Molecular Energy Changes During a Reaction

Transcription

1 Reation Kinetis

2 Moleula Enegy Changes Duing a Reation Chemial Enegy of Speies E xn E* +BP E* P+B Moleules above this enegy level (defined somewhat abitaily) ae alled ativated omplexes Poduts Reatants Pogession of Reation (Reation Coodinate) Effets of onentation? Tempeatue? Revese eation?

3 Reations equie ollisions. Ineasing onentation ineases ollision fequeny and eation ate. B2P kf B Ineasing T ineases the kineti enegy of the moleules and the likelihood that the enegy of the ollision will exeed the ativation baie. ll eations ae evesible, but in some ases the ate is muh faste in one dietion than the othe. 2 2PB kp k k 2, net, f, b f B b P

4 Common Rate Expessions fo Ievesible Reations st Ode: k 2 nd Ode: k 2 2 n th Ode: k n n Mihaelis-Menten: k k max

5 Reation Rates in Well-Mixed, Bath Reatos Rate expessions desibe instantaneous, loalized eation ates. Diffeent ates might apply at diffeent points in a single system (i.e., eato). If a eato is well-mixed, the omposition and theefoe the eation ates ae unifom thoughout. k k 2 2 In a bath eato, thee is no inflow o outflow, so omposition an hange only via eations. The ate of onentation hange at a loation is d / dt. That ate applies eveywhee in a well-mixed bath eato. k k k n max n

6 Rates of Typial Ievesible Reations in Bath Reatos st Ode: d dt k t t d k 0 0 dt ln t 0 kt 0exp t kt

7 vs. t and ln() vs. t fo a st Ode Reation in a Bath Reato 00 5 (mmo/l) Time (min) ln ( in mmol/l) k Time (min) 0exp t kt ln t 0 kt

8 Rates of Typial Ievesible Reations in Bath Reatos 0 Ode: 2 nd Ode: d dt k 0 d dt k 2 2 t t d k dt 0 0 t k t 0 t k t 0 t t d k t t kt dt kt 2 0

9 Rates of Typial Ievesible Reations in Bath Reatos n th Ode (n ): Mihaelis-Menten d dt k n n d kmax dt k Fo n : n 0 n n t k t n 0 k 0 ln k k t t max max t

10 The eation and ate expession fo dehydation of CO 2 (aq) to H 2 CO 3 an be epesented as HCO CO aq HO k HCO 2 3 with k = 2.2 s. If the ph of a solution is quikly adjusted fom 7.0 to 5.0, most of the HCO 3 in the solution is onveted to H 2 CO 3, whih then dehydates to CO 2 (aq); the CO 2 (aq) an subsequently tansfe to the gas phase (if the Heny s onstant indiates that suh a tansfe is favoable). How long is equied fo 99% onvesion of H 2 CO 3 to CO 2 (aq) in a bath eato? HCO

11 HCO CO aq HO HCO k HCO Solution. Fo a fist ode eation in a bath eato ln t 0 kt t t k ln ln s s

12 Example. The destution of nitite ion by monohloamine (NH 2 Cl) an poeed via the eation shown below. NO 2 + NH 2 Cl + H 2 O NO 3 + NH 4+ + Cl In a wastewate solution at ph 7.5 that has been dosed with exess monohloamine, the ate of this eation is given by k NO.7 2 NO2 k 0.7 L 2.3 min mol (a) If the wastewate initially ontains 3.0 x 0 5 mol/l NO 2, how muh NO 2 would emain afte 30 minutes of eation in a well-mixed bath eato? (b) How muh time would be equied fo 90% of the NO 2 to be oxidized in the solution desibed in pat (a), if all othe onditions wee held onstant?

13 (a) If the wastewate initially ontains 3.0 x 0 5 mol/l NO 2, how muh NO 2 would emain afte 30 minutes of eation in a well-mixed bath eato? n 2 2 n 0 n n t k t () t (0) nk NO NO nt n n NO 2 mol min 3x min 0.7 L mol -min L 2.86x0 5 mol L Thus, less than 5% of the NO 2 is destoyed in 30 minutes.

14 (b) How muh time would be equied fo 90% of the NO 2 to be oxidized in the solution desibed in pat (a), if all othe onditions wee held onstant? When 90% of the NO 2 has eated, only 0% (o 3x0 mol/l) emains. The time equied to ahieve this amount of onvesion is: t t k n n () (0) NO NO n n mol 5 mol x x L L L mol -min 3652 min 2.5 d

15 Expessions fo the Half-Time of Reations in Bath Reatos st Ode: ln t 0 ln 2 kt kt /2 t /2 ln 2 k ny Ode n : t n 2 /2,0 kn n n

16 Finding Reation Ode fom a Plot of log(t /2 ) vs. log( init ) n=.7 log (t/2) n=.0 n= log (C init ) init

17 Kinetis of Revesible Reations k B B kb Fo ideal solutes, K eq = k B /k B. Theefoe: k k B B B Keq k k * k * B B B whee: *= B /K eq, i.e., *isthevalueof that would be in equilibium with B

18 20 00 B B Conentation Conentation Time, min Time, min k B =.0/min, k B = 0./min

19 Sequential Ievesible Reations in a Bath Reato B P d dt k d dt B k k B B d dt P k B B Conentation (mmol/l) B C; k = 0.02 min ; k 2 = min Time (min) B C

20 Sequential eations ae often haateized by a ate-limiting step, whih epesents the bottlenek in the pathway fom eatants to poduts. Only by opening that bottlenek an the oveall eation ate be ineased signifiantly.