Chapter 11, Problem 47QAP

Interpretation Introduction

Interpretation:

To determine the half-life of Br-82.

Concept introduction:

Integral equations for various order of reaction:

• For Zero order reaction:

${\text{[A]}}_{\text{t}}\text{=}{\text{[A]}}_{\text{o}}\text{-}\text{kt}$

• For first order reaction:

$\text{ln}\left(\frac{{\text{[A]}}_{\text{t}}}{{\text{[A]}}_{\text{o}}}\right)\text{=-kt}$

• For second order reaction:

$\frac{\text{1}}{{\text{[A]}}_{\text{t}}}\text{=}\frac{\text{1}}{{\text{[A]}}_{\text{0}}}\text{+kt}$

Where,

$\begin{array}{l}{\text{[A]}}_{\text{t}}\text{=}\text{concentration}\text{at}\text{t=t}\\ {\text{[A]}}_{\text{0}}\text{=}\text{concnetration}\text{at}\text{t=0}\\ \text{k=}\text{rate}\text{constant}\\ \text{t=}\text{time}\end{array}$

Relation between rate constant and half-life for first order reaction:

$\begin{array}{l}{\text{t}}_{1/2}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{where,}\\ {\text{t}}_{1/2}\text{=}\text{Half-life}\\ \text{k}\text{=}\text{rate}\text{constant}\end{array}$