Advanced Organic Chemistry

Transcription

1 Lalic, G. Chem 53A Chemisry 53A Advanced Organic Chemisry Lecure noes 1 Kineics: A racical Approach Simple Kineics Scenarios Fiing Experimenal Daa Using Kineics o Deermine he Mechanism Doughery, D. A., "Modern hysical Organic Chemisry", Chaper 7 p

2 Reacion Kineics as a Tool in Sudies Of Reacion Mechanism Chem 53A Reacion Kineics and Reacion Mechanism The mechanism of he reacion ells us how he saring maerials are ransformed ino producs. Ideally, we would like o know he energies of all he SM,, Inermediaes, and all ransiion saes (i.e. he full energy diagram). Ofen we sele for less and we ry o disinguish beween several reasonable general hypoheses. The ulimae goal of kineics experimens is o derive a rae law which gives a quaniaive relaionship beween he concenraions of he saring maerials and he rae of he reacion. Tha means ha we know quie a bi abou he mechanism of he reacion. We experimenaly observe he changes in concenraions of reacans, inermediaes, and/or producs over ime and ry o fi he daa o heoreical rae laws ha correspond o our mechanisic hypoheses. We also ry o deermine kineic order of reacans and he overall kineic order of he reacion which can be very helpful in discrediing wrong hypoheses. Firs order kineics: d[]/d = -d[a]/d = k[a] Second order kineics: Simple Kineics Scenarios A 2A reacion is second order in A A+B seudo-f irs order kineics: -d[a]/d = k[a] rae law ln[a] = ln[a] - k inegraed rae law [A] = [A] e -k inegraed rae law -d[a]/d = k[a] 2 rae law 1/[A] = k + 1/[A] inegraed rae law -d[a]/d = k[a][b] rae law [1/([B] -[A] )]ln([a] [B]/[B] [A]) = k inegraed rae law [B] =[A] goes o 1/[A] = k + 1/[A] A+B Wha if, in a reacion of second order, [A] does no change during he course of he reacion? -d[a]/d = k[a][b] becomes d[]/d = -d[a]/d = [B] =k[a] Reacion becomes pseudo-firs order. Behaves like i is 1s order, bu i is no. We use large excess of A relaive o B, so [A] does no change during he course of he reacion. This removes [A] for he overall order of he reacion. As a reasul, we can isolae [B] and deermine he order in B more easily. Even when dealing wih complicaed reacions, we can isolae he influence ha he change in he concenraion of one of he reagens has on he rae of he reacion by making he saring concenraion of all he oher subsraes large relaive o he subsrae we are isolaing, We usually need a 1 fold excess of oher subsraes. n-h order kineics: relaive concenraion na -d[a]/d = k[a] n 1/(n-1)(1/[A] n-1-1/[a] n-1 )=k Ideal picure looks like his (excep for order reacions): /2 5x 1/2 1x 1/2 rae law inegraed rae law Monioring concenraion changes over ime: In Siu mehod: Concenraion of relevan species is deermined in siu, usually by NMR (reacion performed in an NMR ube) or IR (IR probe inside he reacion flask). Sampling mehod: Taking samples from he reacion mixure a differen ime poins and deermining concenraions of relevan species by an appropriae analyical echnique (NMR, GC,HLC, MS ec.). [] [SM] A+B Every kineics experimen requires monioring he change in he concenraion of he saring maerials, producs, and/or inermediaes wih ime.

