Chapter 7, Problem 7B.3BST

Interpretation Introduction

Interpretation:

The time taken by cyclopropane to get reduced from $1.0\text{mol}\cdot {\text{L}}^{-1}$ to $0.0050\text{mol}\cdot {\text{L}}^{-1}$ 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.

    $\begin{array}{c}\ln \frac{{\left[\text{A}\right]}_{\text{t}}}{{\left[\text{A}\right]}_0}=-k_{\text{r}}t\\ {\left[\text{A}\right]}_{\text{t}}={\left[\text{A}\right]}_0{\text{e}}^{-k_{\text{r}}t}\end{array}$