Rates of chemical reactions

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1 Rtes of chemicl rections

2 Mesuring rtes of chemicl rections Experimentl mesuring progress of the rection Monitoring pressure in the rection involving gses 2 NO( g) 4 NO ( g) + O ( g) n(1 α) 2αn 1 αn 2 3 p= (1 + α) p0 2 Asorption t prticulr wvelength (e.g. Br 2 elow) H ( g) + Br ( g) 2 HBr( g) 2 2 Conductnce of the ionic solution ( CH ) CCl( q) + H O( q) ( CH ) COH ( q) + H + ( q) + Cl ( q)

3 Mesuring rtes of chemicl rections Flow method Stopped-flow method Flsh photolysis Chemicl quench flow Freeze quench method

4 Rtes of chemicl rections A + 2B 3C+ D Instntneous rte of consumption of rectnt: d[ R]/ Instntneous rte of formtion of product: From stoichiometry dp [ ]/ dd [ ] 1 [ ] [ ] 1 [ ] = dc = da = db 3 2 Rte of the rection: 1 1 dni 1 dξ v = = V ν V i where ξ = In cse of heterogeneous rection the rte will e defined s mol/m 2 s n n i i0 ν i the extent of the rection

5 Rection order Rection rte is generlly proportionl to the concentrtion of the regents to some power v= k[ A] [ B]... Depends only on T nd not on the concentrtion The power is generlly not equl to the stoichiometric coefficients! Order of rection: v= k[ A][ B] First order in A, first order in B, overll second order. v = k Zero order. v k A B 1/2 = [ ] [ ] Hlforder in A, first order in B, overll tree-hlves order.

6 Experimentl determintion of the rte lw Isoltion method A + B P where ll the components except one re present in lrge mounts (therefore their concentrtion is constnt) experiment repeted t severl concentrtion v= k[ A] [ B ] = k [ A] 0 Advntges: esy interprettion of dt non-integrl orders cn e esily determined Disdvntges needs to e repeted for every rectnt physiologicl conditions cn not lwys e used if high concentrtion re required high concentrtions might ffect rection mechnism

7 Experimentl determintion of the rte lw Method of initil rtes A + B P severl initil concentrtion of A mesured (gin ssuming tht the concentrtions re constnt) v= k[ A ] [ B ] = k [ A ] v = k [ A ] logv = logk+ log[ A ] Advntges: esy interprettion of dt non-integrl orders cn e esily determined not necessry to use lrge ccess of ny regent Disdvntges needs to e repeted for mny times for every rectnt rection processes involving e.g. products cn e missed

8 Rection order Exmple 2 2 I( g) + Ar( g) I ( g) + Ar( g) [I 0 ] x mol dm -3 [Ar] x mmol dm

9 Integrted rte lws First order rection. Let s find concentrtion of regent A fter time t Slope -> k da [ ] = ka [ ] A A da [ ] = k [ A ] 0 0 t [ A] ln = kt [ A0 ] [ A] = [ A ] e kt 0

10 Integrted rte lws First order rection [ A] = [ A ] e kt 0 Hlf-life time required for concentrtion to drop y ½. kt 1 [ A0 ] 2 ln 2 1/2 = ln = ln 2 t1/2 = [ A0 ] k Time constnt time required for concentrtion to drop y 1/e: τ = 1 k

11 Integrted rte lws Second-order rections da [ ] = ka [ ] 2 A A 0 da [ ] 2 [ A ] = k t = [ A] [ A ] 0 kt [ A] [ A ] 0 = + kt A 0 1 [ ] Second order Hlf-life depends on initil concentrtion, long when concentrtion is low First order 1 [ A ] 1 [ A ] = t = 2 1 [ ] [ ] 0 0 1/2 + kt1/2 A0 k A0

12 Integrted rte lws

13 Rection pproching equilirium Generlly, most kinetics re mde fr from equilirium where reverse rections re not importnt. Close to equilirium the mount of products is significnt nd reverse rection should e considered. A B v= k[ A] B A v= k'[ B] da = ka [ ] + k [ B] [ A] + [ B] = [ A] 0 da = ka [ ] + k ([ A] 0 [ A]) ( k+ k ) t k + ke [ A] = [ A] 0 k+ k k k [ B] k [ A] eq = [ A], [ B] = [ A], K = = k+ k k+ k A k eq 0 eq 0 [ ] eq k k K k k Generlly, for multistge rection: =...

14 Rection pproching equilirium Relxtion denotes return of the system to equilirium fter externl influence, e.g. temperture jump (vi electricl dischrge, or microwve, or lser pulse) 1 τ t / τ x= x0e = k + k Indeed t the new condition: da = k( x+ [ A] eq) + k( x+ [ B] eq) = = ( k + k ) x x k nd k cn e found from the relxtion experiment (s K is known)

15 The temperture dependence of rection rte The rte constnts of most rection increse with the temperture (usully 2-4 times for every T rise 25 ->35 C) Experimentlly for mny rections k follows Arrhenius eqution E ln k = ln A RT A pre-exponentil (frequency) fctor, E ctivtion energy High ctivtion energy mens tht rte constnts depend strongly on the temperture, zero would men rection independent on temperture

16 The temperture dependence of rection rte Stges of rection: Regents Activtion complex Product Trnsition stte k = Ae E / RT Frction of collision with required energy Activtion energy is the minimum kinetic energy rectnts must hve to form the products. Pre-exponentil is rte of collisions Arrhenius eqution gives the rte of successful collisions.

