Chapter 18, Problem 18.9P

(a)

Interpretation Introduction

Interpretation:

The reaction order on each reactant and the overall reaction order have to be predicted along with the classification of reaction.

  $N_2{O}_{(g)}+O_{(g)}\to 2N{O}_{(g)}$

Concept Introduction:

Rate law or rate equation: The relationship between the reactant concentrations and reaction rate is expressed by an equation.

  $\begin{array}{l}\text{aA + bB}\to x\text{X}\\ \\ {\text{Rate of reaction = k [A]}}^{\text{m}}{\text{[B]}}^{\text{n}}\\ \\ \text{Total}\text{order}\text{of reaction = }\left(\text{m + n}\right).\end{array}$

Order of a reaction: The order of a reaction with respect to a particular reactant is the exponent of its concentration term in the rate law expression, and the overall reaction order is the sum of the exponents on all concentration terms.

Elementary step: The first step in a reaction mechanism is said to be elementary step.

Unimolecular: A molecule undergoes rearrangement itself to give one or more products is said to be unimolecular reactions.

Bimolecular: Two molecules undergo collision to give one or more products is said to be bimolecular reactions.

Trimolecular: Three molecules undergo collision to give one or more products is said to be trimolecular reactions.

Explanation of Solution

Given,

    $N_2{O}_{(g)}+O_{(g)}\to 2N{O}_{(g)}$

$\begin{array}{l}\text{Reaction Rate}\text{ = k }{\left[\text{A}\right]}^{\text{m}}{\left[\text{B}\right]}^{\text{n}}\text{,where m, and n are orders of the reactants}\text{.}\\ \\ \text{Given}\text{reaction rate : }\mathrm{rate}=k{\left[N_{2}O\right]}^1{\left[O\right]}^1\text{.}\end{array}$

Reaction order on each reactant:

The order of $\left({\text{N}}_{\text{2}}\text{O}\right)$ reactant is FIRST ORDER.

The order of $\left(\text{O}\right)$ reactant is FIRST ORDER.

  $\begin{array}{l}\underset{\_}{\text{Order}\text{of}\text{the}\text{overall}\text{reaction:}}\\ \\ \text{Known:Total}\text{order}\text{of}\text{reaction = m + n}\\ \\ \mathrm{rate}=k{\left[N_{2}O\right]}^1{\left[O\right]}^1.\end{array}$

The overall order of the given reaction is,

$\text{Total}\text{order}\text{of}\text{reaction = 1 +}\text{1 = 2 }\left(Secondorder\right)\text{. }$

In the given elementary steps, there are two molecules undergo collision to form a product. So, from the definitions above said the given elementary step is bimolecular.

(b)

Interpretation Introduction

Interpretation:

The reaction order on each reactant and the overall reaction order have to be predicted along with the classification of reaction.

  $2{\text{O}}_2{}_{(g)}\to O_{(g)}+O_3{}_{(g)}$

Concept Introduction:

Refer to (a).

Explanation of Solution

Given,

    $2{\text{O}}_2{}_{(g)}\to O_{(g)}+O_3{}_{(g)}$

  $\begin{array}{l}\text{Reaction Rate}\text{ = k }{\left[\text{A}\right]}^{\text{m}}{\left[\text{B}\right]}^{\text{n}}\text{,where m, and n are orders of the reactants}\text{.}\\ \\ \text{Given}\text{reaction rate : rate}\text{=}\text{k}{\left[{\text{O}}_{\text{2}}\right]}^{\text{2}}.\end{array}$

Reaction order on each reactant:

The order of $\left({\text{O}}_{\text{2}}\right)$ reactant is SECOND ORDER.

  $\begin{array}{l}\underset{\_}{\text{Order}\text{of}\text{the}\text{overall}\text{reaction:}}\\ \\ \text{Known:Total}\text{order}\text{of}\text{reaction = m + n}\\ \\ \text{rate}\text{=}\text{k}{\left[{\text{O}}_{\text{2}}\right]}^{\text{2}}.\end{array}$

The overall order of the given reaction is,

$\text{Total}\text{order}\text{of}\text{reaction = 2 }\left(Secondorder\right)\text{. }$

In the given elementary steps, there are two molecules undergo collision to form two products. So, from the definitions above said the given elementary step is bimolecular.

(c)

Interpretation Introduction

Interpretation:

The reaction order on each reactant and the overall reaction order have to be predicted along with the classification of reaction.

  ${\text{ClCO}}_{\text{(g)}}\text{+}{\text{Cl}}_{\text{2}}{}_{\text{(g)}}\to {\text{Cl}}_{\text{2}}{\text{CO}}_{\text{(g)}}\text{+}{\text{Cl}}_{\text{(g)}}$

Concept Introduction:

Refer to (a).

Explanation of Solution

Given,

    ${\text{ClCO}}_{\text{(g)}}\text{+}{\text{Cl}}_{\text{2}}{}_{\text{(g)}}\to {\text{Cl}}_{\text{2}}{\text{CO}}_{\text{(g)}}\text{+}{\text{Cl}}_{\text{(g)}}$

  $\begin{array}{l}\text{Reaction Rate}\text{ = k }{\left[\text{A}\right]}^{\text{m}}{\left[\text{B}\right]}^{\text{n}}\text{,where m, and n are orders of the reactants}\text{.}\\ \\ \text{Given}\text{reaction rate : rate}\text{=}\text{k}{\left[\text{ClCO}\right]}^{\text{1}}{\left[{\text{Cl}}_{\text{2}}\right]}^{\text{1}}\text{.}\end{array}$

Reaction order on each reactant:

The order of $\left(\text{ClCO}\right)$ reactant is FIRST ORDER.

The order of $\left({\text{Cl}}_2\right)$ reactant is FIRST ORDER.

  $\begin{array}{l}\underset{\_}{\text{Order}\text{of}\text{the}\text{overall}\text{reaction:}}\\ \\ \text{Known:Total}\text{order}\text{of}\text{reaction = m + n}\\ \\ \text{rate}\text{=}\text{k}{\left[\text{ClCO}\right]}^{\text{1}}{\left[{\text{Cl}}_{\text{2}}\right]}^{\text{1}}\end{array}$

The overall order of the given reaction is,

$\text{Total}\text{order}\text{of}\text{reaction = 1 +}\text{1 = 2 }\left(Secondorder\right)\text{. }$

In the given elementary steps, there are two molecules undergo collision to form products. So, from the definitions above said the given elementary step is bimolecular.