山大物理化学英文下6

1、 9.6 Rate Theories of elementary reaction Extensive reading: Levine, pp. 879-881Two important empirical rules: Rate equation (law of mass action) Arrhenius equation RTEAkaexpType of reactionUnimolecular reactionBimolecular reactionTermolecular reactionA1013 s1011 mol-1 dm3 s-1109 mol-2 dm6 s-1A seem

2、s related to collision frequency.RTEaexpBoltzmann distribution termABrk It is obvious that 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., collid

3、es with each other. A reaction can take place only if the molecules of the reactants collide. 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 i

4、n 1918. Thereafter, C. Hinshelwood made modification on its. Basic consideration and brief history/wiki/Collision_theory6.1 Fundamental assumptions of SCTfor gaseous bimolecular reaction 1) The reaction rate of reaction is proportional to the collision frequency (Z), which can

5、be solved by kinetic theory of molecule; ABrZq 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 m

6、olecules 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).6.2 Calculation of ZAB SCT assumes that molecules can be taken as rigid ball without inner structure. dAdB dA and dB are the diam

7、eter of A and B molecule, respectively. Definition: mean collision diameter: dABABBAddd2The way to collide:Definition:collision cross-section2ABdS2ABABdZVNBAAVNBmotionless When the concentration of A is NA/V (molecm-3):2ABABdZVNVNBAAWhen both A and B moves, the relative velocity VAB should be used.2

8、2BAABiiMRT8according to the kinetic theory of gasesABABABAB888MMRTRTRTMMM MAB8RTABABM MMM(reduced mass) 22ABABBAB22888ABABAABNNLnLnRTRTZddVVVVRTL dDecomposition of HI: 2HI = H2 + I2222AAAAA28A2RTZL dM22ABAB8ABRTZL d?For exampleAt 1.0 105 Pa and 700 K, d = 3.50 10-10 m, Z HI-HI = ?53111.0 10 PaHI17.4

9、1mol m8.314J Kmol700KpRT23 210 22AA3343128 8.314 7003.1416(6.02 10 ) (3.50 10)(17.41)23.1416 128 101.017 10 m sZ Generally, ZAB of gaseous reactions at ambient temperature and pressure is of the magnitude of 1035 m-3 s-1. If reaction takes place whenever the molecules collides:22ABAB8ABRTZL dAABANdd

10、VrLZdtdt 2ABABA8ABZdRTdLdtLAABdkdt2AB8RTkdLbecausek = 7.88 104 mol-1dm3s-1 When c0 = 1.00 mol dm-3, the half-life of HI is 1.27 10-5 s. This result differs greatly from the experimental fact. In 1909, Max Trantz introduced fraction of reactive collision (q) to solve this great discrepancy. 6.3 Calcu

11、lation of q Only the molecules posses energy excess to a critical value (Ec) can lead to reactive collision. It is apparent that E of translational energy of motion is related to the relative motion of two molecules. And Ec is thus the minimum translational energy of motion (critical / threshold ene

12、rgy) along the connecting line between the mass-point of the two molecules which are to collide. If the energy exchange between colliding molecules is much rapid than reaction, the energy distribution of molecules may still obey the Maxwell-Boltzmann distribution equation. RTEnnqcexp*Boltzmann facto

13、r If Ec = 120 kJmol-1, T = 300 K, then q = 1.27 10-21 This suggest than among 7.8 1020 collision only one collision is effective.The fraction of the collision with the energy equal to or greater than Ec is:6.4 Calculation of k ABrZq22ABABABAB8ABMMRTZL dM M2AB8expABcERTrdLRTABrk2SCTAB8expcERTkdLRTRTE

14、BTkcSCTexp21B is a constant independent of T.RTEnnqcexp*RTEAkaexpcaERTE21RTEBTkcSCTexp21The experimental activation energy (Ea) depends on temperature.Using Ea for substitution of Ec, 2AB8expcSCTERTkdLRT2AB8expaSCTERTekdLRT The pre-exponential factor corresponds to the collision frequency. This is t

15、he reason why A is also named as frequency factor.6.5 Comment on SCT 1) The expression for the rate coefficient given by SCT conforms qualitatively to the Arrhenius equation observed experimentally. This suggests that SCT reveal the principal features of the reaction, i.e., in order to react, molecu

16、les have to collide (the pre-exponential term) and the collision should be sufficiently energetic (the exponential term)(1) Success SCT gives a vivid physical image of the reaction process:2) As pointed out by SCT, the pre-exponential factor, dependent only on the masses of the species involved in t

17、he collision, can be calculated easily. caERTE21 SCT reveals the physical meaning of the pre-exponential factor, i.e., the collision frequency. 3) SCT demonstrated theoretically that experimental activation energy depends on temperature.(2) Shortcomings 1) For calculating k, Ec is needed. However, S

18、CT can not give Ec. Calculation of k depends on the experimental determination of Ea. Therefore, SCT can not predict the kinetic features of the reaction theoretically. 2) The quantitative agreement between SCT and experiments is poor.Reaction EaAcalAexpAcal./Aexp.2NOCl2NO+Cl2107.82.951093.231090.91

19、H+Br2 HBr+Br3.764.610106.761096.76NO+O3NO2+O29.617.941096.311071.25102CH3+CHCl3 CH4+CCl324.21.510101.261061.191042-cyclopentadiene dimer60.68.131092.451033.32106 In some cases, the agreement between experimental and calculated A values can be quite good. However, in many cases, the observed rate is definitely too small. It was found that the more complex of the reactant molecules, the greater the discrepancy between Acal and Aexp. In fact, the reactant is of complex molecul