Thanh-Phong Mai Experimental Investigation of Heterogeneously Catalyzed Hydrolysis of Esters

Transcription

1 Thanh-Phng Ma Expermental Investgatn f Hetergeneusly Catalyzed Hydrlyss f Esters Fakultät für Verfahrens- und Systemtechnk Ott-vn-Guercke-Unverstät Magdeburg

2 Expermental Investgatn f Hetergeneusly Catalyzed Hydrlyss f Esters Dssertatn zur Erlangung des akademschen Grades Dktrngeneur (Dr.-Ing.) vn M. Eng. Thanh-Phng Ma geb. am 03/02/1972 n Ha-Tnh, Vetnam genehmgt durch de Fakultät für Verfahrens- und Systemtechnk der Ott-vn-Guercke-Unverstät Magdeburg Gutachter: Prf. Dr.-Ing. Andreas Sedel-Mrgenstern Prf. Dr.-Ing. Achm Kenle Prmtnskllquum am 19. Dezember 2006

3 II Abstract The thermdynamcs and knetcs f the hydrlyss f fur esters (methyl frmate, methyl acetate, ethyl frmate, and ethyl acetate) were nvestgated expermentally and theretcally. An acdc n-exchange resn was used as hetergeneus catalyst and adsrbent. Alternatvely, hydrchlrc acd was used as a hmgeneus catalyst. The chemcal reactn equlbrum was measured fr varus temperatures and ntal cncentratns f the reactants usng cnventnal batch reactr runs. The nfluence f the absence and presence f the sld catalyst n the lqud-phase equlbrum cmpstn was als studed n a batch reactr. The relevant dstrbutn equlbra f the cmpnents nvlved were quantfed based n pulse chrmatgraphc experments. T nvestgate the knetcs f the fur reactns, a reactn calrmeter was emplyed. Systematc experments t measure heat flws due t reactn were carred ut wth catalyst suspensns n the calrmeter. Reactn rate cnstants were quantfed frm the measured heat flws. The fur hydrlyss reactns were fund t prceed wth very dfferent reactn rates. The fastest reactn was the hydrlyss f methyl frmate. The slwest was the hydrlyss f ethyl acetate. Fr cmparsn, reactn rate cnstants were als quantfed frm cncentratn-tme prfles recrded n cnventnal batch experments. A smplfed pseud-hmgeneus mdel and the determned parameters were fund t be capable f descrbng the heat flws measured n the reactn calrmeter fr all reactns studed under dverse peratng cndtns. The thermdynamc and knetc parameters determned n ths wrk frm a platfrm t desgn and ptmze chrmatgraphc reactrs fr the hydrlyss reactns nvestgated and the crrespndng esterfcatns.

4 III Zusammenfassung In deser Arbet wurde de Thermdynamk und Knetk der hmgen und hetergen katalyserten Hydrlyse vn ver Estern (Methylfrmat, Methylacetat, Ethylfrmat und Ethylacetat) theretsch und expermentell untersucht. En saurer Inenaustauscher wurde als fester Katalysatr und glechzetg als Adsrbent verwendet. Außerdem wurde alternatv Salzsäure als hmgener Katalysatr engesetzt. Das Reaktnsglechgewcht wurde für verschedene Temperaturen und Ausgangsknzentratnen der Reaktanten expermentell untersucht. Der Enfluss des Feststffkatalysatrs auf de Glechgewchtsknzentratnen n der flüssgen Phase wurde analysert. Für de Ermttlung der Reaktnsknetk der ver Reaktnen wurde en Reaktnskalrmeter engesetzt n dem Katalysatrsuspensnen vrgelegt werden knnten. De Glechgewchtsvertelung der Kmpnenten zwschen der flüssgen und festen Phase wurde mttels chrmatgraphscher Pulsexpermente quantfzert. Zur Bestmmung der Reaktnsgeschwndgketsknstanten denten gemessene Wärmeströme. Es wurde festgestellt, dass de Reaktnsraten der ver untersuchten Reaktnen sehr unterschedlchen snd. De schnellste Reaktn st de Hydrlyse vn Methylfrmat, de langsamste st de Hydrlyse vn Ethylacetat. Darüber hnaus wurden de Reaktnsraten auch n knventnellen Batch-Versuchen durch Messung vn Knzentratns-Zet- Prflen quantfzert. Ene gute Überenstmmung der Ergebnsse aus kalrmetrchen Messungen und Batch-Versuchen wurde festgestellt. Für de quanttatve Beschrebung der Wärmeströme m Reaktnskalrmeter knnte erflgrech en verenfachtes pseudhmgenes Mdell engesetzt werden. De n deser Arbet ermttelten Parameter (Reaktnsglechgewchtsknstanten und Reaktnsgeschwndgketsknstanten) knnten durch unabhängge Versuche valdert werden. Dese Parameter können für de Auslegung und Optmerung chrmatgraphscher Reaktren zur effzenten Durchführung deser reversblen Hydrlysereaktnen bzw. der krrespnderenden Veresterungen verwendet werden.

