Chapter 7, Problem 7B.2BST

Interpretation Introduction

Interpretation:

The data given for the decomposition of ${\text{CH}}_3{\text{N}}_2{\text{CH}}_3$ at $460\text{K}$, follows first order kinetics has to be confirmed and the rate constant for the decomposition of ${\text{CH}}_3{\text{N}}_2{\text{CH}}_3$ has to be determined.

Concept Introduction:

According to the integrated rate law for the first order reaction, the concentration of reactant is the exponential function of time.  The two equations that represent the integrated rate law for the first order kinetics is shown below.

    $\ln {\left[\text{A}\right]}_{\text{t}}=\ln {\left[\text{A}\right]}_0-k_{\text{r}}t$

The plot of natural logarithm of concentration of reactant against time is the straight line and the slope of the graph is $-k_{\text{r}}$.  Therefore, the rate constant for the first order reaction is equal to the negative of slope of concentration against time.