04. Kinetics of a second order reaction

Transcription

1 4. Kineics of a second order reacion Imporan conceps Reacion rae, reacion exen, reacion rae equaion, order of a reacion, firs-order reacions, second-order reacions, differenial and inegraed rae laws, rrhenius Law, acivaion energy, conducance, conduciviy, molar conduciviy. Objecive In his experimen you will follow he reacion rae of a hydrolysis in ime by measuring he conducance of a reacion mixure. Mehyl-aceae hydrolyses in a basic medium according o second-order kineics. From his fac, and from he measured conducance ime funcion you can calculae he rae consan of his reacion. By carrying ou his measuremen a differen emperaures, he acivaion energy of his reacion can be calculaed using he rrhenius Law. From he compuer assised measuremen you will also learn how a compuer direcs and handles he daa sampling, daa ransforming and calculaing processes. Theoreical background Le s consider a general chemical reacion: + B P + Q. B Facors, represen soichiomeric coefficiens, while componens of reacion are he reacans ( and B) B, P, Q and he producs (P and Q). d P d Q The producs have posiive rae of producion (hese species are produced, > ), he reacans have d[ ] d[ B] negaive ones (hese species are consumed, < ). The reacion rae in a closed sysem under consan-volume condiions can be defined as: dc v P Q [ ] [ ] [ ] d[ B] d[ P] d[ Q] d For several reacions he reacion rae can be wrien in he following form (called rae equaion): B v k [ ][ B] We invesigae in his lab he hydrolyses of mehyl-aceae in a basic medium. The chemical equaion is he following: P Q CH COOCH + OH CH COO + CH OH () The reacion is a second-order one, herefore if he concenraions of he reacans are he same he inegraed reacion equaion has he following form: [ ] [ ] [ ] [ ] [ ] [ ] k (2) Since he elecric conducance significanly decreases during he reacion (he high mobile OH ions are replaced by he much slower aceae ions), he progress of he reacion can be followed by conducomery. Le s go hrough some basic quaniies relaed o conducomery! d The elecric resisance (Ω) of he conducomery cell is given as: R ρ where d is he disance beween wo parallel plaes and is he surface area of one of he plainum shees. The maerial consan, ρ is referred o as specific resisiviy. 2//25 4hou25

2 The specific conduciviy (Ω - m - ): κ ρ The conducance (Ω - ): G R The molar conduciviy (Ω - m - mol - m Ω - mol - m 2 ): κ λ c Here, we derive he kineic equaion in erms of a physical parameer ha is proporional o he concenraion. The elecric conducance (G) of a reacion mixure is summed up of he conduciviies of all he componens of he sysem. In general, for any physical quaniy (Y) ha is proporional o he concenraion of he componens, [M]: where z M is a proporionaliy consan. z M [ M] The oal (measurable) conducance of he reacion mixure: Y () Y (4) oal Ysolven + YMec. + Y - + Y - + Y + Y Na + OH c MeOH The conducance of he solven and he consan: Y Y + Y + consan solven Na + Na ion does no change during he reacion, since heir concenraion is Due o small conribuion of he mehyl-aceae and mehanol heir conducance can be negleced: Y +Y Mec. Taking ino accoun hese he oal conducance: Y Y + Y + Y z OH + z c + Y (5) oal OH c consan OH MeOH [ ] [ ] consan where z - and z - are proporionaliy consans. OH c Le us noe he reacan concenraion by []. From he soichiomery of he reacion we know ha c. [ ] [ ] [ ] he beginning of he reacion ( ) [] [] and [c ], herefore Y, hus he iniial oal conducance, Y : c - c [ OH ] + Yconsan z [ ] Yconsan Y + z OH OH fer he compleion of he reacion ( ) [] and he final oal conducance, Y : [ c ] + Yconsan z - [ ] consan Y z + (7) - Y c c because he amoun of aceae formed is he same as ha of OH ions reaced. (6) The elecric conducance during he reacion is: Y z OH + z c + Y z + z + Y [ ] [ ] [ ] [ ] [ ] OH C consan OH C ( ) consan (8) Then we receive he following expressions from equaion (6)-(8): Y ( z z ) [ ] C OH ( z z ) [ ] [ ] The inegraed rae law can be subsequenly ransformed: Y (9) C OH ( ) Y Y () 2//25 4hou25 2

