   # The rate of the reaction NO 2 ( g ) + CO ( g ) → NO ( g ) + CO 2 ( g ) depends only on the concentration of nitrogen dioxide below 225°C. At a temperature below 225°C, the following data were collected: Time(s) [NO 2 ](mol/L) 0 0.500 1.20 × 10 3 0.444 3.00 × 10 3 0.381 4.50 × 10 3 0.340 9.00 × 10 3 0.250 1.80 × 10 4 0.174 Determine the rate law, the integrated rate law, and the value of the rate constant. Calculate [NO 2 ] at 2.70 × 10 4 s after the start of the reaction. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 39E
Textbook Problem
47 views

## The rate of the reaction NO 2 ( g )   +   CO ( g ) → NO ( g )   +   CO 2 ( g ) depends only on the concentration of nitrogen dioxide below 225°C. At a temperature below 225°C, the following data were collected: Time(s) [NO2](mol/L) 0 0.500 1.20 × 103 0.444 3.00 × 103 0.381 4.50 × 103 0.340 9.00 × 103 0.250 1.80 × 104 0.174 Determine the rate law, the integrated rate law, and the value of the rate constant. Calculate [NO2] at 2.70 × 104 s after the start of the reaction.

Interpretation Introduction

Interpretation: The reaction between NO2 and CO is given. The rate law, integrated rate law and the value of rate constant is to be calculated. The concentration of NO2 at the given instant is to be determined.

Concept introduction: The change observed in the concentration of a reactant or a product per unit time is known as the rate of the particular reaction. The differential rate law provides the rate of a reaction at specific reaction concentrations.

### Explanation of Solution

To determine: The rate law for the given reaction.

Given

The stated reaction is,

NO2(g)+CO(g)NO(g)+CO2(g)

A plot of 1[NO2] versus time (t) is obtained using the given concentration values of NO2 .

The values obtained are,

 Time (s) [NO2] (mol/L) 1[NO2] 0 0.500 2 1.20×103 0.444 2.25 3.00×103 0.381 2.62 4.50×103 0.340 2.94 9.00×103 0.250 4 1.80×103 0.174 5.74

The graph obtained by these values is,

Figure 1

The plot of 1[NO2] versus t is a straight line. This corresponds to a second order reaction.

Therefore, the rate law for the given reaction is calculated by the expression,

Rate=k[NO2]2

Where,

• [NO2] is the concentrations of NO2 .
• k is the rate constant.
• 2 is the order of the reaction.

To determine: The integrated rate law for the given reaction.

Given

The stated reaction is,

NO2(g)+CO(g)NO(g)+CO2(g)

The rate law in integral form is known as integrated rate law. It gives the relation between concentration of reactant or product with time. The integrated rate law is represented as,

1[NO2]=kt+1[NO2]ο

Where,

• k is rate constant.
• [NO2]0 is initial concentration of reactant.
• t is time.

To determine: The value of rate constant for the given reaction.

Given

The stated reaction is,

NO2(g)+CO(g)NO(g)+CO2(g)

The plot of 1[NO2] versus t is a straight line. This corresponds to a second order reaction. The slope of a second order reaction gives the value of the rate constant.

The slope is calculated by the formula,

Slope=ΔyΔx=Δ(1[NO2])Δt

Where,

• Δ(1[NO2]) is the difference between the final and initial 1[NO2] value

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