山东大学：《物理化学》课程教学资源（讲义资料）10.8 Kinetics of reactions in solution

10. 8 Kinetics of reactions in solution Extensive reading Levine, p. 573-576, Section 17.15

10.8 Kinetics of reactions in solution Extensive reading: Levine, p. 573-576, Section 17.15

10.8 Kinetics of reactions in solution Brainstorm: What factors will affect the rate of reaction in solution? Does a reaction differs a lot when it occurs in gaseous state or in solution ○ What is your hypothesis?

Brainstorm: What factors will affect the rate of reaction in solution? Does a reaction differs a lot when it occurs in gaseous state or in solution? What is your hypothesis? 10.8 Kinetics of reactions in solution

10.8 Kinetics of reactions in solution (2)Theoretical model-solvent cage SOME REMARKS ABOUT FREE RADICALS AND THE PHOTOCHEMISTRY OF SOLUTIONS BY PROFESSOR J. FRANCK AND DR. E. RABINOWITSCH(Gottingen) Ill. Secondary Recombination and the Temperature- Coefficient. The equilibrium concentration of free atoms or radicals in a solution as compared with a gas, is affected not only by a decreased rate of forma- tion and the possibility of "primary recombination "but also by an increased probability of norm or“ secondary"” recombination, resulting from the fact that every collision of two radicals or atoms in solution is made a"triple "or"multipl ole ) collis ision by the presence the molecules of the solvent. Thus the velocity of normal recombina- tion will in every solution be greater by the factor I03 to Iof than it i in a gas at atmospheric pressure. J. Franck and E Rabinowitch, Trans. Faraday Soc., 1934, 30: 120

(2) Theoretical model—solvent cage 10.8 Kinetics of reactions in solution J. Franck and E. Rabinowitch, Trans. Faraday Soc., 1934, 30: 120

10.8 Kinetics of reactions in solution (2) Theoretical model-solvent cage 1934. J. Franck and E. Rabinowitch established that. once reactant molecules meet in one solvent cage through diffusion (an encounter), they will be trapped in the cage for a relatively long time during which they collide repeatedly with each other, providing more chance to react Solvent cage: capture reactant molecules diffuse Within a solvent cage(for 1-100 ns),two in or out from or to other solvent cages reactant molecules can collide 10 105 times

(2) Theoretical model—solvent cage Solvent cage: capture reactant molecules diffuse in or out from or to other solvent cages. 1934, J. Franck and E. Rabinowitch established that, once reactant molecules meet in one solvent cage through diffusion (an encounter), they will be trapped in the cage for a relatively long time during which they collide repeatedly with each other, providing more chance to react. Within a solvent cage (for 1~100 ns), two reactant molecules can collide 10 ~105 times. 10.8 Kinetics of reactions in solution

10.8 Kinetics of reactions in solution (2)Theoretical model OOoOOooo P8900 A+B→{AB}→P fAB term represents the caged reactants including the encounter pair and the activated complex 10-12 10-10 s collides for 10 105 times diff reaction control Edit> ere diffusion control

A + B → {AB} → P {AB} term represents the caged reactants including the encounter pair and the activated complex. 10-12 ~ 10-10 s, collides for 10 ~ 105 times. Ere > Ediff. Reaction control. Ediff. > Ere, diffusion control. (2) Theoretical model 10.8 Kinetics of reactions in solution

10.8 Kinetics of reactions in solution ()Kinetics treatment A+B→{AB}→P A+B、M[A:B] diffusion [A:B] P reaction dA: B kainlajb]-kdoula B]-k [A: B=0 [A: B]=Kain LAJ[BI k, +k kk r=k,A: B [AJB=KALB ut

(3) Kinetics treatment diffusion reaction , , [A:B] [A][B] [A:B] [ : B] 0 dt d in d out r d = − − = k k k A , , [A][B] [A:B] d in d out r k k k = + , , [A:B] [A][B] [A][B] r d in r d out r k k r k k k k = = = + 10.8 Kinetics of reactions in solution A + B → {AB} → P

10.8 Kinetics of reactions in solution (3)Kinetics treatment kk [A]B] k, tk d out Discussion: d out k kd out << k 六、kkm[AIB]=kK[A[B r=knabl k=kd, in dout If reaction is much slow than diffusion If diffusion is much slow than reaction activation control or kinetics control diffusion control

, , [A][B] r d in d out r k k r k k = + Discussion: d out r , k k , , [A][B] [A][B] r d in r d d out k k r k K k = = If reaction is much slow than diffusion, activation control or kinetics control d out r , k k  , [A][B] d in r k = d in, k k = If diffusion is much slow than reaction, diffusion control (3) Kinetics treatment 10.8 Kinetics of reactions in solution

10.8 Kinetics of reactions in solution (3)Kinetics treatment Resembles gaseous reaction, no effect of solvent Solvents gas CS2 CH6 C2H_OH 106 k/dm. mol-l s-16 20 Solvent effect on reaction between species of low polarity is weak activation control

activation control Resembles gaseous reaction, no effect of solvent. Solvents gas CS2 C6H6 C2H5OH 106 k/ dm3  mol-1 s -1 6 6 10 20 2 Solvent effect on reaction between species of low polarity is weak. (3) Kinetics treatment 10.8 Kinetics of reactions in solution

10.8 Kinetics of reactions in solution (3)Kinetics treatment For diffusion control Fickian first law Flux DA d diffusion coefficient with unit of m2.s-1 For second-order reaction r=-4TARD dn B Integration yields r=4T(TA +BDBNB

For diffusion control Fickian first law B B dn dc DA dt dx Flux  = = − D diffusion coefficient with unit of m2 s -1 . For second-order reaction 2 AB 4 B B dN r r D dx = −  Integration yields A B B B r r r D N = + 4 ( )  (3) Kinetics treatment 10.8 Kinetics of reactions in solution

10.8 Kinetics of reactions in solution (3)Kinetics treatment For diffusion control ka=4(ra+r36nAB r=4丌(r+3)(D、+D3)NANB AB ka=4T(rA +B(Da +Db) 8k T n= Aexp 77 RT For spherical particle Einstein-Storks equation 8k T E exp 3A RT k T D tnr For diffusion.ex 10 kJ. mol-I Macro-viscosity or micro-viscosit

A B A B A B A B 4 ( )( ) d r r r D D N N k N N = + +  = A B A B 4 ( )( ) d k r r D D = + +  B A B A B 1 1 4 ( ) ( ) 6 d k T k r r r r   For diffusion control = + + (3) Kinetics treatment 6 B k T D r = For spherical particle, Einstein-Storks equation If rA = rB B 8 3 d k T k  = exp E a A RT    =     B 8 exp 3 a d k T E k A RT   = −    For diffusion, Ea  10 kJmol-1 Macro-viscosity or micro-viscosity? 10.8 Kinetics of reactions in solution