17 Elementry rections Most rections occur in sequence of steps clled elementry rections. Moleculrity of n elementry rection is the numer of molecules coming together to rect (e.g. uni-moleculr, imoleculr) Uni-moleculr: first order in the rectnt da [ ] A P = k[ A] Bimoleculr: first order in the rectnt da [ ] A + B P = k[ A][ B] Proportionl to collision rte H + Br2 HBr + Br

18 Consecutive elementry rections Rection cn proceed through formtion of n intermedite: k k A I P da [ ] = k[ A] di [ ] = k[ A] k[ I] dp [ ] = k[ I] Solution for A should e in form: [ A] = [ A] 0e kt di [ ] k + k[ I] = k[ A] e [ I] = ( e e )[ A] k k kt kt kt 0 0 [ A] + [ I] + [ P] = [ A] ke [ P] = 1 + ke [ A] kt kt 0 0 k k

19 Consecutive elementry rections The stedy-stte pproximtion Assumption: fter initil induction period the concentrtion of intermedite stys constnt di [ ] 0 Then nd di [ ] dp [ ] = k [ A] k [ I] 0 = k [ I] k [ A] ( kt ) 0 [ P] 1 e [ A]

20 Consecutive elementry rections The rte-limiting step Suppose k >>k thn if intermedite is formed it decys rpidly into P, so forming intermedite is rte-limiting step. kt kt ke ke kt [ P] = 1 + [ A] [ P] = ( 1 e )[ A] k k 0 0 Rte of formtion of P doesn t depend on decy rte of I.

21 Consecutive elementry rections Kinetic nd thermodynmic control of rections kinetic control: fr from equilirium A+ B P v P = k [ A][ B] ( ) A+ B P v P = k [ A][ B] ( ) [ P ] [ P] = k k thermodynmic control : concentrtion t equilirium re defined y equilirium constnts (Gis energies)

22 Consecutive elementry rections Pre-equiliri k k A+ B I P k This condition rises when k >>k. Then nd K dp [ ] = [ I] k [ A][ B] = k = k [ I] = k K[ A][ B] k Second order form with composite rte constnt

23 The kinetic isotope effect Oservtion of slowing down the rection upon replcement n tom with hevier isotope fcilitte determining the rte limiting step Primry kinetic isotope effect: rte limiting requires reking ond involving the isotope Secondry kinetic isotope effect: reduction of the rection rte even when the rte limiting step doesn t require reking ond involving the isotope

24 Unimoleculr rections As the molecule cquires the energy s result of collision why the rection is still first order? Lindemnn-Hinshelwood mechnism * k * da [ ] 2 A+ A A + A = k[ A] * * k da [ ] * A + A A+ A = k [ A ][ A] * * k da [ ] * A P = k[ A ] If the lst step is rte-limiting the overll rection will hve first order kinetics

25 Lindemnn-Hinshelwood mechnism * k * da [ ] 2 A+ A A + A = k[ A] * * k da [ ] * A + A A+ A = k [ A ][ A] * * k da [ ] * A P = k[ A ] da * [ ] * [ ] A = k A k A A k A 2 * * [ ] [ ][ ] [ ] 2 k[ A] = k + k [ A] 2 dp * kk [ A] = k [ A ] = k + k [ A] If the rte of dectivtion is much higher tht unimoleculr decy thn: dp kk A kk A = k + k [ A] k 2 [ ] [ ] The Lindemnn-Hinshelwood mechnism cn e tested y reducing the pressure (slowing down the ctivtion step) so the rection will switch to the second order.

26 Lindemnn-Hinshelwood mechnism testing for the theory 2 dp kk [ A] = k + k [ A] 1 k 1 = + k k k k [ A] isomeriztion of CHD=CHD

27 RRK-model RRK (Rice-Rmsperger-Kssel) model is correction to Lindemnn-Hinshelwood mechnism tht tkes into ccount energy distriution over the modes of motion s 1 E * k( E) = 1 k E s numer of modes E* - energy required to rek the ond

28 The ctivtion energy of the composite rection Let s consider Lindemnn-Hinshelwood mechnism nd pply Arrhenius-like temperture dependence to ech rte constnt k ( E ( )/ )( ( )/ ) RT E RT Ae Ae ( E ( )/ ) RT Ae = kk AA k = = A { E ( ) + E ( ) E ( )}/ RT e Overll ctivtion energy cn e positive or negtive E ( ) + E ( ) > E ( ) E ( ) + E ( ) < E ( )

29 Prolems E22.6 At 518 C, the hlf-life for the decomposition of smple of gseous cetldehyde (ethnl) initilly t 363 Torr ws 410 s. When the pressure ws 169 Torr, the hlf-life ws 880 s. Determine the order of the rection. E22.10 The second-order rte constnt for the rection CH 3 COOC 2 H 5 (q) + OH - (q) CH 3 CO 2- (q) + CH 3 CH 2 OH(q) is 0.11 dm 3 mol -1 s -1. Wht is the concentrtion of ester fter () 10 s, () 10 min when ethyl cette is dded to sodium hydroxide so tht the initil concentrtions re [NOH] = mol dm -3 nd [CH 3 COOC 2 H 5 ] = mol dm -3? E22.16 The effective rte constnt for gseous rection tht hs Lindemnn Hinshelwood mechnism is s -1 t 1.30 kp nd s -1 t 12 P. Clculte the rte constnt for the ctivtion step in the mechnism.

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