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It allows chemists to determine the amounts of substances required or produced in a reaction. In our exercise, we calculate the stoichiometry of the overall reaction by:
  • Adding up the steps: \( 2 \mathrm{NO}_{2} + \mathrm{CO} \rightarrow \mathrm{NO} + \mathrm{NO}_{2} + \mathrm{CO}_{2} \)
  • Simplifying by canceling intermediates: \( \mathrm{NO}_{2} + \mathrm{CO} \rightarrow \mathrm{NO} + \mathrm{CO}_{2} \)
Mastering stoichiometry is essential for correctly predicting the outcome of chemical reactions and for scaling reactions for practical uses.
Gas-Phase Reactions
Gas-phase reactions involve reactants and products that are in the gaseous state. These reactions can be greatly influenced by changes in pressure and temperature. In our example, the reaction occurs entirely in the gaseous state:
  • Reactants: \( \mathrm{NO}_{2} \) and \( \mathrm{CO} \)
  • Products: \( \mathrm{NO} \) and \( \mathrm{CO}_{2} \)
Gas-phase reactions are often homogeneous, meaning the reactants and products are in the same phase. Studying these reactions helps in understanding atmospheric chemistry and industrial chemical processes, where gases play a major role. Understanding the dynamics of gas-phase reactions is important for fields like environmental science and engineering.

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Most popular questions from this chapter

OBJECTIVE. Relate temperature, activation energy, and rate constant through the Arrhenius equation. Consider the results of an experiment in which nitrogen dioxide reacts with ozone at two different temperatures, \(13^{\circ} \mathrm{C}\) and \(29^{\circ} \mathrm{C}\) $$ \mathrm{NO}_{2}(\mathrm{~g})+\mathrm{O}_{3}(\mathrm{~g}) \rightarrow \mathrm{NO}_{3}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) $$ If the activation energy is \(29 \mathrm{~kJ} / \mathrm{mol}\), by what factor does the rate constant increase with this temperature change?

What is the difference between the integrated and differential forms of the rate law?

OBJECTIVE. Calculate the concentration-time behavior for a second-order reaction from the rate law and the rate constant. A Consider the second-order decomposition of nitrosyl chloride. $$ 2 \mathrm{NOCl}(\mathrm{g}) \rightarrow 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ At \(450 \mathrm{~K},\) the rate constant is \(15.4 \mathrm{~atm}^{-1} \mathrm{~s}^{-1}\) (a) How much time is needed for \(\mathrm{NOCl}\) originally at a partial pressure of 44 torr to decay to 22 torr? (b) How much time is needed for \(\mathrm{NOCl}\) originally at a concentration of \(0.0044 M\) to decay to \(0.0022 M ?\)

The reactant in a first-order reaction decreases in concentration from 0.451 to \(0.235 M\) in 131 seconds. How long does it take to decrease from 0.235 to \(0.100 \mathrm{M}\) ?

OBJECTIVE. Calculate the concentration-time behavior for a second-order reaction from the rate law and the rate constant. A The decomposition of ozone is a second-order reaction with a rate constant of \(30.6 \mathrm{~atm}^{-1} \mathrm{~s}^{-1}\) at \(95^{\circ} \mathrm{C}\). $$ 2 \mathrm{O}_{3}(\mathrm{~g}) \rightarrow 3 \mathrm{O}_{2}(\mathrm{~g}) $$ If ozone is originally present at a partial pressure of 21 torr, calculate the length of time needed for the ozone pressure to decrease to 1.0 torr.
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