   # Experimental values for the temperature dependence of the rate constant for the gas-phase reaction NO + O 3 → NO 2 + O 2 are as follows T (K) k (L/mol s) 195 1.08 × 10 9 230. 2.95 × 10 9 260. 5.42 × 10 9 298 12.0 × 10 9 369 35.5 × 10 9 Make the appropriate graph using these data, and determine the activation energy for this 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 88AE
Textbook Problem
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## Experimental values for the temperature dependence of the rate constant for the gas-phase reaction NO   +   O 3 → NO 2 + O 2 are as follows T(K) k (L/mol s) 195 1.08 × 109 230. 2.95 × 109 260. 5.42 × 109 298 12.0 × 109 369 35.5 × 109 Make the appropriate graph using these data, and determine the activation energy for this reaction.

Interpretation Introduction

Interpretation: The data obtained when NO reacts with O3 is given. The appropriate graph is to be plotted using these data and activation energy is to be calculated for this reaction.

Concept introduction: The differential rate law provides the rate of a reaction at specific reaction concentrations.

The Arrhenius equation is,

k=AeEaRT

To determine: An appropriate graph and activation energy using given data.

### Explanation of Solution

Explanation

The reaction that takes place is,

NO+O3NO2+O2

The value of 1T and lnk is calculated from the given data.

 T(K) 1T(K) k(L/mol⋅s) lnk 195 0.0051 1.08×109 20.800 230 0.0043 2.95×109 21.805 260 0.0038 5.42×109 22.413 298 0.0033 12.0×109 23.208 369 0.0027 35.5×109 24.292

The graph is plotted for lnk versus 1T is,

The obtained graph is almost a straight line. The slope of graph is 1439 .

The value of Ea for the given reaction is 12.096kJ/mol_ .

The relationship between the rate of reaction andactivation energy is given by the Arrhenius equation. The Arrhenius equation is,

k=AeEaRT

Where,

• k is the rate constant.
• A is the Arrhenius parameter

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