Chapter 15, Problem 31E

(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 first order rate law is,

  $t_{1/2}=\frac{\ln 2}{k}$

(c)

Interpretation Introduction

Interpretation:

Time required for the concentration of A to decrease to $2.50\times {10}^{-3}\text{ M}$ should be calculated.

Concept Introduction:

Integrated rate law for first order reaction.

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

k − rate constant

t − time

[A] − concentration at time t

[A]₀ − initial concentration