Chapter 12, Problem 12.118CHP

Interpretation Introduction

Interpretation:

By the use of integrated rate law, general equation for the half-life of a zeroth order, first order and second order reaction has to be given.

Concept Introduction:

Integrated rate law for a first order reaction:

A first order reaction is defined as the reaction whose rate depends only on the concentration of a single reactant raised to the first power.

$\text{Rate}\text{=}\text{-}\frac{\text{Δ}\left[\text{A}\right]}{\text{Δt}}\text{=}\text{k}\left[\text{A}\right]$

Integrated rate law for a first order reaction is given below

$\begin{array}{l}\text{ln}\frac{{\left[\text{A}\right]}_{\text{t}}}{{\left[\text{A}\right]}_{\text{0}}}\text{=}\text{-}\text{kt}\\ \text{where,}\\ \text{ln}\text{-}\text{natural}\text{logarithm}\\ {\left[\text{A}\right]}_{\text{o}}\text{-}\text{concentration}\text{of}\text{A}\text{at}\text{time}\text{t}\text{=}\text{0}\\ {\left[\text{A}\right]}_{\text{t}}\text{-}\text{concentration}\text{of}\text{A}\text{after}\text{time}\text{t}\\ \text{k}\text{-}\text{rate}\text{constant}\end{array}$