3 Iniial rae measuremens Iniial and "Toal" Kineics Experimens "Toal kineics" Chem 53A In he firs 5 o 1% conversion, we can assume ha he rae is consan because concenraions of reacans do no change significanly. As a resul, we obain a linear plo (relaive concenraion vs. ime). The slope of his plo gives as he rae of he reacion. relaive concenraion.1.5 -d[sm]/d = d[]/d = rae Slope = rae of he reacion A single measuremen of iniial rae does no allow us o deermine he overall kineic order of he reacion or he kineic order in any of he reagens. If we repea he experimen and sysemaically change [SM] under pseudofirs order condiions we can obaine he order in SM. rae Iniial rae kineics: firs order zero order [A] The shape gives us he order. Fla line is, sloped line is a firs order, parabole is second order and so on. Noice ha every daa poin is a separae experimen in which we moniored change in [SM] and/or [] over ime. Allows us o make cerain simplificaions because changes in concenraions are small. Good for monioring slow reacions. We assume ha he firs 5% of he reacion are represenaive of he whole reacion! We monior he concenraions of relevan species hroughou he course of he recion. In pricinple, a single measuremen does allow us o deermine he overall order or he order in a reagen. relaive concenraion 1..5 reacion 1/2 5x 1 /2 rae law k[a] 1x 1/2 [SM] To obain informaion abou he reacion's rae law, we fi he experimenal daa o he heoreical rae law in he inegraed form. There are several mehods o fi he experimenal daa. A inegraed rae law ln([a]/[a] ) = -k 2A k[a] 2 1/[A] = k + 1/[A] A+B k[a][ B] [1/([B] - [A] )]ln([a] [B]/[B] [A]) = k [B] = [A] goes o 1/[A] = k + 1/[A] na k[a] n 1/(n-1)(1/[A] n-1-1/[a] n-1 ) = k Direc fi: [] The experimenal daa are fied direcly o he inegraed rae law in he form of [A] = f(). Ofen, fi will be good for muliple rae laws and i is hard o esablish which one fis he bes, bu worh rying.

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5 Mechanisms of Complex Organic Reacions Chem 53A Consider he following ransformaion. Wha can we learn abou he mechanism of his reacion from kineics experimens? Hypoheses: Kineics redicions rae law rae = [R][] S N 1 rae law rae = k 2 [R + ][] [R + ] hard o deermine seady sae approximaion (SSA) The ne rae of he formaion of I is assumed o be negligible. This approximaion allows us o ge a rae law independan of [R + ] S N 1 + k -1 k 2 Reacion diagrams of complex reacions Single sep. Elemenary reacion. TS E + d[r + ]/d = [R] = k 2 [R + ][] + k -1 [R + ][] S N 1 rae law [R + ] = [R]/(k 2 [] + k -1 []) rae = k 2 [R][]/(k 2 [] + k -1 []) SSA works ofen, because common inermediaes are ofen unsable and an appreciable concenraion of inermediaes rarely accumulaed. If SSA is valid for a sysem hen -d[sm]/d = d[]/d. case 1: k 2 > k -1 under normal reacion condiions [] ~ [] during mos of he reacion. k 2 [] >> k -1 [] rae = [R] R R Inuiive picure: every ime he caion is formed, i is rapped by, and i never has a chance o ge back o bromide. S N 1 Two-sep processes wih wo ransiion saes. Assuming ha we know relaive sabiliies of all species involved, here are wo scenarios: E R k 2 > k -1 k -1 > k 2 E I R R I R This siuaion is discribed in he firs reacion diagram. In his scenario, he firs sep deermines he rae of he overall reacion and we call his sep he rae deermining sep. In general, he rae deermining sep is he sep associaed wih he highes energy ransiion sae. No he one wih he highes acivaion energy! This also means ha his sep is he firs irreversible sep. However read he paper!!!!!!! No k 2, [] or [] in he rae law Using kineics experimens we canno obain informaion abou he pars of he reacion mechanism ha ake place afer he rae deermining sep.

