Chapter 15, Problem 54E

(a)

Interpretation Introduction

Interpretation:

The value of k for the reaction should be calculated.

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 experiment 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 first order rate law is,

  $t_{1/2}=\frac{\ln 2}{k}$

(c)

Interpretation Introduction

Interpretation:

The concentration of A after 13.0 seconds should be calculated.

Concept Introduction:

Integrated rate law for a first order reaction is,

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

[A]_t − concentration of A at time t

[A]₀ − initial concentration of A

k − rate constant

t - time

(d)

Interpretation Introduction

Interpretation:

The concentration of C after 13.0 seconds should be calculated.

Concept Introduction:

Integrated rate law for a first order reaction is,

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

[A]_t − concentration of A at time t

[A]₀ − initial concentration of A

k − rate constant

t - time