Chapter 2.1, Problem 2.7E

Interpretation Introduction

Interpretation: The value of $k$ at $500°\text{C}$ is to be calculated with the help of Arrhenius equation.

Concept introduction: Arrhenius gave the temperature dependence of rate in terms of activation energy as follows:

  $k=A\exp \left(E_{\text{a}}\text{/}RT\right)$

Where,

• $E_{\text{a}}$ represents activation energy.
• $T$ represent final temperature.
• $k$ denotes rate constant at $T$ .
• $R$ represents gas constant.

The temperature dependence of rate in terms of activation energy as follows:

  $k=A\exp \left(E_{\text{a}}\text{/}RT\right)$

Take natural logarithm on both sides above equation,

  $\begin{array}{c}k=A\exp \left(E_{\text{a}}\text{/}RT\right)\\ \ln k=\ln \left[A\exp \left(E_{\text{a}}\text{/}RT\right)\right]\\ \ln k=\ln A-\frac{E_{\text{a}}}{RT}\end{array}$

If natural logarithm is removed, the expression is written as follows:

  $\log k=\log A-\frac{E_{\text{a}}}{2.303RT}$