Chapter 7, Problem 7B.5AST

(a)

Interpretation Introduction

Interpretation:

The half-lives of decomposition of ${\text{N}}_2\text{O}$ in the first order reaction have to be determined.

Concept Introduction:

The half-life of the particular chemical reaction is the time in which exactly half of the reactant gets consumed.  The mathematical expression for the half-life for a reaction follows first order kinetics is shown below.

  $t_{1/2}=\frac{\ln 2}{k_{\text{r}}}$

(b)

Interpretation Introduction

Interpretation:

The time taken by ${\text{N}}_2\text{O}$ to get reduced into one-eighth of its initial concentration 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.

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