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, Arrhenius Law, acivaion energy, conducance, conduciviy, and 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 hydrolyzes 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 Arrhenius Law. From he compuer assised measuremen you will also learn how a compuer direcs and handles he daa sampling, daa ransforming and calculaing processes. Background As can be seen from he reacion equaion of he hydrolysis of mehyl-aceae, CH3COOCH3 CH3COO CH3 (1) he elecric conducance significanly decreases during he reacion since he high mobiliy ions are replaced by he much slower aceae ions. The progress of he reacion can hen be followed by conducomery. If he iniial concenraions of he reacans in equaion (1) are he same, hen he inegraed second-order reacion equaion has he following form: A A A A A A 1 1 k (2) Here we will derive he kineic equaion in erms of a physical parameer ha is proporional o he concenraion. The elecric conducance of a reacion mixure is he sum of he conduciviies of all he componens of he sysem. In general, for any physical quaniy () ha is proporional o he concenraion of he componens, [M] z M M (3) where zm is a proporionaliy consan. The oal (measurable) conducance of he reacion mixure: - (4) oal solven Me. - Me Na The conducance of he solven and he concenraion is consan: consan solven Na ion does no change during he reacion, since heir Na

2 Due o small conribuion of he mehyl-aceae and mehanol heir conducance can be negleced: Me. Taking ino accoun hese, he oal conducance: Me oal consan z consan z (5) where z - and z - are proporionaliy consans. Le us noe he reacan concenraion by [A]. From he soichiomery of he reacion we know A A. ha A he beginning of he reacion ( = ) [A] = [A] and [ ] =, herefore, hus he iniial oal conducance, : - consan z consan z A (6) Afer he compleion of he reacion [A] = and he final oal conducance, : consan z - A consan z -, (7) because he amoun of aceae formed is he same as ha of ions reaced. The elecric conducance during he reacion is: z z z A z A A consan consan (8) Then we receive he following expressions from equaion (6)-(8): A z z (9) z z A The inegraed rae law can be subsequenly ransformed: (1) A In anoher form: k 1 A ka (11) (12) Ploing he quaniy (le us denoe i as Z) as he funcion of ime (), he reacion rae consan (k), can be calculaed from he slope of he linear relaionship (m) if we know he iniial concenraion A :

3 Therefore he reacion rae consan is: The ask: Z m (13) m k (14) A The elecric conducance has o be measured 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 1.

4 The asks of he individual unis: - he hermosa keeps he emperaure of he reacion mixure consan; - he conducomeer wih he conducance cell is used o measure he elecric conducance of he reacion mixure; - he analog-o-digial converer ransforms he volage signal of he conduciviy meer o a binary number usable for he compuer; - he 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 A/D converer. Tools, chemicals The sudens need he following ools and chemicals for he measuremen: Procedure - 2 cm 3 plasic syringe; - 5 cm 3 and 1 cm 3 graduaed cylinders; - vacuum pump; -,3 mol / dm 3 Na soluion; - disilled waer; - mehyl-aceae; I is a pair-work. Every pair has hree measuremens a hree differen emperaures (beween 2 5 o C, given by he insrucor). 1. Se he hermosa o a emperaure which is old you by he insrucor. 2. Fill he reacion vessel wih 157 ml disilled waer and 43 ml of.3 molar Na. Sar he sirrer. Wai approximaely 1 minues while he reacion vessel conaining he 2 ml liquid reaches is equilibrium emperaure. 3. Sar he daa collecing program by he command: meac. our insrucor will help you in filling ou he fron page of he program. Record he file name in your lab repor. Check he sabiliy of he desired 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 RANGE and CALIBRATION 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 ONL 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 1 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. Afer 1-12 seconds you have ime o injec

5 mehylaceae down in he well mixed zone of he vessel. The graph consruced from he conduciviy ime daa appear on he monior. 8. Afer a calculaed ime elapsed he compuer sops collecing daa and he measuremen is finished. Please do no sop he daa acquisiion sooner! 9. Afer washing ou he mixure from he vessel and rinsing i wih disilled waer urn o he nex measuremen a anoher emperaure. Repea seps 1 8 (excep sep 5). Calculaions The measured daa are in ASCII files. The firs 4 lines are he main header conaining informaion abou he circumsances of he experimen. Afer he header wo columns conain he measured ime and conducance, in his order. Impor he ASCII file and process in he following way: - ake he average of he firs 5 poins resuling - ake he average of he las 5 poins resuling - calculae Z for he ime inerval corresponding he 1-7% conversion Plo he Z funcion and fi a linear on i. Calculae he reacion rae consan from he slope. Deermine he reacion rae consan for all daa files. Creae an Arrhenius plo and deermine he acivaion energy. Calculae he confidence inerval of he acivaion energy based on he sample calculaion. The Arrhenius plo Significan par of he homogeneous reacions (a leas for a narrow emperaure inerval) follows he Arrhenius equaion: ~ ~ Ea lgk lga, RT ln1 where k is he reacion rae consan, A is he pre-exponenial facor, Ea is he acivaion energy, R is he gas consan and T is he hermodynamic emperaure. The wave denoes ha he value of he quaniy is used wihou unis. This equaion is he linear form of he Arrhenius equaion. If we plo he logarihm of he rae consan versus he reciprocal emperaure (creae he Arrhenius plo) we ge a line. The slope of he line: Ea m R ln1 Therefore, he acivaion energy can be calculaed from he slope of he Arrhenius line: E R ln1 m Sample calculaion of he confidence inerval of he acivaion energy a The confidence inerval of he slope of he Arrhenius line can be calculaed from he sandard deviaion of he slope (S) muliplying i by a criical value (). The slope wih his confidence inerval can be given in he following form: slope m S

6 Convering he slope o he acivaion energy we muliply i by he gas consan and he logarihm conversion facor (ln ): Ea R ln1 m S This convers boh he mean value and he confidence inerval. Le us do his calculaion wih real numbers! The slope of he Arrhenius line, m = K, is sandard deviaion S = 7.6 K Since we have 5 daa poins and fi wo parameers he degree of freedom is 3 he corresponding value is 3.18 (for 95% saisical confidence). The confidence inerval is 3.18 * 7.6 K = K. Including hese values o he equaion of he acivaion energy: E R ln K K J/mol a kj/mol E a kJ/mol Lab repor our lab repor mus conain he following informaion: - name of your pair - he file names and he corresponding emperaures of your own measuremens - he file names and he corresponding emperaures of he daa files you go - he iniial concenraion calculaed from he concenraion of he Na soluion in uni mol/dm 3 aking he diluion ino accoun (4 significan figures) - elecric conducance ime graph for each daa file - Z - graph and he slope (m) of he linear fi for each daa file - a summary able conaining he following iems for each daa file: o / C (wih 3 significan digis) o T / K (wih 5 significan digis) o T 1 / K 1 (wih 5 significan digis) o m / s 1 (wih 4 significan digis) o k / dm 3 mol 1 s 1 (wih 4 significan digis) - he Arrhenius plo: lg(k / dm 3 mol 1 s 1 ) / T 1 / K 1 graph including he fied line, is slope (a leas wih 4 significan digis) and he sandard deviaion of he slope (a leas wih 3 significan digis) - he calculaed acivaion energy Ea in unis kj/mol wih a 95% confidence inerval We wish you a successful measuremen and lab repor wriing!