THE KINETIC HYDROGEN ISOTOPE EFFECT

Transcription

1 Chem 367-2/ Kineic ydrogen Isoope Effec 41 TE KINETIC YDROGEN ISOTOPE EFFECT 1. Purpose In his experimen, he isoope effec arising from subsiuion of deuerium for hydrogen on he rae of a reacion involving proon ransfer will be invesigaed. The resuls will be inerpreed in erms of he heavier isoope subsiued species having a lower zero poin energy. 2. Safey Discard organic solvens o he wase solven conainers. Wear eye proecion a all imes in he laboraory. 3. Pre-Lab Preparaion Before saring his experimen, mae sure 1) ha you undersand he principle of he hydrogen isoope effec and 2) ha you undersand how many soluions mus be prepared and how o prepare hem (see experimenal secion). 4. Inroducion 4.1 TEORY In general, isoopic replacemen of aoms has an insignifican effec (alhough of grea imporance for some applicaions) on he chemical or physical process under consideraion and his is precisely he principle behind he use of isoopic agging in NMR for insance or radioisoope labels used as racers in complex sysems. This comes from he fac ha isoope effecs governed by diffusion processes go roughly as he square roo of he raio of he isoopic masses; for mos common elemens, his raio is beween uniy and 1.1. owever in he case of hydrogen and deuerium 1, since he mass raio differs grealy from uniy, isoope effecs may no longer be negligible and furher hese effecs may be used as mechanisic probes. 1 For his elemen, he range of isoopic masses available can be exended if one includes he radioacive aom 3 (riium, 1/2 12 y, m3 /m 3), he exoic aoms Mu (muonium [µ + e ], 1/2 1.5 µs, m Mu /m 0.1) and Ps (posironium [e + e ], 1/2 11 ns, m Ps /m 0.001).

2 42 Chem 367-2/ Kineic ydrogen Isoope Effec For a chemical reacion, he ineic hydrogen isoope effec is he change observed in he rae of he reacion due o he isoopic replacemen of a hydrogen aom involved in he rae deermining sep of he process. The effec has been bes documened for he case of proon ransfer reacions. The energeic of such a reacion is shown very schemaically in Fig. 1 which illusraes he variaion in he poenial energy of he reacing sysem a differen sage along he reacion coordinae. In paricular, he energy difference beween he lowes poin and he highes poin of he barrier beween reagen and produc represens he classical acivaion energy of he reacion. In simple erms, he sysem has o be provided wih enough energy (has o be acivaed) o overcome he heigh of he barrier for he reacion o occur. Since he inermolecular and iner-aomic forces are pracically unaffeced by a change in nuclear masses, he same poenial energy curve apply for boh isoopic species. owever, he posiion of he lowes energy levels (he zero-poin energy) of boh he iniial and he final saes does depend upon he isoopic mass, wih he ligher isoopic species having a higher zero poin energy. Figure 1. Schemaic diagram of he poenial energy profile of proon ransfer reacion along he reacion coordinaes; he relaive posiion of he zero poin energy corresponding o he and D isoopes are indicaed, boh for he reagens and he ransiion sae. As a resuls, he acivaion energies E and E D corresponding o he wo isoopic species differ o a good approximaion by he difference in zero

3 Chem 367-2/ Kineic ydrogen Isoope Effec 43 poin energy as depiced in Fig. 1. Assuming an Arrhenius behaviour for he reacion, he raio of he rae consans would hen be given by: D ( E E ) D = exp (1) RT owever, in a muli-sep mechanism, one can expec he ineic hydrogen effec o be he produc of wo erms D = D I D (2) II where he firs erm ( / D ) I represens he primary isoope effec and originaes from he effec of isoopic subsiuion of a hydrogen aom involved in he acual bond maing (or bond breaing) in he rae deermining sep. The second erm, ( / D ) II accouns for he secondary isoope effec, which is due o he effecs of isoopic subsiuion on he reacion rae of any oher hydrogen aoms. Theory predics a value of 10.6 for he primary isoope effec erm and a value of 0.48 for he secondary erm[1]. Combining hese wo erms, he overall effec is expeced o be 5, bu experimenally lower values of 3 are observed. 4.2 YDROLYSIS OF ETYL VINYL ETER. This isoope effec will be illusraed in he presen experimen by sudying he ineics of he acid caalysed hydrolysis of ehyl vinyl eher (EVE) ino acealdehyde and ehanol in aqueous medium. In he acceped mechanism, he firs sep is rae deermining and consiss of a proon ransfer o one of he vinyl carbon resuling in a carbonium cener inermediae (Eqn. 3). Nex, in he presence of waer his inermediae rearranges and breas apar o give he final producs and regenerae a proon hrough a series of very fas seps (Eqn. 4). 2 C=COC O + 3 C C + OC O (3) 3 C C + OC O fas C 3 CO + OC (4) Following he above discussion, he primary isoope effec is expeced o arise from proon ransfer from 3 O + o EVE (Eqn. 3) while he subsequen series of fas seps (Eqn. 4) involving 2 O would conribue o he secondary isoope effec.