6 case 2: k 2 ~ k -1 R By changing he [] and [], we can change he rae law. A he high enough [] /[] raio, he rae law will become [R]. R max R max = [R] k max = R iniial = k 2 [R][]/(k 2 [] + k -1 []) k -1 []/k 2 [] will always be posiive so [] k iniial < This is an example of sauraion kineics = reaching he [reacan] a which rae becomes independan of he [racan]. Tha usually means ha we changed he rae deermining sep. Does his mean ha he reacion diagram changes as we change he concenraion of he reacans? NO! The diagram deals only wih rae consans and no wih k 2 [] and k -1 []. In discussing he reacion diagrams and rae deermining seps, we assume ha he concenraions of species involved are similar. case 3: Experimens sauraed in Several reasonable choices ha would allow us o disinguish beween S N 1 and. Overall kineic order of he reacion Kineic order in Kineic order in rae = k 2 [R][]/(k 2 [] + k -1 []) k iniial = k 2 []/(k 2 [] + k -1 []) If [] and [] are consan, for example, when [] and [] large: k iniial = (1/(1+k -1 []/k 2 [])) Wha does he rae law simplify o if k -1 [] >> k 2 []? The choice of our experimens depends on our inuiion and pracical considiraions. A reasonable sar would be o use 1 equivalen of R and 1 equivalen of. Chem 53A Iniial rae measuremens In he firs 5 o 1% conversion, we can assume ha he rae will be consan because he concenraions of R and will no change significanly. A he same ime, [] is going o be much higher han [], and k 2 [] >> k -1 [] is likely o hold d[sm]/d = d[]/d = rae Slope = rae of he reacion Remember, a single measuremen of iniial rae does no allow us o deermine he overall kineic order of he reacion or he kineic order in any of he reagens. Then we vary [] while keeping [R] he same. S N 1 rae = [R] rae/[r] = = k obs k obs no a funcion of [] k obs (1/s) rae = [R] [] rae/[r] = [] = k obs k obs is a funcion of [] [] S N 1 Slope is he order of he reacion in. Order beween zero and one would indicae he S N 1 mechanism operaing under non-sauraion condiions, or ha boh mechanisms are operaional.

7 Compeiion Experimens Chem 53A "Toal kineics" We can do he experimen wih [] ~ [R]. We can fi he daa obained under hese condiions using Van' Hoff's mehod and, wih a lile bi of luck, in a single experimen, we can obain he overall order of he reacion. If Van' Hoff's plo indicaes ha he reacion is firs order, i is likely S N 1 in a sauraion regime. If he plo indicaes he second order, han he reacion is likely. Somehing in beween would indicae ha we are in non-sauraion regime or ha boh mechanism are operaional. If we wan more inf ormaion we can do he f ollowing: An experimen wih high [] relaive o [R] so ha he reacion is pseudofirs order. Besides, his maximizes he probabiliy ha he reacion operaes in he sauraion regime. By using Van' Hoff's mehod, we can obain order in R from a single measuremen. By doing experimens wih differen [], we can obain k obs vs. [] plo ha will give us order in. S N 1 rae = [R] rae/[r] = = k obs k obs no a funcion of [] rae = [R] [] Compeiion experimens rae/[r] = [] = k obs k obs is a funcion of [] Could we use hese reacions under hese condiions o deermine he relaive raes of reacions of hese wo nucleophiles wih a carbocaion? The rae deermining sep obscures he kineics of all subsequen seps. Wha if we did he same experimen bu added boh nucleophiles a he same ime? (same conc. of nucleophiles simplifies he mah, bu i is no necessary) S N 1 k -1 + k 2 N 3 k 2N3 N 3 The observed raio of he wo producs (produc disribuion) is a direc reflecion of k 2 /k 2N3 rae deermining sep produc deermining sep k obs + + k obsn3 + N 3 N 3 + If we did kineics experimens wih he same [R] in he sauraion regime wih N 3 - and - as nucleophiles, would he raes differ? S N 1 Nu + k -1 k 2 -d[r]/d = rae = k 2 [R][Nu]/(k 2 [Nu] + k -1 []) k 2 [Nu] >> k -1 [] rae = [R] Nu + R R RN 3 The rae of he reacion is deermined by raes of all he seps prior o and including he rae deermining sep, i.e., by all he seps ha conribue ohe rae law. The produc disribuion is deermined by he relaive raes of produc deermining sep(s). Compeiion experimens allow us o gain insigh ino he produc deermining seps regardless of heir posiion relaive o he rae deermining sep.