Chapter 14.5, Problem 14.10CYU

Interpretation Introduction

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

Concept introduction:

Arrhenius equation:

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

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

                Where,

                    k=rate constant

                    A=frequency factor

                    e=base of logarithms

                    ${\text{E}}_{\text{a}}$ = energy of activation

                    T=Temperature

Mathematically, the above equation can be written as,

                $\text{ln}\text{k=ln}\text{A-}\frac{{\text{E}}_{\text{a}}}{\text{RT}}$

Determination of activation energy: If the rate constant for a given reaction are measured at several temperatures, graphical techniques used to determine the activation energy of a reaction.

  $\begin{array}{l}\text{ln}\text{k =}\text{-}\left(\frac{{\text{E}}_{\text{a}}}{\text{R}}\right)\frac{\text{1}}{\text{T}}\text{+}\text{lnA }\\ \\ \underset{\_}{\text{Equation for straight line:}}\\ \\ \text{ln}\text{k}\text{indicates y-axis}\text{.}\\ \\ \left(\frac{{\text{E}}_{\text{a}}}{\text{R}}\right)\text{indicates }\text{slope}\\ \\ \frac{\text{1}}{\text{T}}\text{ indicates x-axis}\\ \\ \text{lnA}\text{indicates intercept}\text{.}\end{array}$