1、Chapter 27. Molecular Reaction Dynamics,Purpose: Calculation of rate constants for simple elementary reactions.For reactions to take place: 1. Reactant molecules must meet.2. Must hold a minimum energy.Gas phase reactions: Collision theory. Solution phase reactions: Diffusion controlled.Activation c
2、ontrolled.,27.1 Collision theory,Consider a bimolecular elementary reactionA + B P v = k2ABThe rate of v is proportional to the rate of collision, and therefore to the mean speed of the molecules,Because a collision will be successful only if the kinetic energy exceeds a minimum value. It thus sugge
3、sts that the rate constant should also be proportional to a Boltzmann factor of the form, .Consider the steric factor, P, Therefore, k2 is proportional to the product of steric requirement x encounter rate x minimum energy requirement,Collision rate in gases,Collision density, ZAB, is the number of
4、(A, B) collisions in a region of the sample in an interval of time divided by the volume of the region and the duration of the interval.where = d2 d = (dA + dB) and u is the reduced masswhen A and B are the same, one getsThe collision density for nitrogen at room temperature and pressure, with d = 2
5、80 pm, Z = 5 x 1034 m-3s-1.,The energy requirement,For a collision with a specific relative speed of approach vrelreorganize the rate constant asAssuming that the reactive collision cross-section is zero below a,The steric effect,Steric factor, P, Reactive cross-section, *,* = P Harpoon mechanism: E
6、lectron transfer preceded the atom extraction. It extends the cross-section for the reactive encounter. K and Br2 reaction,Example 27.1 Estimate the steric factor for the reaction H2 + C2H4 - C2H6 at 628K given that the pre-exponential factor is 1.24 x 106 L mol-1 s-1.Solution: Calculate the reduced
7、 mass of the colliding pairFrom Table 24.1 (H2) = 0.27 nm2 and (C2H4) = 0.64 nm2, given a mean collision cross-section of = 0.46 nm2. P = 1.24 x 106 L mol-1 s-1/7.37 x 1011 L mol-1s-1= 1.7 x 10-6,Example 27.2: Estimate the steric factor for the reaction: K + Br2 KBr + BrSolution: The above reaction
8、involves electron flipK + Br2 K+ + Br2-Three types of energies are involved in the above process: (1) Ionization energy of K, I(2) Electron affinity of Br2, Eea(3) Coulombic interaction energy:Electron flip occurs when the sum of the above three energies changes sign from positive to negative,27.2 D
9、iffusion-controlled reactions,Cage effect: The lingering of one molecule near another on account of the hindering presence of solvent molecules. Classes of reactionSuppose that the rate of formation of an encounter pair AB is first-order in each of the reactants A and B:A + B AB v = kdABThe encounte
10、r pair, AB, has the following two fates:AB A + B v = kdABAB P v = kaABThe net rate of change of AB:= kdAB - kdAB - kaAB,Invoking steady-state approximation to ABThe net rate of the production:When kd ka (This is activation-controlled reaction),Reaction and Diffusion,where R* is the distance between
11、the reactant molecules and D is the sum of the diffusion coefficients of the two reactant species. where is the viscosity of the medium. RA and RB are the hydrodynamic radius of A and B.If we assume RA = RB = 1/2R*,27.3 The material balance equation,(a) The formulation of the equationthe net rate of
12、 change due to chemical reactionsthe over rate of changethe above equation is called the material balance equation.,(b) Solutions of the equation,27.4 The Eyring equation,The transition state theory pictures a reaction between A and B as proceeding through the formation of an activated complex in a pre-equilibrium:A + B - CK = ( is represented by in the math style)The partial pressure and the molar concentration has the following relationship:pJ = RTJ thusC = K ABThe activated complex falls apart by unimolecular decay into products, P,C P v = kCSo v = k K ABDefine k2 = k Kv = k2AB,
