山东大学：《物理化学》课程教学资源（讲义资料）9.6 Rate Theories of elementary reaction for bimolecular reaction—simple collision theory SCT

89.6 Rate Theories of elementary reaction for bimolecular reaction--simple collision theory SCT cG→Qo Extensive reading: Levine, pp. 879-881

§9.6 Rate Theories of elementary reaction for bimolecular reaction—simple collision theory SCT Extensive reading: Levine, pp. 879-881

89.6 Rate Theories of elementary reaction Two important empirical rules Rate equation(law of mass action)r=kAIB] A rrhenIus equation k=Aexp RT Type of Unimolecular Bimolecular Termolecular reaction reaction reaction reaction 101 10 moIl·dm3s mor.dm.s A seems related to collision frequency. E exp Boltzmann distribution term RT

Two important empirical rules: Rate equation (law of mass action) Arrhenius equation       = − RT E k A a exp Type of reaction Unimolecular reaction Bimolecular reaction Termolecular reaction A 1013 s 1011 mol-1 dm3 s -1 109 mol-2 dm6 s -1 A seems related to collision frequency.       − RT Ea exp Boltzmann distribution term r k = [A][B] §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction Basic considerations and brief history a molecule of a cannot react with a molecule of b unless the two reactant molecules can somehow interact This interaction can only take place if they come within a certain distance of each other i e. collides with each other Therefore the rate constant of the reaction may be predicted by calculation of the collision frequency of the reactants Collision theory is proposed independently by Max Trautz in 1916 and william Lewis in 1918. Thereafter. C. Hinshelwood made modification on it http:/en.wikipediaorg/wiki/collision_theoR

A molecule of A cannot react with a molecule of B unless the two reactant molecules can somehow interact. This interaction can only take place if they come within a certain distance of each other, i.e., collides with each other. Therefore, the rate constant of the reaction may be predicted by calculation of the collision frequency of the reactants. Collision theory is proposed independently by Max Trautz in 1916 and William Lewis in 1918. Thereafter, C. Hinshelwood made modification on it. Basic considerations and brief history http://en.wikipedia.org/wiki/Collision_theory §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction Basic consideration and brief history Das gesetz der Reaktionsgeschwindigkeit und der Gleich gewichte in Gasen. Bestatigung der Additivitat von Cv-3/2R. Neue Bestimmung der Integrationskonstanten und der Molekildurchmesser Von MAX TRAUTz 2=4y2R丌·A·Vr M+M z. norg. Chem 94(1916)79

Basic consideration and brief history Z. anorg. Chem. 94 (1916), 79 §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction 9.6.1 Fundamental assumptions of Sct For gaseous bimolecular reaction 1) The reaction rate is proportional to the collision frequency(2 which can be solved by kinetic theory of molecule 2) The collision can be either non-reactive(elastic) collision or reactive collision Only the molecules posses energy excess to a critical value (E] can lead to reactive collision. The reaction rate should be in proportion to the fraction of reactive collision(q reaction rate can be expressed as ABg where Zab is the collision frequency of a with B per unit cubic meter per second, q is the portion of effective collision

9.6.1 Fundamental assumptions of SCT For gaseous bimolecular reaction 1) The reaction rate is proportional to the collision frequency (Z) which can be solved by kinetic theory of molecule; AB r Z q = where ZAB is the collision frequency of A with B per unit cubic meter per second, q is the portion of effective collision. reaction rate can be expressed as: 2) The collision can be either non-reactive (elastic) collision or reactive collision. Only the molecules posses energy excess to a critical value (Ec ) can lead to reactive collision. The reaction rate should be in proportion to the fraction of reactive collision (q). §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction Kinetic theory of gases In ca. 50 bCe. the Roman philosopher Lucretius proposed that static macroscopic bodies were composed of a small scale of rapidly moving atoms all bouncing off each ther In 1738 D B Hydrodynamica", which laid the basis or the kinetic theory of ga .The gas consists of very small particles. The volume of molecule is negligible .The number of molecules is so large that statistical treatment is applicable . The rapidly moving particles constantly collide among themselves. All these collisions are perfectly elasti . The interactions among molecules are negligible

§9.6 Rate Theories of elementary reaction Kinetic theory of gases In ca. 50 BCE, the Roman philosopher Lucretius proposed that static macroscopic bodies were composed of a small scale of rapidly moving atoms all bouncing off each other. In 1738 Daniel Bernoulli published “Hydrodynamica”, which laid the basis for the kinetic theory of gases. •The gas consists of very small particles. The volume of molecule is negligible. •The number of molecules is so large that statistical treatment is applicable. •The rapidly moving particles constantly collide among themselves. All these collisions are perfectly elastic. •The interactions among molecules are negligible

89.6 Rate Theories of elementary reaction 9.6.2 Calculation of ZaB SCT assumes that molecules can be taken as rigid ball without inner structure +d AB Definition: mean collision diameter: dAB

9.6.2 Calculation of ZAB SCT assumes that molecules can be taken as rigid ball without inner structure. dA dB Definition: mean collision diameter: dAB AB A B d d d  =      + 2 §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction 9.6.2 Calculation of LaB Definition: collision cross-section S=Ta aB motionless AB ABA

Definition:collision cross-section 2 S =dAB 2 Z AB =dAB V NB  A  A V NB motionless 9.6.2 Calculation of ZAB §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction 9.6.2 Calculation of ZaB When the concentration of a is Na/v(molec.m AB Abv v When both A and B moves, the relative velocity uaR Should be used AB D+U

When the concentration of A is NA /V (molecm-3 ): 2 AB AB Z =d V N V NA B  A When both A and B moves, the relative velocity AB should be used. ( ) 2 2  AB =  A + B 9.6.2 Calculation of ZAB §9.6 Rate Theories of elementary reaction

89.6 Rate Theories of elementary reaction 9.6.2 Calculation of ZaB according to the kinetic theory of gases aRT 8RT 8RT 8RT M+M AB 兀MAMB 丌MM aRT (reduced mass) M0 AB A+M aRT aRT ()学) ILd aRT LABI

i i M RT   8 = according to the kinetic theory of gases A B AB A B A B 8 8 8 RT RT RT M M M M M M     + = + =AB 8RT   = A B A B M M M M  = + (reduced mass) 2 2 A B A B B AB 2 2 8 8 8 [A][B] AB A AB RT RT N N Ln Ln Z d d V V V V RT L d               = =                 = 9.6.2 Calculation of ZAB §9.6 Rate Theories of elementary reaction