Provide a conceptual rationale for the differences in the halflives of zero-, first-, and second-order reactions.

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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 The integrated rate law for a zero order reaction is [ A ] = − k t + [ 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 t 1 2 , the concentration becomes half. The integrated rate law at t 1 2 is, [ A ] ο 2 = − k t 1 2 + [ A ] ο Simplify the above expression, k t 1 2 = [ A ] ο − [ A ] ο 2 t 1 2 = [ A ] ο 2 k The integrated rate law for a first order reaction is ln [ A ] = − k t + 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 t 1 2 , the concentration becomes half. The integrated rate law at t 1 2 is, ln [ A ] ο 2 = − k t 1 2 + ln [ A ] ο Simplify the above expression, k t 1 2 = ln [ A ] ο − ln [ A ] ο 2 t 1 2 = ln ( 2 ) k t 1 2 = 0

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Chemistry: An Atoms First Approach

2nd Edition

Steven S. Zumdahl + 1 other

Publisher: Cengage Learning

ISBN: 9781305079243

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Chemistry: An Atoms First Approach

2nd Edition

Steven S. Zumdahl + 1 other

Publisher: Cengage Learning

ISBN: 9781305079243

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Answer 3

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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]ο−ln[A]ο2t12=ln(2)kt12=0

Provide a conceptual rationale for the differences in the halflives of zero-, first-, and second-order reactions.

Chemistry: An Atoms First Approach

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Chemistry: An Atoms First Approach