山东大学：《物理化学》课程教学资源（讲义资料）9.5 Temperature-dependence of reaction rate ——Arrhenius equation

89.5 Temperature-dependence of reaction rate Arrhenius equation Extensive reading: Levine, pp. 554-559 Section 17.8 oals 1. Describe the effect of temperature on reaction rate 2. Activation energy: definition, measurement, estimation 3. Fundamentals for higher level scientific researches

§9.5 Temperature-dependence of reaction rate -- Arrhenius equation Extensive reading: Levine, pp. 554-559 Section 17.8 Goals: 1. Describe the effect of temperature on reaction rate; 2. Activation energy: definition, measurement, estimation; 3. Fundamentals for higher level scientific researches

89.5 Arrhenius equation qualitative Semi-quantitative quantitative dInk A T+10 2~3 +B kr nK)_△ dInk e aT RT Simplification dT RT

§9.5 Arrhenius equation qualitative Semi-quantitative quantitative 10 2 ~ 3 T T k k + = 2 ln A B d k dT T = + 2 ln r m p K H T RT       =    Simplification 2 d ln d E a k T RT =

89.5 Arrhenius equation △U=E.-E a.+ E=E-E E=E-E a Arrhenius Tolman a:4 E E E

U = Ea,+ − Ea,− §9.5 Arrhenius equation Ea = E − E * Ea = E − E * Tolman Arrhenius Ea,1 Ea,2 Ea,3 Ea,4 Ea,5 Ea,6

89.5 Arrhenius equation 9.5.11 modification of Arrhenius equation 3参数拟合 The Arrhenius plots for some reactions are curved, which suggests that the activation energy of these reactions is a function of temperature. At this situation, the temperature dependence of k can be usually expressed as 2参数拟合 k=AT expl E RT 1.0 20 3.0 4.0 5.0 1000 / E k= Aexp Problem: RT Discussion the relationship dInkA between this equation and tB Deduce the relationship between ea and e vant' Hoff empirical equation

9.5.11 modification of Arrhenius equation The Arrhenius plots for some reactions are curved, which suggests that the activation energy of these reactions is a function of temperature. At this situation, the temperature dependence of k can be usually expressed as:       = − RT E k AT m c exp 2 ln B d k A dT T = + Problem: Discussion the relationship between this equation and vant’ Hoff empirical equation Deduce the relationship between Ea and Ec . exp E c k A RT      = −          §9.5 Arrhenius equation

89.5 Arrhenius equation 9.5.11 modification of Arrhenius equation E=mRT+e However for some reaction such as rT 2 44 kJ mol-I CCl3 COOH>CHCI3+CO2, m=-107 m, usually be 0, 1, 2, 1/2,etc,is CH, Br +ho>CHoh +H++ Br very large m=-34.3 In a relatively small temperature The effect of temperature on the activation range, Ea seems independent on energy of these reactions is too large to ignore temperature Temperature-dependence of e

m, usually be 0, 1, 2, 1/2, etc., is not very large. In a relatively small temperature range, Ea seems independent on temperature. Ea = mRT + Ec However, for some reaction such as: CCl3COOH → CHCl3 + CO2 , m = -10.7 CH3Br + H2O → CH3OH + H+ + Br− , m = -34.3 The effect of temperature on the activation energy of these reactions is too large to ignore. Temperature-dependence of Ea RT= 2.44 kJ mol-1 9.5.11 modification of Arrhenius equation §9.5 Arrhenius equation

89.5 Arrhenius equation 9.5.11 modification of Arrhenius equation 9.5.12 A on reaction rate To measure activation energy of the E reaction over a large span of temperature k= Expl RT would result in exceptional difficulties Type of Unimolecular Bimolecular Termolecular In k a+ln a reaction reaction reaction reaction RT 1013 101l 109 mol1dm3s1mol2dm° When t→>∞,A=k. Is this correct How can we measure the experimental activation energy of an reaction?

To measure activation energy of the reaction over a large span of temperature would result in exceptional difficulties. A RT E k a ln = − + ln When T →, A = k. Is this correct? How can we measure the experimental activation energy of an reaction? 9.5.11 modification of Arrhenius equation §9.5 Arrhenius equation 9.5.12 A on reaction rate       = − RT E k A a exp

89.5 Arrhenius equation 9.5.13 Application of Arrhenius equation 第28卷第2期 大学化学 Val: 28 No. 2 2013年4月 UNIVERSITY CHEMISTRY Ink= 代+nA Arrhenius活化能理论的修正 刘国杰黑思成 (华东理工大学化学系上海200237) 1) make explanation for some experimental results 2)calculate the reaction rate at different temperature 3)determine the optimum temperature for reaction

9.5.13 Application of Arrhenius equation 1) make explanation for some experimental results; 2) calculate the reaction rate at different temperature; 3) determine the optimum temperature for reaction. A RT E k a ln = − + ln §9.5 Arrhenius equation

89.5 Arrhenius equation Summary: Pathway for scientific researches Problem Qualitative Experimental facts Quantitative Empirical law Prediction Hypothesis 胡适: 大胆假设、小心求证! Bold hypothesis, careful verification Testify heory Bring up hypothesis boldly while prove it conscientiously and carefully Modified Theory

胡适： 大胆假设、小心求证！ Bold hypothesis, careful verification Bring up hypothesis boldly while prove it conscientiously and carefully Summary: Pathway for scientific researches §9.5 Arrhenius equation