Chapter 17, Problem 17D.2AE

Interpretation Introduction

Interpretation:

The rate constant for the decomposition of a certain substance is $\text{k = 3}{\text{.80×10}}^{\text{-3}}{\text{dm}}^{\text{3}}{\text{mol}}^{\text{-1}}{\text{s}}^{\text{-1}}$ at , $\text{T = 308 K}$ and $\text{k = 2}{\text{.67×10}}^{\text{-2}}{\text{dm}}^{\text{3}}{\text{mol}}^{\text{-1}}{\text{s}}^{\text{-1}}$ at $\text{T = 323 K}$.  The Arrhenius parameters has to be evaluated.

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:

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