temperature-dependence of reaction rate -- Arrhenius equation

1. temperature-dependence of reaction rate -- Arrhenius equation

2. k T From the middle of 19 century, people began to study the effect of temperature on the reaction rate. Many empirical relations have been founded. 1 Types of rate-temperature curves Type I: k increases exponentially with T. This kind of curve can be observed in most of the reactions.

3. k k T T Type II This kind of k~T relation was observed in thermal explosions. At ignition temperature, the rate constant makes a sharp increase. Type III usually encountered in the catalytic reaction that has an optimum temperature.

4. k k T T Type IV: observed in oxidation of carbon and gaseous oxidation of hydrocarbons. Type V : The only example is 2NO + O2 = 2NO2

5. It was found that for homogeneous reaction, an important generalization is that reaction rate double or treble for every 10 degree increase in temperature. Vant’ Hoff’s Law in which A and B are experimental / empirical constants.

6. 2 Arrhenius equation In 1889, Arrhenius made detailed theoretical consideration on the hydrolysis of sucrose. C12H22O11 + H2O  C6H12O6 + C6H12O6 in which sucrose molecules were surrounded by water, if all sucrose molecules could react directly with water, the reaction should completed instantly. However, this is not the case. Arrhenius concluded that only a small part of sucrose molecules with higher energy (activated molecules) can react with water and, therefore, the reaction can only proceed at a low rate. By taking enough energy, the common sucrose molecules can change into activated molecules. The energy needed for this conversion was called activation energy.

7. Arrhenius extended the ideas of Vant’ Hoff and suggested a similar empirical equation. Defined the activation energy (Ea) The first definition of activation energy: experimental activation energy

8. If Ea is independent on temperature, integration of the equation Arrhenius equation yields A is the pre-exponential factor which has the same unit as the rate constant. In those five r ~ T relation types, only Type I obey Arrhenius equation. Type I is usually named as Arrhenius type.

9. 3 Experimental measurement activation energy 1) Experimental measurement: • Graphic method • Calculation method Graphic method: to plot lnk against 1/T, for the reaction of Arrhenius type, a straight line may be obtained, the slope of which equals –Ea/R

10. ClCOOCH3 + H2O  CO2 + CH3OH + H+ + Cl R = 0.99992 Ea = 70.80 kJ mol-1, A =1.32  109

11. (2) calculation method:

12. 4 Definition of Ea The minimum energy that the molecules must absorb before the reaction can take place is known as theactivation energy. According to Tolman,the activation energy of elementary reaction is the difference between the average energy of the activated molecules and the average energy of total molecules: Boltzmann distribution

13. 5 Ea and energy change of reaction the difference in internal energy reactant, product, activated state, reaction path. When Ea,->Ea,+, U < 0, the reaction is exothermic.

14. When Ea,-< Ea,+, U > 0, the reaction is a endothermic one. For a strong endothermic reaction, the activation energy for backward reaction is very small. principle of micro-reversibility

15. Only the activation energy of elementary reaction has definite physical meaning. The activation energies of some overall reactions can be taken as a combination of the activation energy of elementary reactions composing of the overall reaction. The activation energy of some overall reactions, usually named as apparent activation, may be meaningless physically.

16. 6 theoretical evaluation of Ea: The activation energy can be related to the energy change of the reaction. The energy change can be calculated using dissociation energy of chemical bond. To do this, some empirical rules may be used: • dissociation reaction: • Cl-Cl  2 Cl Ea will not be less than and need not be larger than the dissociation energy of the bond, i.e., Ea = DCl-Cl Dissociation energy of the bond is different from energy of bond.

17. 2) combination reaction of radicals 2 CH3·  CH3CH3 Ea = 0 3) Radicals react with molecules: A + BC  A-B + C If the reaction is a exothermal one, Ea 5% DB-C; 4) Molecules react with molecules: AB + CD  AC + BD If the reaction is exothermal, Ea = 30% (DAB + DCD)

18. T1 T2 Ea 7 Ea on reaction rate Table half-life of first-order reaction with different activation energy At high temperature, the fraction of activated molecule increases. When Ea was lowered, the fraction of activated molecule also increases.

19. For first-order reaction, when Ea increases by 4 kJ mol-1, k decreases by 80%. The effect of Ea on reaction rate is significant. Ea ranges between 40 ~ 400 kJ mol-1. Reaction with Ea less than 80 kJ mol-1 belongs to fast reactions. To study their kinetics, special method have to be used. For reaction with Ea larger than 100 kJ mol-1 , it is too slow to study.

20. 8 temperature-dependence of Ea 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: This equation suggests that, Ea depends on temperature.

21. The value of m, usually be 0, 1, 2, 1/2, etc., is not very large. Therefore, mRT is not very large with comparison to Ea, and in a relatively small temperature range, Ea seems independent on temperature. 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.

22. To measure activation energy of the reaction over a large span of temperature would result in exceptional difficulties. when plot lnk against T-1, a straight line may be obtained and the slope of the line equals to –Ea/R, and the intercept is lnA. That when T, A = k. Is this correct?

23. 9 A on reaction rate 10 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.