Chapter 14.5, Problem 14.11CYU

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# 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

The activation energy is calculated as,

â€‚Â Given:k1Â =Â 4.5Ã—103â€‰sâˆ’1;â€‰â€‰T1=Â 274â€‰Kk2Â =Â 1.00Ã—104â€‰sâˆ’1;â€‰â€‰T2=Â 283â€‰KArrheniusÂ equation:_lnÂ k1=â€‰â€‰-(EaRT1)+â€‰lnAâ€‰;â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰lnÂ k2=â€‰â€‰-(EaRT2)+â€‰lnAlnÂ k2âˆ’lnÂ k1=â€‰lnk2k1=â€‰âˆ’â€‰(EaR)[1T2âˆ’1T1]Byâ€‰substituting,â€‰ln(1

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