Chapter 13, Problem 13.29P

(a)

Interpretation Introduction

To write:

the balanced reaction

b)

Interpretation Introduction

To propose:

a reaction mechanism

Explanaiton:

Proposed Mechanism

1^st Step: Determine equilibrium ratios
Rate Law from the slow step

$Rate=k_2[N{O}_3][NO]$

Rate law form the fast step

$\begin{array}{l}rat{e}_{forward}=k_1[NO][O_2]\\ rat{e}_{reverse}=k_{-1}[N{O}_3]\end{array}$

In equilibrium, we know that
$rat{e}_{forward}=rat{e}_{reverse}$

Then
$rate=k_{-1}[N{O}_3]=k_1[NO][O_2]$

2^nd step: Get this based on the slow step reactants, that is $N{O}_3$

$[N{O}_3]=\frac{k_1}{k_{-1}}[NO][O_2]$

3^rd Step: substitute in rate law
$\begin{array}{l}Rate=k_2[N{O}_3][NO]\\ [N{O}_3]=\frac{k_1}{k_{-1}}[NO][O_2]\\ Rate=k_2\cdot \frac{k_1}{k_{-1}}[NO][O_2][NO]\end{array}$

Assume all constant as “K”
$Rate=K{[NO]}^2[O_2]$

(c)

To propose:

expression for k.