Chapter 12, Problem 12.63SP

(a)

Interpretation Introduction

Interpretation:

The concentration of trans-cycloheptene after $\text{1600 s}$ has to be calculated.

Concept introduction:

The rate law for a second order reaction:

A second order reaction is defined as the reaction whose rate depends only on the concentration of both reactants.

$\begin{array}{l}\frac{\text{1}}{\left[\text{A}\right]}\text{=}\text{kt}\text{+}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}\\ \text{where,}\\ \\ {\left[\text{A}\right]}_{\text{0}}\text{-}\text{concentration}\text{of}\text{A}\text{at}\text{time}\text{t}\text{=}\text{0}\\ \left[\text{A}\right]\text{-}\text{concentration}\text{of}\text{A}\text{after}\text{time}\text{t}\\ \text{k}\text{-}\text{rate}\text{constant}\end{array}$

(b)

Interpretation Introduction

Interpretation:

The time required to drop the concentration of trans-cycloheptene to its one-twentieth of the initial value has to be calculated

Concept introduction:

The rate law for a second order reaction:

A second order reaction is defined as the reaction whose rate depends only on the concentration of both reactants.

$\begin{array}{l}\frac{\text{1}}{\left[\text{A}\right]}\text{=}\text{kt}\text{+}\frac{\text{1}}{{\left[\text{A}\right]}_{\text{0}}}\\ \text{where,}\\ \\ {\left[\text{A}\right]}_{\text{0}}\text{-}\text{concentration}\text{of}\text{A}\text{at}\text{time}\text{t}\text{=}\text{0}\\ \left[\text{A}\right]\text{-}\text{concentration}\text{of}\text{A}\text{after}\text{time}\text{t}\\ \text{k}\text{-}\text{rate}\text{constant}\end{array}$

(c)

Interpretation Introduction

Interpretation:

The half-life of trans-cycloheptene at an initial concentration of $\text{0}\text{.075 M}$ has to be calculated

Concept introduction:

Half-life time: It is the time required for the reactant (substrate) concentration reduces to one-half of its initial concentration.

$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{1}}{\text{k}{\left[\text{A}\right]}_{\text{0}}}\left(\text{for}\text{a}\text{second}\text{order}\text{reaction}\right)\\ \text{where,}\\ {\left[\text{A}\right]}_{\text{0}}\text{-}\text{Concentration}\text{of}\text{A}\text{at}\text{time}\text{=}\text{0}\\ {\text{t}}_{\text{1/2}}\text{-}\text{half life}\text{time}\\ \text{k}\text{-}\text{rate}\text{constant}\end{array}$