3 k Y Y [ ] Y Y () In anoher form: Y Y Ploing he Y Y Y Y Y Y k[ ] quaniy (le us denoe i as Z) as he funcion of ime (), he reacion rae consan (k), can be compued from he slope of he linear relaionship (m) if we know he iniial concenraion,[ ] : Z m () (2) Therefore he reacion rae consan is: m k (4) [ ] The ask: The elecric conducance has o be during he hydrolysis reacion a leas a wo emperaures. The sudens will also ge five slope values of he Z - funcion belonging o five emperaures from a daabase. The acivaion energy should be deermined from he given daa only. The apparaus The measuremen is performed using an on-line daa collecing sysem. The scheme of he apparaus is shown in Figure. 2//25 4hou25

4 The asks of he individual unis: - The hermosa keeps he emperaure of he reacion mixure consan. - The conducomeer wih he conducance cell is used o measure he elecric conducance of he reacion mixure. The conducance cell conains a pair of plainized plainum shee for deecing conduciviy. The conduciviy of liquid volume beween he shees is measured. The parallel oriened shees are in a proecing glass ube. Mos of he elecrochemical reacions do no proceed on plainum (noble meal), herefore measuring added reacion resisance is eliminaed. - The analog-o-digial converer ransforms he volage signal of he conduciviy meer o a binary number usable for he compuer. - The inerface is a special elecric circui ha provides he connecion beween he compuer and he laboraory environmen, hrough which he compuer can read he digial signals of he /D converer. Tools, chemicals The sudens need he following ools and chemicals for he measuremen: Procedure - 2 cm plasic syringe; - 5 cm and cm graduaed cylinders; - vacuum pump; -, mol / dm NaOH soluion; - disilled waer; - mehyl-aceae; I is a pair-work. Every pair has wo measuremens a wo emperaures (beween o C, given by he insrucor). The conduciviy ime daa are colleced and parly evaluaed by he compuer.. Se he hermosa o a emperaure which is old you by he insrucor. 2. Fill he reacion vessel wih 57 ml disilled waer and 4 ml of. mol/dm NaOH. Sar he sirrer. Wai approximaely minues while he reacion vessel conaining he 2 ml liquid reaches is equilibrium emperaure.. Sar he daa collecing program by he command: meacgy. Your insrucor will help you in filling ou he fron page of he program. Record he file name belonging o he firs measuremen in your lab repor. Check he emperaure of he reacion vessel by wriing down he emperaure readings every half minue. When he emperaure readings are he same in he las 5 minue inerval he kineics experimen is ready for a sar. 4. Turn he RNGE and CLIBRTION knobs on he conduciviy meer unil he oupu volage on he screen of he analog o digial converer (METEX digial mulimeer) will show 9 95 millivols. 5. DO THIS STEP ONLY IN THE FIRST EXPERIMENT! Fix he measure range of he METEX digial mulimeer pushing he R-H buon once. Please do no hi he buon more han once! 6. Take up ml of mehylaceae in a plasic syringe wihou bubble. 7. Choose he menu iem: MÉRÉS Hi ener and give he emperaure by one decimal precision for he reacion mixure and hi ener again. fer -2 seconds you have ime o injec mehylaceae down in he well mixed zone of he vessel. The graph consruced from he conduciviy ime daa appear on he monior. 8. fer a calculaed ime elapsed he compuer sops collecing daa and he measuremen is finished. Please do no sop he daa acquisiion sooner! 9. sk for he insrucor s help o evaluae he graph.. fer washing ou he mixure from he vessel and rinsing i wih disilled waer urn o he nex measuremen a an elevaed emperaure. Repea seps 9 (excep sep 5). The rrhenius plo Significan par of he homogeneous reacions (a leas for a narrow emperaure inerval) follows he rrhenius equaion: k e 2//25 4hou25 4 RT

