Chapter 12, Problem 12.79SP

Interpretation Introduction

Interpretation:

The activation energy of the thermal decomposition reaction of $N{O}_2$ has to be calculated by plotting an appropriate graph with the given information.

Concept introduction:

Arrhenius equation:

The dependence of the rate constant $\left(\text{k}\right)$ of a chemical reaction on the activation energy, gas constant and temperature is given by Arrhenius equation.

$\begin{array}{l}\text{k}\text{=}{\text{Ae}}^{{\text{-E}}_{\text{a}}\text{/RT}}\\ \text{where,}\\ \text{k}\text{-}\text{rate}\text{constant}\\ \text{A}\text{-}\text{frequency}\text{factor}\left(\text{=}\text{pZ}\right)\\ {\text{E}}_{\text{a}}\text{-}\text{activation}\text{energy}\\ \text{R}\text{-}\text{gas}\text{constant}\text{and}\text{T-}\text{temperature}\text{.}\end{array}$

From the graph between $\text{1/T}$ and $\ln k$, activation energy can be determined by

${\text{E}}_{\text{a}}\text{=}-\text{R}\left(\text{slope}\right)$