Chapter 20, Problem 43E

Interpretation Introduction

Interpretation:

The case which shows zero order and which shows second order is to be decided according to following statement and the reason for situation for both is not the same is to be explained.

The value of half-lives for second order as well as for zero order reactions depend upon the rate constant and as well as on the initial concentration. But, in one case; the half-life gets longer when the initial concentration increases and in other case the half-life get shorter.

Concept introduction:

• The half-life ( ${\text{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ ) is defined as the time required by reactant A to reduce to half of its initial amount.
• Half-life for zero order reaction is -
${\text{t}}_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{{[\text{A]}}_0}{\text{2k}}$ Where k is the rate constant and ${\text{[A]}}_0$ is the initial concentration of reactant.
• Half-life for first order reaction is

$t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{\ln 2}{k}=\frac{0.693}{k}$

Where k is the rate constant.

• Half-life for second order reaction is

$t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=\frac{1}{k{[\text{A]}}_0}$

[A]₀ is the initial concentration of reactant and k is the rate constant.