Chapter 15, Problem 32E

(a)

Interpretation Introduction

Interpretation:

The rate law, the integrated rate law and the value of the rate constant for the reaction should be determined.

Concept Introduction:

Differential rate law gives an expression for the rate of concentration change while integrated rate law gives an expression of concentration versus time.

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:

The half-life for the reaction should be calculated.

Concept Introduction:

Half-life of a substance is the time it takes for the concentration of that substance to fall to half of its initial value.

Half-life expression for a zeroth order reaction is,

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

(c)

Interpretation Introduction

Interpretation:

Time required for all the ethanol to decompose should be calculated.

Concept Introduction:

Integrated rate law for zeroth order reaction.

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

k − rate constant

t − time

[A] − concentration at time t

[A]₀ − initial concentration