厦门大学：《物理化学 Physical Chemistry》课程电子教案（PPT教学课件）反应动力学 Reaction-Kinetics（7/7）

Physical chemistr Reaction Kinetics(7) Xuan Cheng Xiamen University

1 Reaction Kinetics (7) Xuan Cheng Xiamen University Physical Chemistry

Ch ical chemistr Reaction Kinetic Thermodynamic Aspects Activated Complex Theory: structure of the activated complex(? The concepts: an equilibrium between the reactants and the activated complex The activation process is expressed in terms of thermodynamic function 二≠/NA re h T (2324 (EB/NAVEC/NAV) /NAV K f=BIC]…(=B/N4(=c/N) (23.10 1(2m7ck)28 h (23.15) 1/2 Kr=K h (2325)

2 Physical Chemistry Thermodynamic Aspects Activated Complex Theory: structure of the activated complex (?) The concepts: an equilibrium between the reactants and the activated complex The activation process is expressed in terms of thermodynamic function k T (23.24) B A C A A c e z N V z N V z N V K   −    0 ( / )( / ) / '     h m k T K K rc c f 1/ 2 2         =  (23.25)   k T B A C A f A f e z N V z N V z N V B C X K   −    = 0 ( / )( / ) / [ ][ ]    (23.10) (23.15) ' 1/ 2 (2 ) 2 1  =  z h m kT z  rc  Reaction Kinetics

Ch ical chemistr Reaction Kinetic Thermodvnamic aspects kT kr =Ko (2326) In terms of AGO=-RT hn Ko =-RT In concentration 0\An/mot (2327) For the process B+c+…→少 △/mol=1-n By analogy to(23.27), define Gibbs energy of activation△G*=- RT ktc(°y-1 23.28 kT Rate constant kr (c0)1-n-△GO=/RT h (2329) Thermodynamic version of the tst expression for the rate constant

3 Physical Chemistry Thermodynamic Aspects          = − = − o n mol o c c o c c K G RT K RT / ( ) ln ln (23.27)   n/mol =1−n →  B +C + X f For the process   (23.28) 1 ln ( )   −   − o n c o c G RT K c By analogy to (23.27), define  r = Kc h kT k (23.26) In terms of concentration Gibbs energy of activation o n G RT r o c c e h k T k 1 / ( )  − − = (23.29) Thermodynamic version of the TST expression for the rate constant. Rate constant Reaction Kinetics

choical Chemistry Reaction Kinetic Thermodvnamic aspects KdE RTc 23.30 Enthalpy of activation aho+=AHo*= dhn Kp (2331) Entropy of activation △S≠=△HO≠-△G≠/T 9i6 gy of activation△G2=△H2-T^S2 (23.32) kr O1-n-△G/RT (2329) .、kTo1-na-AS/R-△He=/RT h (23.33)

4 Physical Chemistry Thermodynamic Aspects (23.30) n o o o c o P P RTc K K −            1 dT d K H H RT o o o P c     =   2 ln (23.31) S ( H G ) T o c o c o c /    Entropy of activation    −  (23.32)     =  −  o c o c o Gc H T S o n G RT r o c c e h k T k 1 / ( )  − − = (23.29) o n S R H RT r o c o c c e e h k T k 1 / / ( )   − − − = (23.33) Enthalpy of activation Gibbs energy of activation Reaction Kinetics

choical Chemistry Reaction Kinetic Thermodynamic Aspects a=Rr2 dInk 17.68) En≡RT dn k dhKO≠ -RT+rT d T' K (2326) dhn kc dIn kox KB≡K O≠ (23.30) =△HO/R2+(n-1)T T =△HO≠=RT 2dIn kp (2331) dT Ea=△HO≠+ nr Gas-phase reaction(23.34) △HO≠=△U0+(1-n)RT (5.10) E=△U+RT

5 Physical Chemistry Thermodynamic Aspects dT d k Ea RT 2 ln  (17.68)  r = Kc h kT k (23.26) dT d K RT RT dT d k E RT o r c a   = + 2 ln 2 ln (23.30) n o o o c o P P RTc K K −            1 dT d K H H RT o o o P c     =   2 ln (23.31) H RT n T T n dT d K dT d K o o P o c / ( 1) ln ln 1 2 =  + − − = +    E H nRT o a =  +  Gas-phase reaction (23.34) RT (5.10) H U n o o  =  + (1− )   E U RT o a =  +  Reaction Kinetics

choical Chemistry Reaction Kinetic Thermodynamic aspects E/RT a=k ea ktoI-n-ASO/R-AHO/RT kr=",( e (23.33) ea=Ah+nRt Gas-phase reaction (23.34) kT A=Acoyl-me"eASc R Gas-phase reaction (23.35)

