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（2/7）

Physical chemistr Reaction Kinetics(2) Xuan Cheng Xiamen University

1 Reaction Kinetics (2) Xuan Cheng Xiamen University Physical Chemistry

Ch ical chemistr Reaction Kinetic Simple order reactions Order reaction Rate Law kA≡ak A→)P k 2k A→>P r=k4[小=[Aek k A→)P [ 1+k[4 LAlok n>2A→>P r=4广 1+[4(n-1kn 2 n-1 (n-DIALk

2 Order Reaction Rate Law t1/2 0 A → P 1 A → P 2 A → P n2 A → P o r = k r = kA   2 r = k A   n r = k A     k t o A A A e − =       A o o k t A A A + = 1 k A  ak k A ln 2 [A] o k A 1   A n o n n A k 1 1 ( 1) 2 1 − − − −   A o k A 2     A n k t A A A n o n o 1 ( 1) 1 1 = + −         − − A A k At o = − Simple Order Reactions Physical Chemistry Reaction Kinetics

Ch ical chemistr Reaction Kinetic Typical Complex reactions (Reversible Opposing AC reaction reaction (2) Consecutive reaction (3) Competing arae」 reaction reaction →)D

3 Typical Complex Reactions Physical Chemistry Reversible reaction Consecutive reaction Opposing reaction Competing reaction Parallel reaction A C f k ⎯→ kb A B C k k ⎯⎯1→ ⎯⎯2→ A C k ⎯⎯1→ A D k ⎯⎯2→ (1) (2) (3) Reaction Kinetics

Ch ical chemistr Reaction Kinetic Reversible first-Order reactions aA+bB+…→>eE+fF+ (171) Consider the reverse reaction(opposing reaction) A>C the first order in both forward and back directions rh= kb kfla da nh= kbl

4 Physical Chemistry Reversible First-Order Reactions Consider the reverse reaction (opposing reaction) r k [A] f = f A C f k ⎯→ kb aA+ bB +→ eE + fF + (17.1) the first order in both forward and back directions r k [C] b = b [ ] [ ] r k A dt d A f f f  = =      − [ ] [ ] r k C dt d A b b b  = =      Reaction Kinetics

Ch ical chemistr Reaction Kinetic Reversible first-Order reactions d4(44)+/4 kfla+ kbe (1731) △[C]=-[ ]-[Cb=-{41-[ C=Clo +[Alo-[a [4 一kf[4]+k{C+[4-[ kblClo +kblA]o-(k +kb)laj (1732)

5 Physical Chemistry [ ] [ ] [ ] [ ] [ ] k A k C dt d A dt d A dt d A f b f b  = − +       +      = (17.31) [C] = −[A] [C]−[C] o = −[A]−[A] o  [C] [C] [A] [A] = o + o − [ ] [ ] [ ] [ ] [ ] k A k C A A dt d A = − f + b o + o − [ ] [ ] ( )[ ] [ ] k C k A k k A dt d A = b o + b o − f + b (17.32) Reversible First-Order Reactions Reaction Kinetics

Ch ical chemistr Reaction Kinetic Reversible first-Order reactions MC1+k1[1(k+k)1 (1732) At equilibrium, 0 [A]=LAleg kB[Clo +kb[Alo=(kf+kb lAleg (17.33) (k,+k)4- f tnb [44g=4-g}J≡k+(1734

6 Physical Chemistry 0 [ ] = dt d A At equilibrium, k k t A A A A f b o eq eq ( ) [ ] [ ] [ ] [ ] ln = − + − − A A eq [ ] =[ ] Reversible First-Order Reactions [ ] [ ] ( )[ ] [ ] k C k A k k A dt d A = b o + b o − f + b (17.32) and b o b o f b A eq k [C] + k [A] = (k + k )[ ] (17.33) ( )[ ] [ ] [ ] k k A A dt d A = f + b eq −   (17.34) jt eq o eq A A A A e − [ ]−[ ] = [ ] −[ ] f b j  k + k Reaction Kinetics

Ch ical chemistr Reaction Kinetic Reversible first-Order reactions []-[Al e e j≡kf+b(17.34 (17.14) Fg.17.2 Au>C When lale =0, kb=0 [AJ/LAlo k,/kh-2 g.17.1(a) /C//AI

7     k t o A A A e − = (17.14)*   (17.34) jt eq o eq A A A A e − [ ]−[ ] = [ ] −[ ] f b j  k + k Physical Chemistry Reversible First-Order Reactions [A]/[A]o [C]/[A]o kf / kb=2 A  C jt Fig. 17.2 When [A]eq=0, kb=0 [A]/[A] o t Fig. 17.1(a) Reaction Kinetics

Ch ical chemistr Reaction Kinetic Consecutive first-Order reactions Consider two consecutive irreversible first-order reactions B k2 C (1735) 71=[4 db n=kla B 2=-k2[B 2 [B]_(B],(a[B] d,=64-k2B1 kila dB =h4-k2[B d|[C」 k2[B](17.36)

8 Physical Chemistry Consecutive First-Order Reactions Consider two consecutive irreversible first-order reactions A B C k k ⎯⎯1→ ⎯⎯2→ (17.35) [ ] r 1 = k1 A [ ] r 2 = k2 B [ ] [ ] 1 1 1 r k A dt d B  = =      [ ] [ ] 2 2 2 r k B dt d B  = − = −      [ ] [ ] [ ] [ ] [ ] 1 2 1 2 k A k B dt d B dt d B dt d B  = −       +      = (17.36) [ ] [ ] k1 A dt d A  = −      [ ] [ ] [ ] k1 A k2 B dt d B  = −      [ ] [ ] k2 B dt d C  =      Reaction Kinetics

Ch ical chemistr Reaction Kinetic Consecutive first-Order reactions Let only a be present in the system at t=0 [A1o≠0Bo=0C1o=0 (1737) k1[ dB dt t=包B1(4c k2[B](1736) dt=-k (1711) k (1738) B -ki[Ale l-k (1739) Integration 6/=41 k1-。-k2 (1740)

9 Physical Chemistry Let only A be present in the system at t = 0 [A] o  0 (17.37) Consecutive First-Order Reactions [B] o = 0 [C] o = 0     k t o A A e = − 1 (17.38) (17.36) [ ] [ ] k1 A dt d A  = −      [ ] [ ] [ ] k1 A k2 B dt d B  = −      [ ] [ ] k2 B dt d C  =      dA/ dt = −k AA (17.11) (17.39) [ ] [ ] [ ] 1 2 k A e 1 k B dt d B k t  = o −      − ( ) [ ] [ ] 1 2 2 1 1 o k t k t e e k k k A B − − − − = (17.40) Integration Reaction Kinetics ?

Ch ical chemistr Reaction Kinetic Consecutive first-Order reactions At all times(conservation of matter) [A+[B]+[C]=LAlo (17.38 BI h,toke k2-kI 1740) C]=[4o1l 2-k1t kt (1741) 2 k1≈k2 k1>>k2 k1<<z

10 Physical Chemistry Consecutive First-Order Reactions A B C A o At all times (conservation of matter) [ ]+[ ]+[ ] =[ ]     k t o A A e = − 1 (17.38) ( ) [ ] [ ] 1 2 2 1 1 o k t k t e e k k k A B − − − − = (17.40)         − + − = − −k t −k t o e k k k e k k k C A 1 2 2 1 1 2 1 2 [ ] [ ] 1 (17.41) Reaction Kinetics