   # The colorless gas N 2 O 4 , decomposes to the brown gas NO 2 in a first-order reaction. N 2 O 4 (g) → 2 NO 2 (g) The rate constant k = 4.5 × 10 3 s ‒1 at 274 K and k = 1.00 × 10 4 s ‒1 at 283 K. What is the activation energy, E a ? ### 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 14.5, Problem 2CYU
Textbook Problem
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## The colorless gas N2O4, decomposes to the brown gas NO2 in a first-order reaction.N2O4(g) → 2 NO2(g)The rate constant k = 4.5 × 103 s‒1 at 274 K and k = 1.00 × 104 s‒1 at 283 K. What is the activation energy, Ea?

Interpretation Introduction

Interpretation: The value of activation energy has to be given.

Concept introduction:

Arrhenius equation:

Arrhenius equation is used to calculate the rate constant of many reactions. Arrhenius equation takes the form

k=Ae-Ea/RT

Where,

k=rate constant

A=frequency factor

e=base of logarithms

Ea = energy of activation

T=Temperature

Mathematically, the above equation can be written as,

lnk=lnA-EaRT

### Explanation of Solution

The activation energy is calculated as,

Given:k1 = 4.5×103s1;T1= 274Kk2 = 1.00×104s1;T2= 283KArrhenius equation:_ln k1=-(EaRT1)+lnA;ln k2=-(EaRT2)+lnAln k2ln k1=lnk2k1=(EaR)[1T21T1]Bysubstituting,ln(1

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