   # Calculate the activation energy, E a , for the reaction 2 N 2 O 5 (g) → 4 NO 2 (g) + O 2 (g) from the observed rate constants: k at 25 °C = 3.46 × 10 −5 s −1 and k at 55 °C = 1.5 × 10 −3 s −1 . ### 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 37PS
Textbook Problem
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## Calculate the activation energy, Ea, for the reaction2 N2O5(g) → 4 NO2(g) + O2(g)from the observed rate constants: k at 25 °C = 3.46 × 10−5 s−1 and k at 55 °C = 1.5 × 10−3 s−1.

Interpretation Introduction

Interpretation:

The activation energy has to be calculated.

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

Given,

T1=25C=298.15KT2=55C=328.15KK1=3.46×10-5s1K2= 1.5×10-3s1Ea=?

In order to determine the activation energy for the given reaction we need to use the following expression which relates the rate constant, activation energy and the temperature.

lnK1K2=EaR1T2-1T1Ea=lnK1K2×RT1×T2/T1T2

Ea=ln3

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