Chapter 15, Problem 109AE

(a)

Interpretation Introduction

Interpretation:

The order of the reaction in butadiene should be determined.

Concept Introduction:

Integrated rate laws for zero, first and second order reactions are,

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

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

Second order: $\frac{1}{{\left[\text{A}\right]}_t}=kt+\frac{1}{{\left[\text{A}\right]}_0}$

(b)

Interpretation Introduction

Interpretation:

Time taken for dimerization to complete 1% should be determined.

Concept Introduction:

Integrated rate law for a second order reaction;

  $\frac{1}{{\left[\text{A}\right]}_t}=kt+\frac{1}{{\left[\text{A}\right]}_0}$

[A]_t − concentration of A at time t

[A]₀ − initial concentration of A

k − rate constant

t − time

(c)

Interpretation Introduction

Interpretation:

Time taken for dimerization to complete 2% should be determined.

Concept Introduction:

Integrated rate law for a second order reaction;

  $\frac{1}{{\left[\text{A}\right]}_t}=kt+\frac{1}{{\left[\text{A}\right]}_0}$

[A]_t − concentration of A at time t

[A]₀ − initial concentration of A

k − rate constant

t − time

(d)

Interpretation Introduction

Interpretation:

The half-life for the reaction if the initial concentration of butadiene is 0.0200 M should be calaculated.

Concept Introduction:

The half-life for a second order reaction can be calculated by,

  $t_{1/2}=\frac{1}{k{[\text{A]}}_0}$

k − rate constant

[A]₀ − initial concentration of A

(e)

Interpretation Introduction

Interpretation:

The activation energy for the dimerization of butadiene should be calculated.

Concept Introduction:

Arrhenius equation

  $\ln k=-\frac{E_a}{R}\left(\frac{1}{T}\right)+\ln A$

k − equilibrium constant

E_a − activation energy

R − universal gas constant

T − temperature

A − pre-exponential factor.