Chapter 14, Problem 14.34QP

Interpretation Introduction

Interpretation:

The activation energy for the given reaction has to be determined.

Concept introduction:

Arrhenius equation:

• Arrhenius equation is a formula that represents the temperature dependence of reaction rates.
• The Arrhenius equation is

$\text{k}{\text{=Ae}}^{{\text{-E}}_{\text{a}}\text{/RT}}$

• ${\text{E}}_{\text{a}}$ 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

The activation energy of the given reaction has to be calculated from the modified Arrhenius equation:

$\text{ln}\frac{{\text{k}}_{\text{1}}}{{\text{k}}_{\text{2}}}\text{=-}\frac{{\text{E}}_{\text{a}}}{\text{R}}\left[\frac{\text{1}}{{\text{T}}_{\text{2}}}\text{-}\frac{\text{1}}{{\text{T}}_{\text{1}}}\right]$

${\text{E}}_{\text{a}}\text{=}\text{Activation}\text{energy}$

$\begin{array}{c}{\text{T}}_2=\text{Final}\text{temperature}\\ {\text{T}}_1=\text{Initial}\text{temperature}\end{array}$

$\begin{array}{c}{\text{k}}_1\text{=}\text{Rate}{\text{constant at temperature T}}_1\\ {\text{k}}_2\text{=}\text{Rate}\text{constant}{\text{at temperature T}}_2\end{array}$