6 Physical Chemistry Thermodynamic Aspects o n S R H RT r o c o c c e e h k T k 1 / / ( )   − − − = (23.33) E H nRT o a =  +  Gas-phase reaction (23.34) E RT r a A k e /  o n n S R o c c e e h k T A 1 / ( )  −  = Gas-phase reaction (23.35) Reaction Kinetics

Ch ical chemistr Reaction Kinetic Catalysis Catalyst: a substance that increases the rate of a reaction and can be recovered chemically unchanged at the end of the reaction A catalyst Lower the activation energy Avoiding the slow, rate-determining step of the uncatalysed reaction Results in a higher reaction rate at the same temperature Activation energies of catalysed reactions Reaction Catalyst E。/kJmo1 2H→H2+l2 None 184 Au 105 Pt 59 2NH3>N2+3H2 None 350 W 162

7 Physical Chemistry Catalysis Catalyst: a substance that increases the rate of a reaction and can be recovered chemically unchanged at the end of the reaction. A catalyst Lower the activation energy Avoiding the slow, rate-determining step of the uncatalysed reaction Results in a higher reaction rate at the same temperature Activation energies of catalysed reactions Reaction Catalyst Ea / kJmol-1 2 2 2 HI → H + I 2NH3 → N2 +3H2 None 184 Au 105 Pt 59 None 350 W 162 Reaction Kinetics

Ch ical chemistr Reaction Kinetico Catalvsis (a) participate the reaction E0, the reaction can not proceed even with catalysts (2 )The catalysts cant change standard equilibrium constants A, Gm(T, P)=-RT In Ko (3) The catalysts change both forward and backward reaction rates

8 Physical Chemistry Catalysis (a) Participate the reaction Can’t change the reaction direction and reaction equilibrium E1 E2 { Ea E } Reaction coordinate E1<Ea E2<Ea A B AB catalyst(K) + ⎯⎯⎯⎯⎯→ A+K →AK AK+B→AB+K (b) Lower the activation energy (c) High selectivity (1) If , r Gm(T,P)  0 the reaction can not proceed even with catalysts (2) The catalysts can’t change standard equilibrium constants o r Gm(T, P) = −RT ln K (3) The catalysts change both forward and backward reaction rates Reaction Kinetics

Ch ical chemistr Reaction Kinetic Catalvsis Ethanol Conversion 25 types of products Cu 200-250 c)CH,CHO÷2 A2O3T2→C2H4+H2O 350-360°C Alo CHOH →(C,H,O+H,O 250°C Zno. CrO ->CH=CH-CH=Ch+ho+h 400-4500C Na >ChoH+ho

9 Physical Chemistry Catalysis Ethanol Conversion ( )                   ⎯⎯→ + → = − = + + −  → + → + − → + ............................................. ............................................. C H O H H O C H C H C H C H H O H 400 450 C ZnO C r O C H O H O 250 C Al O C H H O 350 360 C Al O 或 ThO C H CHO H 200 - 250 C C u C H O H 4 9 2 N a o 2 2 2 2 2 3 o 2 5 2 2 2 3 o 2 4 2 2 3 2 o 3 2 2 5 or 25 types of products Reaction Kinetics

choical Chemistry Reaction Kinetic Homogeneous Catalvsis The kinetics of the bromide-catalysed decomposition of hydrogen peroxide 2H2O2(cg)→>2H2O(cg)+O2(8) The reaction is believed to proceed through the following pre equilibrium [HOOH 2 I H3O+Hooh<>H00H2+h,O K 「 HOOH TH2O+ HOOH+Br→HOB+H2O r=k[HOOH2 Br HOBr+HOOH>H3O+O Br (in the equilibrium constant, the activity of H,o has been set equal to 1. d|O2] kKTHOOH H3o l Br

10 Physical Chemistry Homogeneous Catalysis The reaction is believed to proceed through the following pre￾equilibrium: 2 ( ) 2 ( ) ( ) H2 O2 aq → H2 O aq +O2 g The kinetics of the bromide-catalysed decomposition of hydrogen peroxide H3 O + HOOH  HOOH 2 + H2 O + + HOOH 2 + Br → HOBr + H2 O + − + − HOBr + HOOH → H O + O + Br 3 2 [ ][ ] [ ] 3 2 + + = HOOH H O HOOH K [ ][ ] 2 + − r = k HOOH Br (fast) (in the equilibrium constant, the activity of H2O has been set equal to 1.) [ ][ ][ ] [ ] 3 2 + − = k K HOOH H O Br dt d O Reaction Kinetics