Physical chemistr Reaction Kinetics(5) Xuan Cheng Xiamen University
1 Reaction Kinetics (5) Xuan Cheng Xiamen University Physical Chemistry
Ch ical chemistr Reaction Kinetic Key words ■ Pyrolysis ■高温分解 ■ Acetaldehyde 乙醛 ethane ■甲烷 ■( Polymerization 聚合 Monomer ■单体 ■ intiator ■引发剂 ■ Relaxation ■迟豫
2 Key Words ◼ Pyrolysis ◼ Acetaldehyde ◼ Methane ◼ Polymerization ◼ Monomer ◼ Initiator ◼ Relaxation ◼ 高温分解 ◼ 乙醛 ◼ 甲烷 ◼ 聚合 ◼ 单体 ◼ 引发剂 ◼ 迟豫 Physical Chemistry Reaction Kinetics
Ch ical chemistr Reaction Kinetic Rice-Herzfeld mechanisms a chain reaction can lead to a simple rate law yrolysis of acetaldehyde CH3CHO(8)-4 >CH4(8)+CO(g) dt-kICH3CHOJ/2 d[Ch4 Simple rate laws can follow from quite complex chain mechanisms The Rice -Herzfeld mechanism for the pyrolysis of acetaldehyde is (a)Initiation: CH3CHO ka、CH3+CHO r=kalch3chol (b) Propagation ChaCHO +oCHa kB CHA+CHaCO. r=kb[CH3 CHOJ. 1 (c) Retardation:CH3CO、k。CH3+CO r=kclCH3. Termination: CH3 +oCH kd CH3CH
3 Physical Chemistry Rice-Herzfeld Mechanisms Simple rate laws can follow from quite complex chain mechanisms. (a) Initiation: CH CHO a CH CHO k ⎯⎯→• +• 3 3 [ ] r = ka CH3 CHO (b) Propagation: CH CHO +•CH ⎯⎯→CH +CH CO• b k 3 3 4 3 [ ][ ] CH3 CHO CH3 r kb = • (c) Retardation: CH CO c CH CO k 3 • ⎯⎯→• 3 + [ ] 3 r = k CH CO• c (d) Termination: CH3 CH3 CH3 CH3 d k • +• ⎯⎯→ 2 3 r k [ CH ] d = • The Rice-Herzfeld mechanism for the pyrolysis of acetaldehyde is A chain reaction can lead to a simple rate law. Pyrolysis of acetaldehyde ( ) ( ) ( ) CH3 CHO g ⎯⎯→CH4 g +CO g 3/ 2 3 4 [ ] [ ] k CH CHO dt d CH = Reaction Kinetics
Ch ical chemistr Reaction Kinetic Rice-Herzfeld mechanisms CH3CHO- Ma oCH3+oCHO r=kalch3chol ChaCHO CHa ks ,CHa+CHaCO. r=kblCH3] CH3COdk foCH+co r=kCH3CO。] QCH3+CH3M、CH3C3 r=ka[CH312 The net rates of the formation of the two intermediates are docH ka[CH3CHO]-k6ICH3EHOCH3]+k[](o CH31=0 d[CH3 CO. kCH3eHOH3-kCO。=0 dt The sum of the two equation is kalch3 cho]-kaloCH3]-=0
4 Physical Chemistry Rice-Herzfeld Mechanisms The net rates of the formation of the two intermediates are [ ] [ ][ ] [ ] [ ] 0 [ ] 2 3 3 3 3 3 3 = − • + • − • = • k CH CHO k CH CHO CH k CH CO k CH dt d CH a b c d [ ][ ] [ ] 0 [ ] 3 3 3 3 = • − • = • k CH CHO CH k CH CO dt d CH CO b c [ ] [ ] 0 2 ka CH3 CHO − kd •CH3 = CH CHO a CH CHO k ⎯⎯→• +• 3 3 [ ] r = ka CH3 CHO CH CHO +•CH ⎯⎯→CH +CH CO• b k 3 3 4 3 [ ][ ] CH3 CHO CH3 r kb = • CH CO c CH CO k 3 • ⎯⎯→• 3 + [ ] 3 r = k CH CO• c CH3 CH3 CH3 CH3 d k • +• ⎯⎯→ 2 3 r k [ CH ] d = • The sum of the two equation is Reaction Kinetics
Ch ical chemistr Reaction Kinetic Rice-Herzfeld mechanisms kalch3choj-kalCh 1/2 lCH [CH3CHOI The rate of formation of Cha is d[CHAzkbCH3CHOJLoCH31=h6/h,)1/2 [CH3CHOI 3/2 in agreement with the three-halves order observed experimentall However, the true mechanism is more complicated thanr-h mechanism Other products(acetone, CH3COCH3, and propanaldehyde, CH CH2 CHO) can be formed Prob.17.81
5 Physical Chemistry The rate of formation of CH4 is 1/ 2 3 1/ 2 3 [ ] [CH CHO] k k CH d a • = 3/ 2 3 1/ 2 3 3 4 [ ][ ] [ ] [ ] CH CHO k k k b CH CHO CH k dt d CH d a b = • = Rice-Herzfeld Mechanisms [ ] [ ] 0 2 ka CH3 CHO − kd •CH3 = in agreement with the three-halves order observed experimentally. However, the true mechanism is more complicated than R-H mechanism. Other products (acetone, CH3COCH3 , and propanaldehyde, CH3CH2CHO) can be formed. Prob. 17.81 Reaction Kinetics
Ch ical chemistr Reaction Kinetic Free-Radical polymerizations Chain polymerization Results in the rapid growth of an individual polymer chain for each activated monomer, and often occurs by a radical chain process Let and m stand for the initiator and monomer (a)Initiation ki 72I R● R●+M一 ka>RM· (b)Propagation M+M1 ● M+Mn-1 ● (c) Termination·Mn+·M mm m+n
