Chapter 15, Problem 42E

(a)

Interpretation Introduction

Interpretation:

The time for the final representation if the reaction $2{\text{ NO}}_2\text{(g) }\to \text{ 2 NO}\left(\text{g}\right){\text{ + O}}_2\text{(g)}$ is first order reaction should be determined.

Concept Introduction:

Integrated rate laws for first order reaction is,

First order: $\ln {\left[\text{A}\right]}_t=\ln {\left[\text{A}\right]}_0-kt$

Half-life expression for a first order rate law is,

  $t_{1/2}=\frac{\ln 2}{k}$

(b)

Interpretation Introduction

Interpretation:

The time for the final representation if the reaction $2{\text{ NO}}_2\text{(g) }\to \text{ 2 NO}\left(\text{g}\right){\text{ + O}}_2\text{(g)}$ is second order reaction should be determined.

Concept Introduction:

Integrated rate laws for second order reaction is, $\frac{1}{{\left[\text{A}\right]}_t}=kt+\frac{1}{{\left[\text{A}\right]}_0}$

Half-life expression for a second order rate law is,

  $t_{1/2}=\frac{1}{k{\left[\text{A}\right]}_0}$

(c)

Interpretation Introduction

Interpretation:

The time for the final representation if the reaction $2{\text{ NO}}_2\text{(g) }\to \text{ 2 NO}\left(\text{g}\right){\text{ + O}}_2\text{(g)}$ is zeroth order reaction should be determined.

Concept Introduction:

Integrated rate laws for zeroth order reaction is, ${\left[\text{A}\right]}_t={\left[\text{A}\right]}_0-kt$

Half-life expression for a zeroth order reaction is,

  $t_{1/2}=\frac{{\left[\text{A}\right]}_0}{2k}$