Elements Of Physical Chemistry
Elements Of Physical Chemistry
7th Edition
ISBN: 9780198796701
Author: ATKINS, P. W. (peter William), De Paula, Julio
Publisher: Oxford University Press
Question
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Chapter 6, Problem 6D.2E

(a)

Interpretation Introduction

Interpretation:

The half-life time of cyclobutane at 20oC has to be found.

Concept introduction:

Half-life period:

Half-life is defined as the time taken for amount of the sample to reduce to half of its starting value.  The symbol is t12.

t12=ln(2)k

Half-life for a first order reaction is, t12=0.693k

Arrhenius equation:

  • Arrhenius equation is a formula that represents the temperature dependence of reaction rates
  • The Arrhenius equation has to be represented as follows

k=AeEa/RT

  • Ea represents the activation energy and it’s unit is kJ/mol
  • R represents the universal gas constant and it has the value of 8.314 J/K×mol
  • T represents the absolute temperature
  • A represents the frequency factor or collision frequency

(a)

Expert Solution
Check Mark

Explanation of Solution

Given gas-phase decomposition reaction is,

C4H8(g)2C2H4(g)

logA=15.6A=antilog(15.6)=3.98×1015Ea=261kJmol1=2.61×105Jmol1

Arrhenius equation is,

k=AeEa/RTT=20oC=293Kk=3.98×1015e(2.61×105/8.314×298)k=3.98×1015×2.30×1018k=9.154×103s1

Therefore, the half-life is,

t12=0.693k=0.6931.17×1031s1t12=5.923×1032s

Hence, the cyclobutane half-life time value is t12=5.923×1032s.

(b)

Interpretation Introduction

Interpretation:

The half-life time of cyclobutane at 500oC has to be found.

Concept introduction:

Half-life period:

Half-life is defined as the time taken for amount of the sample to reduce to half of its starting value.  The symbol is t12.

t12=ln(2)k

Half-life for a first order reaction is, t12=0.693k

Arrhenius equation:

  • Arrhenius equation is a formula that represents the temperature dependence of reaction rates
  • The Arrhenius equation has to be represented as follows

k=AeEa/RT

  • Ea represents the activation energy and it’s unit is kJ/mol
  • R represents the universal gas constant and it has the value of 8.314 J/K×mol
  • T represents the absolute temperature
  • A represents the frequency factor or collision frequency

(b)

Expert Solution
Check Mark

Explanation of Solution

Given gas-phase decomposition reaction is,

C4H8(g)2C2H4(g)

logA=15.6A=antilog(15.6)=3.98×1015Ea=261kJmol1=2.61×105Jmol1

Arrhenius equation is,

k=AeEa/RTT=500oC=773Kk=3.98×1015e(2.61×105/8.314×773)k=2.30×1018s1

Therefore, the half-life is,

t12=0.693k=0.6932.30×1018s1t12=3.01×1019s

Hence, the cyclobutane half-life time value is t12=3.01×1019s at 500oC.

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Chapter 6 Solutions

Elements Of Physical Chemistry

Ch. 6 - Prob. 6C.4STCh. 6 - Prob. 6D.1STCh. 6 - Prob. 6D.2STCh. 6 - Prob. 6D.3STCh. 6 - Prob. 6E.1STCh. 6 - Prob. 6E.2STCh. 6 - Prob. 6F.1STCh. 6 - Prob. 6F.2STCh. 6 - Prob. 6G.1STCh. 6 - Prob. 6G.2STCh. 6 - Prob. 6G.3STCh. 6 - Prob. 6H.1STCh. 6 - Prob. 6I.1STCh. 6 - Prob. 6I.2STCh. 6 - Prob. 6A.1ECh. 6 - Prob. 6A.2ECh. 6 - Prob. 6A.3ECh. 6 - Prob. 6B.1ECh. 6 - Prob. 6B.2ECh. 6 - Prob. 6B.3ECh. 6 - Prob. 6B.4ECh. 6 - Prob. 6B.5ECh. 6 - Prob. 6C.1ECh. 6 - Prob. 6C.2ECh. 6 - Prob. 6C.3ECh. 6 - Prob. 6C.4ECh. 6 - Prob. 6C.5ECh. 6 - Prob. 6C.6ECh. 6 - Prob. 6C.7ECh. 6 - Prob. 6C.8ECh. 6 - Prob. 6C.9ECh. 6 - Prob. 6C.10ECh. 6 - Prob. 6C.11ECh. 6 - Prob. 6C.12ECh. 6 - Prob. 6D.1ECh. 6 - Prob. 6D.2ECh. 6 - Prob. 6D.3ECh. 6 - Prob. 6D.4ECh. 6 - Prob. 6D.5ECh. 6 - Prob. 6D.6ECh. 6 - Prob. 6D.7ECh. 6 - Prob. 6D.8ECh. 6 - Prob. 6D.9ECh. 6 - Prob. 6D.10ECh. 6 - Prob. 6D.11ECh. 6 - Prob. 6E.1ECh. 6 - Prob. 6E.2ECh. 6 - Prob. 6E.3ECh. 6 - Prob. 6F.1ECh. 6 - Prob. 6F.2ECh. 6 - Prob. 6F.3ECh. 6 - Prob. 6G.1ECh. 6 - Prob. 6G.2ECh. 6 - Prob. 6G.3ECh. 6 - Prob. 6G.5ECh. 6 - Prob. 6H.1ECh. 6 - Prob. 6H.2ECh. 6 - Prob. 6H.3ECh. 6 - Prob. 6H.4ECh. 6 - Prob. 6I.1ECh. 6 - Prob. 6I.2ECh. 6 - Prob. 6I.3ECh. 6 - Prob. 6.1DQCh. 6 - Prob. 6.2DQCh. 6 - Prob. 6.3DQCh. 6 - Prob. 6.4DQCh. 6 - Prob. 6.5DQCh. 6 - Prob. 6.6DQCh. 6 - Prob. 6.7DQCh. 6 - Prob. 6.8DQCh. 6 - Prob. 6.9DQCh. 6 - Prob. 6.10DQCh. 6 - Prob. 6.11DQCh. 6 - Prob. 6.12DQCh. 6 - Prob. 6.13DQCh. 6 - Prob. 6.14DQCh. 6 - Prob. 6.1PCh. 6 - Prob. 6.2PCh. 6 - Prob. 6.3PCh. 6 - Prob. 6.4PCh. 6 - Prob. 6.5PCh. 6 - Prob. 6.6PCh. 6 - Prob. 6.9PCh. 6 - Prob. 6.10PCh. 6 - Prob. 6.11PCh. 6 - Prob. 6.12PCh. 6 - Prob. 6.13PCh. 6 - Prob. 6.15PCh. 6 - Prob. 6.16PCh. 6 - Prob. 6.17PCh. 6 - Prob. 6.19PCh. 6 - Prob. 6.20PCh. 6 - Prob. 6.21PCh. 6 - Prob. 6.22PCh. 6 - Prob. 6.24PCh. 6 - Prob. 6.25PCh. 6 - Prob. 6.26PCh. 6 - Prob. 6.27PCh. 6 - Prob. 6.28PCh. 6 - Prob. 6.29PCh. 6 - Prob. 6.30P
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