山东大学：《物理化学》课程教学资源（讲义资料）10.2 Approximate treatment of rate equation and mechanism assumption

8 10.2 Approximate treatment of rate equation and mechanism assumption Extensive reacting: Levine: p545 17.6

§10.2 Approximate treatment of rate equation and mechanism assumption Extensive reacting: Levine: p.545 17.6

Summary k k k x Re A b K (k+k_)t=kt k C X -x (x。-x) K1 B dx yK =k(a-x)+k(-x)=(k+k2)a-x) A ∠ 0 A-4>B->C kk dt k2-K, lexp(kt)-exp(-k2t)

A B C 1 2 ⎯⎯→ ⎯⎯→ k k − + = k k Kc e e e ln ( ) x x k at x x + = − e e ln ( ) ( ) x k k t kt x x = + = + − − ( ) ( ) ( )( ) 1 2 1 2 k a x k a x k k a x dt dx = − + − = + − 2 1 k k z y = = 0 dt dy   1 2 1 2 2 1 dc ak k Z exp( k t ) exp( k t ) dt k k = − − − − Summary

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism Necessary of approximation treatment 1)Br2->2Br AA>B—kC 2)Br·+H,—>HBr+H k, 3)正.+Br2->HBr+Br exp(k,)-exp(] k-k A4)H+HBr→→H2+Br 5)2Br·—>Br2 k exp(k,t) k2-k1 dhAr ? k1 exp(kt) k2-k1

Necessary of approximation treatment 10.2.1 Approximation treatment of complex reaction mechanism A B C 1 2 ⎯⎯→ ⎯⎯→ k k exp( ) exp( ) 1 2 2 1 1 k t k t k k k a y − − − − =               − − + − − − = exp( ) 1 exp( ) 2 2 1 1 1 2 1 2 k t k k k k t k k k z a 1) Br2 ⎯→ 2Br 2) Br + H2 ⎯→ HBr + H 3) H + Br2 ⎯→ HBr + Br 4) H + HBr ⎯→ H2 + Br 5) 2Br ⎯→ Br2 d[HBr] ? dt = §10.2 Mechanism assumption and Approximate treatment

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism Br.>2Bro To certify the correctness of a proposed Br,+H、kHBr+H mechanism. the mechanism must undergo strict H+Br2→HBr+Br examination H+hbr- kA >h+Br. Whether or not the rate equation derived from aBro BI the proposed mechanism is consistent to the dhAr experimental one is an important criterion However, because of the complexity of the mechanism. the exact treatment of the mechanism k H2IBr is usually impossible and some approximation have 1+k THBr to be introduced

To certify the correctness of a proposed mechanism, the mechanism must undergo strict examination. Whether or not the rate equation derived from the proposed mechanism is consistent to the experimental one is an important criterion. However, because of the complexity of the mechanism, the exact treatment of the mechanism is usually impossible and some approximation have to be introduced. 10.2.1 Approximation treatment of complex reaction mechanism §10.2 Mechanism assumption and Approximate treatment 0.5 2 2 2 [H ][Br ] [HBr] 1 ' [Br ] r k k = + d[HBr] ? dt = 1 2 3 4 5 2 2 2 2 2 Br 2Br Br H HBr H H Br HBr Br H HBr H +Br 2Br Br k k k k k ⎯⎯→ + ⎯⎯→ + + ⎯⎯→ + + ⎯⎯→ ⎯⎯→

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism ZEITSCHRIFT FUR ELEKTROCHEMIE (Bd. 19, 1913 Herr Prof. Dr. M. Bodenstein- Hannover PHOTOCHEMISCHE KINETIK DES CHLORKNALLGASES Max bodenstein was the first man to demonstrate that, in the reaction of hydrogen with chlorine, the high performance could be explained by means of a chain reaction In his kinetic studies he used the quasi-steady state approximation to derive the rate equation of the Max Ernst august bodenstein reactior German physical chemist

Max Bodenstein was the first man to demonstrate that, in the reaction of hydrogen with chlorine, the high performance could be explained by means of a chain reaction. In his kinetic studies, he used the quasi-steady state approximation to derive the rate equation of the reaction. Max Ernst August Bodenstein German physical chemist 10.2.1 Approximation treatment of complex reaction mechanism §10.2 Mechanism assumption and Approximate treatment

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism Es ist danach hier +-=+?=kC4 When an overall reaction is subdivided und daher k2 Jo[Cll+k, leI(Clal into elementary steps, Bodenstein's quasi- oe s8I-kIO1IOal+k,lelICll Die Geschwindigkeit mit der das Elektron steady state approximation neglects the verbraucht wird, ist gemaB lla und llb variations in the concentrations of reaction dt Im stationaren Zustand, der sich praktisch intermediates by y assuming that the unmittelbar nach Beginn der Belichtung ein- stellt, ist concentration of these intermediates would d dt remain quasi-constant. These reactive dem Absolutwert nach, und deswegen ka Jo Cla-tkslelcI intermediates can be radicals. carbonium k4O2]+k。C2 woraus folgt ions. molecules in the excited state. etc Ju[,I

