   # Provide a conceptual rationale for the differences in the halflives of zero-, first-, and second-order reactions. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 11, Problem 8ALQ
Textbook Problem
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## Provide a conceptual rationale for the differences in the halflives of zero-, first-, and second-order reactions.

Interpretation Introduction

Interpretation: An explanation regarding the difference in the half-lives of zero-, first- and second order reactions is to be stated.

Concept introduction: The time taken by the reactants to decrease to half of their initial concentration is known as the half-life of the reaction.

To determine: An explanation regarding the difference in the half-lives of zero-, first- and second order reactions.

### Explanation of Solution

The integrated rate law for a zero order reaction is [A]=kt+[A]ο .

The time taken by the reactants to decrease to half of their initial concentration is known as the half-life of the reaction.

Therefore, at t12 , the concentration becomes half.

The integrated rate law at t12 is,

[A]ο2=kt12+[A]ο

Simplify the above expression,

kt12=[A]ο[A]ο2t12=[A]ο2k

The integrated rate law for a first order reaction is ln[A]=kt+ln[A]ο .

The time taken by the reactants to decrease to half of their initial concentration is known as the half-life of the reaction.

Therefore, at t12 , the concentration becomes half.

The integrated rate law at t12 is,

ln[A]ο2=kt12+ln[A]ο

Simplify the above expression,

kt12=ln[A]οln[A]ο2t12=ln(2)kt12=0

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