5 where k is he reacion rae consan, is he pre-exponenial facor, E a is he acivaion energy, R is he gas consan and T is he hermodynamic emperaure. If we ake he based logarihm of his equaion we ge he linear form of he rrhenius equaion: lg( k ) lg( ) RT ln If we plo he logarihm of he rae consan versus he reciprocal emperaure (creae he rrhenius plo) we ge a line. The slope of he line: m R ln Therefore, he acivaion energy can be calculaed from he slope of he rrhenius line: E R ln m Resuls o hand in a - he iniial concenraion calculaed from he concenraion of he NaOH soluion in mol/dm uni aking he diluion ino accoun (4 significan figures); - elecric conducance ime graphs for wo emperaures; - Z ime graphs for wo emperaures; - he able conaining five slope values of he Z - funcions measured a five differen emperaures; he lg( k / dm mol s ) - T / K graph wih he fied line and he value of he slope (4 significan figures); - he acivaion energy in kj/mol uni (4 significan figures). Sample quesions and answers for he enrance quiz. These quesions are devoed for pracicing and preparing o labs a home. Please noe ha hese are samples only and he quesion of he enrance quiz are no resriced o hese ones! MLT Q and : Q. Give he chemical reacion of mehyl aceae wih sodium hydroxide and he formal order of his reacion.. CH COOCH + NaOH CH COONa +CH OH, I is a second order process overall in he direcion of produc formaion. Q2. Wha is he value of reacion order of in he following equaions? dc dc 2 k c k c 2. The exponens of concenraion in hese rae equaions are one and wo, herefore he reacion order is and 2, respecively. Q. Which componens cause he ime dependence of he elecric conduciviy for he reacion mixure?. The concenraion of Na + is no alered during he reacion. One OH produces one aceae anion which process is accompanied a decrease in elecric conduciviy. The conduciviy of mehanol and mehyl aceae are negligible. Q4. How can be he general inegraed rae law of second order kineics made simpler? 4. In he general he second order rae equaion can be given for he process + B P in he following form: [ ] d d k[ ][ B] The inegraed rae law: 2//25 4hou25 5

6 k [ ] [ B] ln [ ][ B] [ ] [ B] By choosing he saring concenraions of he reacans o be equal (i.e. [] [B], he rae equaion can be given [ ] d k [ ] 2 and he inegraed rae law is much more simplified: k [ ] [ ] We apply his laer condiion in his pracice. Q5. Wha are he main pars of a conducance cell? 5. The conducance cell conains a pair of plainized plainum shee for deecing conduciviy. The conduciviy of liquid volume beween he shees is measured. The parallel oriened shees are in a proecing glass ube. Q6. Give he emperaure dependence of rae consan. Find a linearized form of rrhenius law. 6. The rrhenius law in is exponenial form: RT k e where k is he reacion rae consan, is he pre-exponenial facor, E a is he acivaion energy, R is he gas consan and T is he hermodynamic emperaure. If we ake he based logarihm of his equaion we ge he linear form of he rrhenius equaion: ln k ln RT Q7. Calculae he acivaion energy using he linearized rrhenius equaion from he ln k /T plo. Daa: slope 6 K, R 8.4 J mol - K When ploing ln k agains he slope of his funcion is T E a ( ln k) slope R T R 6K J mol molk T ( ln k) J Q8. Calculae he saring concenraion of he reacion mixure! 8. [] can be calculaed from daa given in Procedure par: "Fill he reacion vessel wih 57 ml disilled waer and 4 ml of. mol/dm NaOH. Sar he sirrer.", Take up ml of mehylaceae in a plasic syringe wihou bubble.,...injec mehylaceae down in he well mixed zone of he vessel. n.4 dm. mol/dm [ ].6479 mol/dm V dm ( ) Q9. Summarize he main seps of he experimenal procedure! 9.. Se he hermosa o he desired emperaure. 2. Fill he reacion vessel wih disilled waer, NaOH soluion and sar he sirrer. Wai minues for he hermal equilibrium.. Sar he daa acquisiion program and fill he fields. 4. djus your conduciviy meer and is oupu o he desired values. 5. If his is he firs experimen push he R-H buon of he digial mulimeer once. 2//25 4hou25 6

7 6. Take up ml of mehylaceae in a plasic syringe wihou bubble and sar he daa collecion. 7. fer -2 seconds injec mehylaceae. 8. Wai ill he program ends he daa collecion. 9. Clean he reacion vessel. Q. Draw a schemaic picure abou he apparaus you are using in his lab!. See Figure. 2//25 4hou25 7