5 IV Acknwledgements I wuld lke t express my sncere grattude and thanks t my advsr Prf. Andreas Sedel-Mrgenstern fr prvdng ths nterestng research tpc, hs gudance, valuable advce, and cntnuus supprt wth patence and encuragement thrughut the perd f ths wrk. I have nt nly receved academc assstance, but als tremendus help frm hm. I am very grateful t Prf. Achm Kenle fr revewng ths dssertatn and gvng me helpful cmments and suggestns. I acknwledge the assstance, supprt and dscussn f clleagues and staff frm Char f Chemcal Engneerng, Magdeburg Unversty and frm Grup fr Physcal and Chemcal Fundatns f Prcess Engneerng, the Max-Planck Insttute Magdeburg. Specal thanks g t Frau Marls Chrbg and Frau Marn Hesse. I recrd specal thanks t the state f Sachsen-Anhalt and the Max-Planck Insttute Magdeburg fr ther generus fnancal supprt. I thank Prf. Ma Xuan Ky fr nsprng me t pursue dctral study n Germany. Last, but nt least, I wuld lke t express my grattude t my belved famly and frends wh have been a cnstant surce f nspratn and encuragement t me durng ths study.

6 Cntents 1 Intrductn Thermdynamcs Knetcs f Chemcal Reactns Chrmatgraphc Reactrs Am and Outlne Theretcal Aspects Phase Equlbra Phase Equlbrum n a Tw-Phase Clsed System Phase Equlbrum n a Slvent Plymer System Adsrptn Equlbra Lnear Adsrptn Istherms Nn-lnear Adsrptn Istherms Heat f Adsrptn Chemcal Reactn Equlbra Sngle Reactns Multple Reactns Calculatn f Equlbrum Cmpstns Heat f Reactn Influence f Temperature n Reactn Equlbrum Cnstants Reactn rates Hmgeneus Systems Hetergeneus Systems Actvty and Actvty Ceffcents Mdel Reactns, Catalysts and Adsrbents Mdel Reactns Hydrlyss f Esters Chemcal Reactn Equlbra Catalysts and Adsrbents Summary and Outlne f Expermental Prgram 51 V

7 VI Cntents 4 Calrmetrc Technques Reactn Calrmetry Methds f Calrmetry Basc Reactn Calrmeter Types Operatn Mdes Cntrbutns t Heat Balance Mdelng f Case Study Mass Balances Energy Balances Lqud Phase Energy Balance Sld Phase Energy Balance Expermental Sectn Expermental Equpments Reactn Calrmeter Equlbratn Equpment Gas Chrmatgraphy Expermental Prcedures Characterzatn f the Catalysts Calrmetrc Experments Usng Catalyst Suspensns Prelmnary Experments Reactn Enthalpes and Rates f Reactns Measurement f Reactn Equlbrum Cnstants Hydrlyss f Esters Esterfcatn f Acds wth Alchls Reactn Knetc Experments n Batch Reactrs Chrmatgraphc Reactr Measurements Results and Dscussn Catalyst Characterzatn Dstrbutn Equlbrum Cnstants Chemcal Reactn Equlbra Reactn Equlbrum Cnstants Reactve Bnary Ester Water Mxtures Reactve Ternary Ester Ester Water Mxtures Influence f Temperature n Reactn Equlbrum Cnstants Influence f Sld Catalyst n Equlbrum Cmpstns Calrmetrc Measurements. 96

8 Cntents VII Thermal and Vlume Effects Due t Mxng Thermal Effects Due t Mxng Vlume Effects Due t Mxng Measured Reactn Heat Flws Smulatn f Heat Flws and Estmatn f Reactn Rate Cnstants Ideal Slutn Behavr Nn-Ideal Slutn Behavr Reactn Knetc Estmatn Usng Batch Experments Qualtatve Analyss Estmatn f Reactn Rate Cnstants Errr Evaluatn Mdel Valdatn Summary and Cnclusns 123 Nmenclature 127 References 133 Appendx A Antne Equatn 145 Appendx B GC Calbratn Curves 147