4 44 Chem 367-2/ Kineic ydrogen Isoope Effec The rae of hydrolysis of EVE has been shown o be firs order in boh EVE and acid concenraions wih he rae law: [ EVE ] = [ ] + [ EVE] d (5) d where is he second order rae consan and [EVE] he EVE concenraion a ime. As can be seen from Eqns. 3 and 4, he concenraion of he caalys + (or 3 O + ) does no change over he course of he reacion and herefore he erm [ + ] = [ + ] 0 = consan. Leing 1 = [ + ] 0, Eqn. 5 can be re-wrien as a pseudo firs order rae law [ EVE] d = 1 [ EVE] (6) d which inegraes readily as: [ EVE] = [ EVE] ( ) exp (7) 0 1 Equaion 7 represens an exponenial decay which is convenienly linearized by aing he naural logarihm of boh sides ln [ EVE] = + ln[ EVE] 1 0 (8) Insead of measuring he rae disappearance of EVE, one could measure he rae of appariion of one of he final producs, C 3 CO for example. Since all he seps in Eqn. 5 are much faser han he firs proon ransfer, one has a any ime: [C 3 CO] = [EVE] 0 [EVE] (9) and herefore d[ C 3CO] d[ EVE] d Inegraion leads o = (10) d [ ] [ C 3CO] = [ C 3CO] 1 ( 1) exp (11) where [C 3 CO] = [EVE] 0 is he concenraion of acealdehyde a compleion of he reacion. Equaion 11 is more convenienly processed in a linear

5 Chem 367-2/ Kineic ydrogen Isoope Effec 45 form obained afer some rearrangemen and again aing he naural logarihm of boh sides: ln ([ C 3 CO ] [ C 3 CO ] ) = + ln[ C 3 CO ] 1 (12) The rae of EVE hydrolysis can be measured by following specrophoomerically as a funcion of ime eiher he disappearance of he EVE saring maerial a nm or he appearance of he acealdehyde final produc a nm. A a given wavelengh, he absorbance A λ is relaed o he concenraions of he absorbing species hrough Beer Lamber law A λ = ε λ cl (13) where ε λ is he coefficien of absorpion (also called molar absorpiviy), c he concenraion and l he opical pah lengh hrough he absorbing medium. Looing a he disappearance of EVE and plugging Eqn. 13 ino Eqn. 8, one ges ln[(a EVE ) (A EVE ) ] = 1 + consan erm (14) where he erm (A EVE ) accouns for some residual absorbance presen a compleion of he reacion. On he oher hand, if he appearance of he acealdehyde is followed, plugging Eqn. 13 ino Eqn. 12, one ges ln[(a C3 CO) (A C3 CO) ] = 1 + consan erm (15) wih he obvious noaions. In eiher case, by ploing he lef side of Eqn. 14 or Eqn. 15 versus ime, one should ge a sraigh line wih slope 1 from which he second order rae consan can be calculaed nowing he acid concenraion, = 1 /[ + ], or more precisely, = 1 /[ + ] for he proonaed acid or D = 1 /[D + ] if he deueraed acid is used. 5. Experimenal The ime profile of he reacion will be obained firs a 25 C for boh isoopic species for a series of four 3 O + (D 3 O + ) concenraions, hen a wo oher emperaures a he lowes 3 O + (D 3 O + ) concenraion. The disappearance of EVE will be moniored around 215 nm using a compuer conrolled P-8453 UV/VIS specrophoomeer.

6 46 Chem 367-2/ Kineic ydrogen Isoope Effec 5.1 SOLUTION PREPARATION Soc soluions of Cl/ 2 O and DCl/D 2 O 0.04 M are provided; record heir exac respecive concenraion. Dry mehanol (he elecronic grade is adequae) and a sample of ehyl vinyl eher are also available. Table 1. Suggesed volumes o prepare a series of acid concenraions. Soln # Soc 2 O [ + ]/M Soc DCl D 2 O [D + ]/M Cl ml 0.50 ml ml ml 1.00 ml ml 0.50 ml ml 1.50 ml ml 1.00 ml ml 1.70 ml ml 1.50 ml 0.01 Firs prepare in a weighing bole 1 ml of a 1:1 by volume EVE/MeO soluion. This is pleny since each run uses only 5 µl of his soc soluion. When no in use, eep his soluion capped o preven evaporaion. Two series ( and D) of four acid concenraions are needed and are prepared direcly in he UV/Vis cuvee as suggesed in Table 1. If available, auomaic pipees may be used o measure some of he volumes. 5.2 DATA COLLECTION The specrophoomeer will be se up o record he specra a prese ime inervals; he insrucor will brief you on how o operae his insrumen. Under he iem Mode, acivae Execue Advanced Mehods; his ses a change in he ineracing window panel. On he menu bar, clic on Insrumen hen Seup Specrophoomeer; he pop-up window which is displayed allows you o se he sampling rae and he number of samples hrough various parameers. Se he wavelengh range o 190 nm o 300 nm and mae sure ha he Tungsen Lamp buon if Off while he Deuerium Lamp buon is On. Se he Run Time and he Cycle ime as suggesed in Table 2; leave he oher parameers a heir defauls values. Clic on OK. Prepare he acid soluion in he quarz cell, cap and if necessary wai for 5 min o allow for emperaure equilibraion. While he cell is equilibraing, clic on he Blan buon o collec he baseline specrum, he blan being he acid soluion before injecion of EVE.