When an overall reaction is subdivided into elementary steps, Bodenstein's quasi￾steady state approximation neglects the variations in the concentrations of reaction intermediates by assuming that the concentration of these intermediates would remain quasi-constant. These reactive intermediates can be radicals, carbonium ions, molecules in the excited state, etc. 10.2.1 Approximation treatment of complex reaction mechanism §10.2 Mechanism assumption and Approximate treatment

810.2 Mechanism assumption and Approximate treatment 10.2. 1 Approximation treatment of complex reaction mechanism (1)Steady-state approximation (2)Rate-determining step(r d S) approximation For reaction: H+ Br-2 HBr For reaction: d HBr kh,Br 1/2 HBI 2NO,+F→>2NO3F 1+m B The experimental rate equation is: In 1919.. A. Christiansen. K. F r=k[nO,e Herzfeld and m Polanyi independently proposed the mechanism consisting of No+E-k>NOF+F five elementary reactions F+no-k >NOF

In 1919, J. A. Christiansen, K. F. Herzfeld and M. Polanyi independently proposed the mechanism consisting of five elementary reactions: (1) Steady-state approximation For reaction: H2 + Br2 → 2 HBr 1/ 2 2 2 2 [HBr] [H ][Br ] [HBr] 1 Br d k dt m = + 10.2.1 Approximation treatment of complex reaction mechanism (2) Rate-determining step (r. d. s.) approximation 2 2 2 2NO F 2NO F + → For reaction: 2 2 r k = [NO ][F ] The experimental rate equation is: §10.2 Mechanism assumption and Approximate treatment 1 2 2 2 2 2 2 NO +F NO F F F NO NO F k k ⎯⎯→ + + ⎯⎯→

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism (3)Pre-equilibrium approximation Azo reaction of aniline under catalysis of HBr H+HNO, +C> N2+2H,O r=k[HI[HNO,IBr Its mechanism is proposed as 1)H+HNO,HNo (rapid equilibrium 2)HNO,+Br->NOBr+H,O (r.d. s 3)NOBr+CHNH->CHN,+H,O+Br(rapid reaction) deduce the rate equation according to this mechanism

(3) Pre-equilibrium approximation Azo reaction of aniline under catalysis of HBr. + + Br H +HNO +C H NH C H N +2H O 2 6 5 2 6 5 2 2 − ⎯⎯→ Its mechanism is proposed as: deduce the rate equation according to this mechanism + 2 r k[H ][HNO ][Br ] − = 10.2.1 Approximation treatment of complex reaction mechanism §10.2 Mechanism assumption and Approximate treatment

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism (4)Apparent activation energy (eaapp and e of elementary reactions △ k r=k,[H[HNO, Br EE a22 E a, app k E r=kh THNO,Br E.+E..-E Whether or not the activation energy app a,+ combination of elementary step is consistent to For some reaction with certain reaction order the eapp of overall reaction may be expressed as a the apparent activation energy of the overall activation energy combination of some reaction is the other important criterion for elementary steps examination on reaction mechanism

(4) Apparent activation energy (Ea,app) and Ea of elementary reactions + 2 2 [H ][HNO ][Br ] k r k k + − − = Ea,app = Ea,2 + Ea,+ − Ea,− + 2 r k[H ][HNO ][Br ] − = 10.2.1 Approximation treatment of complex reaction mechanism For some reaction with certain reaction order, the Eapp of overall reaction may be expressed as a activation energy combination of some elementary steps. Whether or not the activation energy combination of elementary step is consistent to the apparent activation energy of the overall reaction is the other important criterion for examination on reaction mechanism. §10.2 Mechanism assumption and Approximate treatment

810.2 Mechanism assumption and Approximate treatment 10.2.1 Approximation treatment of complex reaction mechanism (5) Relation of the three approximate treatments. Reaction:A+B→P dc k[A]-(k1+k2[B])C]=0 A C KLA] Mechanism. +k2[B C+B-2>P dP If the generation rate of c is much less than K,CB k,k2LAJB its depletion rate(i.e,, active species) k+h2B k[A]>k2 Bl, i.e,k[C]>>k2[Cl most C undergoes reverse reaction so that stationary-state approximation equilibrium can attain rapidly A]>[C kk,AB kAb k<<k1+k2[B Reaction l is a rapid equilibrium

(5) Relation of the three approximate treatments. Reaction: A + B → P Mechanism: If the generation rate of C is much less than its depletion rate (i.e., active species): 1 1 2 k k k [A] [C] [B][C]  + − [A] [C]  1 1 2 k k k [B]  + − stationary-state approximation 10.2.1 Approximation treatment of complex reaction mechanism 1 1 2 [ ] [A] ( [B])[C] 0 d C k k k dt = − + = − 1 ss 1 2 [A] [ ] [B] k C k k − = + 1 2 2 1 2 [A][B] [C][B] [B] dP k k r k dt k k − = = = + When k-1 >> k2 [B], i.e., k-1 [C] >> k2 [B][C], most C undergoes reverse reaction so that equilibrium can attain rapidly. 1 2 1 [A][B] [A][B] k k r k k− = = Reaction 1 is a rapid equilibrium. §10.2 Mechanism assumption and Approximate treatment