6 Free-Radical Polymerizations Physical Chemistry Let I and M stand for the initiator and monomer I ⎯⎯→ R• i k 2 R•+M ⎯⎯→RM • a k 1 2 1 M M M p k + • ⎯⎯→• m n k Mn Mm ⎯⎯t→M + • +• m = 0,1,2, , n = 0,1,2, Chain polymerization Results in the rapid growth of an individual polymer chain for each activated monomer, and often occurs by a radical chain process. (a) Initiation (b) Propagation (c) Termination 2 3 2 M M M p k + • ⎯ ⎯→• n k M Mn M p n + • ⎯⎯⎯→• − − , 1 1 Reaction Kinetics
Ch ical chemistr Reaction Kinetic Free-Radical polymerizations (a)Initiation k 2R● kill] R●+M knRM· ( fast) The rate-determining step is the formation of the radicals R (b) Propagation M+M,.-pl >oM M+M2·-2>M3 M+Mn_1·-·M The chain of reactions propagates quickly, 2k[ (1799 f is the yield of the initiation step, the fraction of radicals that R successfully initiate a chain 0.3<f<0.8
7 Free-Radical Polymerizations Physical Chemistry I ⎯⎯→ R• i k 2 R•+M ⎯⎯→RM • a k (a) Initiation (b) Propagation r k [I] = i (fast) 1 2 1 M M M p k + • ⎯⎯→• 2 3 2 M M M p k + • ⎯ ⎯→• n k M Mn M p n + • ⎯⎯⎯→• − − , 1 1 r k [M][ M] p = • The rate-determining step is the formation of the radicals R•. The chain of reactions propagates quickly, f is the yield of the initiation step, the fraction of radicals that R• successfully initiate a chain. 0.3 f 0.8 2 [ ] [ ] fk I dt d M = i • (17.99) Reaction Kinetics
choical Chemistry Reaction Kinetic Free-Radical polymerizations c)ermination k m=0,1,2, n=0.12 m+n Assume that the rate of termination is independent of the length of the chain, the rate of change of radical concentration by this process is ● -2k,[M (17.101 The total radical concentration is approximately constant throughout the main part of the polymerization the rate at which radicals are formed by initiation the rate at which they are removed by termination)
8 Free-Radical Polymerizations Physical Chemistry m n k Mn Mm ⎯⎯t→M + (c) Termination • +• m = 0,1,2, , n = 0,1,2, 2 r k [ M ] t = • Assume that the rate of termination is independent of the length of the chain, the rate of change of radical concentration by this process is The total radical concentration is approximately constant throughout the main part of the polymerization. (the rate at which radicals are formed by initiation the rate at which they are removed by termination) 2 2 [ ] [ ] k M dt d M t = − • • (17.101) Reaction Kinetics
choical Chemistry Reaction Kinetic Free-Radical polymerizations Applying the steady-state approximation d°M=2/M|1-2kM=0 dt The steady-state concentration of radical chains =/)2 k (17102) The rate of propagation of the chains (the monomer is consumed) plmM 1/2 1/2 k (17103) Central the rate of polymerization is proportional to ature the sql uare root of the initiator concentration
9 Free-Radical Polymerizations Physical Chemistry 2 [ ] 2 [ ] 0 [ ] 2 = − • = • fk I k M dt d M i t Applying the steady-state approximation The steady-state concentration of radical chains The rate of propagation of the chains (the monomer is consumed) [ ][ ] [ ] k M M dt d M p = − • 1/ 2 1/ 2 [ ] [I] k fk M t i • = (17.102) [ ] [ ] [ ] 1/ 2 1/ 2 I M k fk k dt d M t i p = − (17.103) The rate of polymerization is proportional to the square root of the initiator concentration. Central feature Reaction Kinetics
Ch ical chemistr Reaction Kinetic Free-Radical polymerizations The degree of polymerization(DP) The number of monomers in the polymer s - -dm]/dt d[pot d[ptot/dt (17104) d[pot/dt 1a|[R =kRor°]=/[小 (17.105) 1/2 d[mi p dt k (17103) = (Rik)I/1/2 for termination by combination (17.104
10 Physical Chemistry Free-Radical Polymerizations The degree of polymerization (DP) The number of monomers in the polymer d P dt d M dt d P d M DP tot tot [ ]/ [ ]/ [ ] [ ] − = − = (17.104) [ ] [ ] [ ] 2 1 [ ]/ 2 k R f k I dt d R d P dt t tot i tot tot = • = • = − (17.105) [ ] [ ] [ ] 1/ 2 1/ 2 I M k fk k dt d M t i p = − (17.103) 1/ 2 1/ 2 for termination by combination ( ) [ ] [ ] fk k I k M DP i t p = (17.104) Reaction Kinetics