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10 C H A P T E R 1 Intrductn Infrmatn and knwledge frm thermdynamcs and chemcal knetcs are f great mprtance t prperly predct chemcal reactns and t desgn chemcal reactrs. Thermdynamcs tell us n whch drectn a reactn system wll develp and hw far t s frm ts equlbrum state. Analyses f knetcs prvde nfrmatn abut the rate wth whch the system wll apprach equlbrum. In recent years, several new and mre sphstcated reactr types have been suggested and attract nterest frm researchers all ver the wrld [Sund05]. One f these new reactr types s the s-called chrmatgraphc reactr. Befre ntrducng the prncple f chrmatgraphc reactrs, whch need t be understd better t apply them successfully, a shrt ntrductn nt thermdynamcs and knetcs wll be gven. 1.1 Thermdynamcs The scence f thermdynamcs was brn n the nneteenth century n rder t descrbe the peratn f steam engnes and t set frth the lmts f what they can accmplsh. Hwever, the prncples bserved t be vald fr engnes were sn generalzed nt pstulates nw knwn as the frst and secnd laws f thermdynamcs [Smth96]. Extensve ntrductns t thermdynamcs can be fund n many textbks (e.g., [Smth96], [Sand99]). Thermdynamcs s a study f energy changes accmpanyng physcal and chemcal changes. It s based n macrscpc-prperty frmulatns dealng wth the average changes that ccur amng larger numbers f mlecules, rather than wth detaled (mcrscpc) changes that ccur n a sngle mlecule. On the ther hand, 1

11 2 Chapter 1 Intrductn knwledge f mcrscpc behavr f matter can be useful n the calculatn f thermdynamc prpertes. The regn f the unverse under study, whch may be a specfed vlume n space r a quantty f matter, s typcally called the system. A system s separated frm the rest f the unverse, called the surrundngs, by a bundary whch may be magnary r nt, but whch by cnventn defnes a fnte vlume. The pssble exchanges f wrk, heat, r matter between the system and the surrundngs take place acrss ths bundary. A system s sad t be slated, f matter and energy can nt crss the bundary,.e., the system des nt change as a result f changes n ts surrundngs. An adabatc system s ne that s thermally slated frm ts surrundngs; that s, heat can nt crss the bundary. If matter can flw nt r ut f a thermdynamc system, the system s sad t be pen; f nt, the system s clsed. The state f a system characterzed by prpertes such as temperature, pressure, densty, cmpstn, etc. s referred t the thermdynamc state f the system. These prpertes d nt depend n the past hstry f the system nr n the means by whch t has reached a gven state. They depend nly n the present cndtns. The crrespndng prpertes are knwn as state prpertes r functns. An mprtant cncept n thermdynamcs s the equlbrum state. General characterstcs f an equlbrum state are that (1) the state des nt vary wth tme; (2) the system s unfrm (.e., there are n nternal temperature, pressure, velcty, r cncentratn gradents) r s cmpsed f subsystems each f whch s unfrm; (3) all flws f heat, mass r wrk between the system and ts surrundngs are zer; and (4) the net rate f all chemcal reactns s zer [Sand99]. There s a cmprehensve theretcal framewrk avalable t predct many essental thermdynamc prpertes f systems cntanng several cmpnents (r speces) [Smth96]. Ths tlbx prvdes e.g., enthalpes f phase transtn and reactn, and allws t predct the dstrbutn f the cmpnents between several phases [O cn05]. Equlbrum requres that the rates f all pssble reactns between the cmpnents f the system are zer. Ths state s ften nt reached n ndustrally appled chemcal reactrs. 1.2 Knetcs f Chemcal Reactns Chemcal knetcs s cncerned wth the rates f chemcal reactns (.e., wth the quanttatve descrptn f hw fast the reactns ccur) and the factrs affectng these rates [Mss99]. In cntrast t thermdynamcs these rates can be ften determned nly

