Chapter 20, Problem 108SAE

Interpretation Introduction

(a)

Interpretation:

Time taken to complete $75\%$ of a first-order reaction should be calculated.

Concept introduction:

A rate law expression defines the relationship between the rate of reaction and the concentration of reactants.

Consider a reaction,

$a\text{A}+b\text{B}\to \text{Products}$

The rate law for the above equation can be defined as,

$r=k{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b$

As the reaction proceeds, the concentration of reactants decreases and the concentration of products increases.

For the first-order reaction, the rate law expression is,

$k=\frac{1}{t}\ln \left(\frac{{\left[\text{A}\right]}_0}{{\left[\text{A}\right]}_t}\right)$

For the first-order reaction, the expression for the half-life is,

$t_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{k}$

Interpretation Introduction

(b)

Interpretation:

Time to complete $75\%$ reaction for zero order reaction should be calculated.

Concept introduction:

A rate law expression defines the relationship between the rate of reaction and the concentration of reactants.

Consider a reaction,

$a\text{A}+b\text{B}\to \text{Products}$

The rate law for the above equation can be defined as,

$r=k{\left[\text{A}\right]}^a{\left[\text{B}\right]}^b$

As the reaction proceeds, the concentration of reactants decreases and the concentration of products increases.

For the zero order reaction, the rate law expression is,

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

For the zero order reaction, the expression for the half-life is,

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