7 Chem 367-2/ Kineic ydrogen Isoope Effec 47 Injec 5 µl of EVE soluion wih an auomaic pipee, sir quicly wih he eppendorf ip, cap he cell hen clic on Sample o collec he specra. A he end of he run save he daa (File - Save as - Samples, give a new name of he ype xxxxxxxx.sd for each run), hen clear his specrum (choose Edi Clear Samples). Measure he emperaure of he sample a he end of he run wih a digial hermocouple hermomeer probe immersed in he soluion in place. Empy, rinse wih aceone and dry he cell horoughly and repea he procedure for he nex soluion. Repea he runs wih soluion 4 a 35 C hen 45 C (o obain hese values in he cuvee, he circulaor should be se a 40 C and 50 C, wih he hermosa cooling waer OFF). Table 2. Suggesed iming parameers for ineic daa collecion. Isoope Temp./C [Acid]/M Run Time/s Cycle ime/s D D D D D D Calculaions and discussion The daa have o be recovered from he compuer aached o he specrophoomeer. Unforunaely a presen, he sample files will have o be rerieved under wo differen Modes o compile all he necessary informaion.

8 48 Chem 367-2/ Kineic ydrogen Isoope Effec To recover he iming informaion, go o he Mode Execue Advanced Mehods, load he relevan sample file. Clic on Configuraion Table, hen ic ou all he proposed iems excep for Relaive Time. Mae sure he Sample/Resuls window is acivaed, hen go o File - Prin o File - Seleced Window, hen when promped give a differen file name of he ype xxxxxxxx.x for each run. This will save in plain ASCII ex forma he informaion displayed on he acive window. Proceed in his way for all your daa. Nex o recover he absorbance informaion, go o File - Load Mehod, choose he mehod DEXPT.M. Then again load one of your sample file; one window displays he specra while he oher window display a able of absorbencies a differen prese wavelenghs. Acivae his las window, hen go o File - Prin o File - Seleced Window and again when promped give a file name of he ype xxxxxxxx.x, differen for each run and differen from he names used in he previous sep. Process all your daa in his way. These xxxxxxxx.x ASCII files can be impored ino any spreadshee program. Use he Copy feaures o exrac he ime hen he absorbance informaion and Pase i ino anoher spreadshee (weighed leas-squares or of your own design) which processes he daa according o Eqn. 14. For he 25 C runs, following Eqn. 14 obain and abulae he values of 1 and 1D for each of he acid concenraion hen calculae he corresponding second order rae consans and D and repor he average value for each isoope. From hese daa, calculae and commen on your observed hydrogen isoope effec. Process similarly he daa obained a differen emperaures, i.e., firs abulae he values of he pseudo firs order rae consan, hen calculae he corresponding second order rae consans. Commen on he isoope effec observed. Nex, o calculae he Arrhenius acivaion energy E for he reacion (or E D for he D reacion), depending on he qualiy of he daa, 1) one can obain E (D) from he slope of he Arrhenius plo of ln( (D) ) versus 1/T (slope = -E (D) /R), or 2) if he scaer is oo large, one can use he emperaure resuls pairwise according o: ( T1 ) ( T ) E 1 1 = exp (16) R T T hen E is aen as he average of he hree values obained; E D is obained in he same way using Eqn. 16 in which he subscrip is replaced by D.

9 Chem 367-2/ Kineic ydrogen Isoope Effec 49 In principle, he acivaion energy E D for he D reacion can also be calculaed from D ( T1 ) ( T ) ( E E ) D = exp (17) RT 1 1 Compare he wo values of E D obained; why are hey differen? Discuss your resuls in erms of he difference in zero poin energies beween he wo isoopes. Wha are he shorcomings of he simple model shown in Fig. 1 and more precisely wha is he meaning of he energies labelled E and E D compared o E and E D? Is he presen model adequae o accoun for he effecs observed in his experimen? Propose a deailed mechanism for he series of fas seps in Eqn. 4. The ehyl vinyl eher commercially available conains 0.1% KO. Wha is he role of his addiive and o wha exend is i affecing he acid concenraions used in he presen experimen? 7. References [1] P. McGuiggan, R. Eliason, B. Anderson and B. Boch, J. Chem. Ed. 64, 718 (1987). [2] R.P. Bell, The Proon in Chemisry, 2nd Ed., Cornell Universiy Press, Ihaca, N.Y. (1973). [3] M.M. Kreevoy, J. Chem. Ed., 41, 636 (1964). [4] J.M. Williams, M.M. Kreevoy, Adv. Phys. Org. Chem., 6, 63 (1969). [5] E.K. Thornon, E.R. Thornon, in Isoope Effecs in Chemical Reacions, C.J. Collins, N.S. Bowman Eds., Van Nosrand Reinhold, N.Y. (1970), chaper 4.

10 50 Chem 367-2/ Kineic ydrogen Isoope Effec