12 1.3 Chrmatgraphc Reactrs 3 expermentally. Typcally, a labratry scale reactr s used t carry ut the reactn t quantfy the dependences f rates n varus factrs, such as cncentratns f speces and temperature. The prmary gal f chemcal knetcs s the develpment and valdatn f a rate law (fr a sngle system) r a set f rate laws (fr cmplex reactn systems). Appraches t study a reactn are nrmally based n the fllwng aspects (nt necessarly n the rder lsted) [Mss99]: 1. Chce f type f reactr t be used and certan features relatng t ts mde f peratn (e.g., a batch reactr perated at cnstant vlume). 2. Chce f speces (reactant r prduct) t fllw durng the experments (e.g., by chemcal analyss). 3. Chce f methd t fllw the extent f reactn wth respect t tme (e.g., by spectrscpc r chrmatgraphc analyss). 4. Chce f methd t determne numercally the values f the parameters, and hence t establsh the frm f the rate law. Fr a smple system, t s nly necessary t fllw the extent f reactn by means f a sutable measurement. Ths may be the cncentratn f ne speces. Batch reactrs are tradtnally used (see e.g., [Mazz97a], [Grp06], [Slva06]). The measurement f the relevant cncentratn-tme curses s ften tme-cnsumng and tedus. A standard peratn mde f reversble reactns s fxed-bed reactr. The cmmn lmtatn n the perfrmance f ths type f reactn s that n cmplete cnversn can be acheved. Fr ths reasn, chrmatgraphc reactrs are used wdely as research tls. 1.3 Chrmatgraphc Reactrs A pwerful cncept t perfrm reversble reactns n an effcent way s based n applyng chrmatgraphc separatn prncples smultaneusly wth the chemcal reactns. Such chrmatgraphc reactrs have attracted the attentn f researchers already fr mre than 40 years [Brr05]. Hwever, there are stll nt much ndustral applcatns. The prncples f chrmatgraphc reactrs that cmbne a reversble chemcal reactn wth a chrmatgraphc separatn are llustrated as n Fgure 1.1. In ths fgure, a reactn f the type A B + C (1.1) s used as an example t explan the peratng prncples.

13 4 Chapter 1 Intrductn In the example cnsdered t s assumed that the reactant A has ntermedate adsrptn behavr and the prducts B and C are the mre strngly and weakly adsrbed cmpnents. Reactant A s njected perdcally as a pulse nt the clumn. Durng ts prpagatn alng the clumn, A reacts t B and C. Owng t the dfferent adsrptn behavr f A, B and C, all cmpnents prpagate wth dfferent velctes and are separated frm each ther. Ths restrcts the backward reactn between B and C. Therefre, the restrctn f an equlbrum-lmted reactn can be vercme t cnvert the reactant A ttally [Brr05]. Speces leavng the chrmatgraphc reactr can be detected usng a sutable detectr and recrded as a sgnal versus tme n the chrmatgram. A A B C B C A B C Fgure 1.1. Prncples f chrmatgraphc reactrs. Fgure 1.2 shws detectr sgnals f a cnventnal UV-detectr placed at the reactr utlet whch were reprted n the wrk f Falk et al. [Falk02]. The hetergeneusly catalyzed hydrlyss f methyl frmate (HCOOCH 3 ) t methanl (CH 3 OH) and frmc acd (HCOOH) was chsen as a mdel reactn. An acdc n exchange resn was used as catalyst and adsrbent. It can be seen frm Fgure 1.2a that nly a part f the ester s cnverted and there s nt suffcent separatn between the tw prducts, whereas wth a lwer flw rate the ester can be cnverted cmpletely and t s suffcent t separate the prducts (Fgure 1.2b). The authrs bserved cmplex shapes f the prfles n Fgure 1.2a revealng that t s nt trval task t select apprprate cndtns t perate successfully such a reactr. Fr ths end, the applcatn f a sutable mathematcal mdel appears t be mandatry. Mathematcal treatments f reactn chrmatgram data are appled t quantfy knetc parameters, and hence t establsh the actual frm f the rate law. Examples f applcatns f chrmatgraphc reactrs fr knetc studes abund. Sme f them can be seen n refs. [Blm83], [Jeng92], [Mazz97b], and [Falk02].

14 1.4 Am and Outlne 5 U [mv] 50 (a) measured calculated HCOOCH 3 20 HCOOH 10 CH 3 OH t [mn] U [mv] 200 (b) measured calculated CH 3 OH HCOOH t [mn] Fgure 1.2. Cmparsns f measured (symbls) and smulated (lnes) detectr sgnals. Influence f the flw rate fr V nj = 20 µl and c A nj = ml/l: a) V & = 2.5 ml/mn, b) V & = 0.1 ml/mn [Falk02]. An alternatve apprach t the quantfcatn f reactn rates that s rarely cnsdered n ths feld s the applcatn f calrmetry [Land91, Land94]. An accurate measurement f the tme dependence f heat effects related t reactns allws ne t quantfy reactn rates [Hass00]. There s a relatvely large number f studes avalable n the lterature whch reprt n the knetcs and chemcal equlbrum f hydrlyss (e.g., [Weth74], [Ch80a], [Falk02]) and esterfcatn (e.g., [Sard79], [Mazz97a], [Pöpk01], [Gel03], [San04], [Grb06]). In mst cases, the same sld actng smultaneusly as adsrbent and catalyst s used. A typcal example f such sld s gven by n-exchange resns, such as thse based n a mcrprus styrene-dvnylbenzene cplymer functnalzed by varus amunts f sulfnc grups, whch prvde the acdty necessary fr the catalytc functn. In ther cases, strngly mneral acds such as hydrchlrc acd and sulfurc acd are used. Hwever, cmprehensve studes f these reactns are stll lackng. Ths reveals that a thrugh study f these reactns under catalyss f n-exchange resns s necessary. 1.4 Am and Outlne The am f ths wrk s t analyze expermentally the thermdynamcs and chemcal knetcs f fur hetergeneusly catalyzed ester hydrlyss reactns, and hence t enlarge the database related t these reactns.

