Chapter 17, Problem 17D.1P

Interpretation Introduction

Interpretation:

From the following data the activation energy has to be estimated.

    $\begin{array}{l}{\text{k}}_{\text{r}}{\text{/(10}}^{\text{-3}}{\text{s}}^{\text{-1}}\text{)}\text{2}\text{.46}\text{45}\text{.1}\text{576}\\ {\text{θ/}}^{\text{o}}\text{C}\text{0}\text{20}\text{.0}\text{40}\text{.0}\end{array}$

Concept Introduction:

Arrhenius Equation:

The temperature dependence characteristics of reaction is normally expressed mathematically by introducing two parameters, one representing the intercept and the other the slop of the straight line of a so-called ‘Arrhenius plot’ of $\text{ln k}$, against $\text{1/T}$ and writing the Arrhenius equation.

    $\text{lnk = lnA - }\frac{{\text{E}}_{\text{a}}}{\text{RT}}$

A is the parameter obtained from the intercept of the line at $\text{1/T = 0}$ is called the frequency factor.  The parameter ${\text{E}}_{\text{a}}$ is called the activation energy.  The two quantities are collectively known as Arrhenius parameters.

Figure.1

If the activation energy of a reaction is known, the value of a rate constant ${\text{k}}_{\text{2}}$ at a temperature ${\text{T}}_{\text{2}}$ can be predicted from its value ${\text{k}}_1$ at another temperature ${\text{T}}_1$

That is:

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