Chapter 19.5, Problem 6PPC

Interpretation Introduction

Interpretation:

The half-life of the reaction should be calculated.

Concept introduction:

For a first order reaction, $A\underset{}{\to }B+C$ the rate constant is,

$\begin{array}{c}\ln \frac{{\left[A\right]}_t}{{\left[A\right]}_0}=-kt\\ where,{\left[A\right]}_0=\text{concentration}\text{of}\text{reactant}atstartingtime\left(t=0\right)\\ {\left[A\right]}_t=\text{concentration}\text{of}\text{reactant}afterttime\\ k=r\text{ate}\text{constant}\\ \text{t}\text{=}\text{time}\end{array}$

Half-life, ${\text{t}}_{\text{1/2}}$: Time needed for a reactant to decrease its concentration to one half of the original concentration. Half-life of first order reaction is,

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