   # The data in the table give the temperature dependence of the rate constant for the reaction N 2 O 5 (g) → 2 NO 2 (g) + ½ O 2 (g). Plot these data in the appropriate way to derive the activation energy for the reaction. ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640

#### Solutions

Chapter
Section ### Chemistry & Chemical Reactivity

9th Edition
John C. Kotz + 3 others
Publisher: Cengage Learning
ISBN: 9781133949640
Chapter 14, Problem 62GQ
Textbook Problem
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## The data in the table give the temperature dependence of the rate constant for the reaction N2O5(g) → 2 NO2(g) + ½ O2(g). Plot these data in the appropriate way to derive the activation energy for the reaction. Interpretation Introduction

Interpretation:

The value for Ea should be determined using the plot obtained by the given set of data.

Concept introduction:

Rate law: It is generally the rate equation that consists of the reaction rate with the concentration or the pressures of the reactants and constant parameters.

Rate constant: The rate constant for a chemical reaction is the proportionality term in the chemical reaction rate law which gives the relationship between the rate and the concentration of the reactant present in the chemical reaction.

Rate order: The order of each reactant in a reaction is represented by the exponential term of the respective reactant present in the rate law and the overall order of the reaction is the sum of all the exponents of all reactants present in the chemical reaction.  The order of the reaction is directly proportional to the concentration of the reactants.

Arrhenius equation:

• Arrhenius equation is a formula that represents the temperature dependence of reaction rates
• The Arrhenius equation has to be represented as follows

k=AeEa/RTlnk=lnAeEa/RTlnk=(EaR)(1T)+lnA

• Ea represents the activation energy and it’s unit is kJ/mol
• R represents the universal gas constant and it has the value of 8.314 J/K.mol
• T represents the absolute temperature
• A represents the frequency factor or collision frequency
• e represents the base of natural logarithm
•  Arrhenius equation equation was proposed by Svante Arrhenius in 1889.

### Explanation of Solution

For the given reaction lnk and 1/T are tabulated as follows by using the given set of data.

The corresponding graph is as follows,

Find the slope for any two value in the graph:

slope=0.0029-0.003055.33+6.50= -1

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