15 6 Chapter 1 Intrductn Fr ths, the reactns were studed n a reactn calrmeter. The am ncludes: the theretcal and expermental analyss f the phase equlbra f the multcmpnent lqud mxtures n the absence and presence f a sld adsrbent/catalyst; the theretcal and expermental study f the chemcal reactn equlbra n the hmgeneus and hetergeneus systems; the expermental nvestgatn f the chemcal knetcs f the reactns catalyzed by a specfc n-exchange resn. In rder t acheve the am f ths wrk, the bascs f thermdynamcs gvernng chemcal and phase equlbra, and f chemcal knetcs are revsed frst n Chapter 2. Ths chapter explans theretcally the phase equlbrum behavr f multcmpnent systems n the absence and presence f an n-exchange resn. Mathematcal equatns fr calculatn f the lqud phase cmpstn at equlbrum n the presence f an n-exchange resn are presented as well n ths chapter. Then expressns capable t descrbe the rates f hmgeneusly and hetergeneusly catalyzed reactns are ncluded. The cncept f actvty and actvty ceffcents used n the treatment f the nn-deal slutns s als ntrduced n ths chapter. The fur mdel reactns, whch are nvestgated durng the wrk, are ntrduced subsequently n Chapter 3. Ths chapter ncludes als the descrptn f the n-exchange resn used. Chapter 4 presents the calrmetrc technque used and the mdels descrbng the reactn calrmeter. The equpments and expermental prcedures used are descrbed n Chapter 5. In Chapter 6, the results btaned frm the study are reprted and dscussed. Ths ncludes n partcular the presentatn f the determned reactn equlbrum data and the rate cnstants f the hetergeneusly catalyzed reactns. Fnally, the summary and cnclusns f the wrk are gven n Chapter 7.

16 C H A P T E R 2 Theretcal Aspects A substantal knwledge f thermdynamcs gvernng chemcal and phase equlbra, and f chemcal knetcs s needed n rder t understand chrmatgraphc reactrs. Cncepts, prncples and theres f thermdynamcs that relate t chemcal and phase equlbra, and chemcal knetcs necessary fr ths wrk are shrtly ntrduced n ths chapter. General classc references are [Smth96], [Sand99], [Prau99], [O cn05], [Smth81], [Cnn90], [Leven99] and [Mss99]. General equlbrum crtera fr systems cntanng multcmpnent mxtures are ntrduced n Sectn 2.1. These crtera are then used t establsh the cndtns f phase equlbrum fr hetergeneus clsed systems (Sectn 2.1.1), phase equlbra fr systems cntanng a crss-lnked elastc plymer phase n cntact wth a surrundng lqud phase (Sectn 2.1.2) and chemcal reactn equlbra fr reactng systems (Sectn 2.2). Adsrptn stherms as a specal case f phase equlbra are dscussed n Sectn Sectn 2.2 als fcuses n the calculatn f equlbrum cmpstns fr systems that cntan a reactng lqud mxture and an n-exchange resn. Reactn knetcs are dscussed n Sectn 2.3. Fnally, the actvtes f cmpnents n slutn and the calculatn f actvty ceffcents are ntrduced n Sectn Phase Equlbra Phase cmpstns at equlbrum depend n several varables, such as temperature and pressure, and n the chemcal nature and cncentratns f the substances n the system. Phase equlbrum thermdynamcs seeks t establsh the relatns amng varus state 7

17 8 Chapter 2 Theretcal Aspects prpertes (n partcular temperature, pressure, and cmpstn) that ultmately preval when ne r mre phases reach the state f equlbrum wheren all tendency fr further change has ceased [Prau99]. The equlbrum crtera fr a clsed multcmpnent system are fund t be as shwn n Eq. (2.1), where S, G, A, and U stand respectvely fr the entrpy, Gbbs free energy, Helmhltz free energy and nternal energy f the system; M, T, p and V fr the mass, temperature, pressure and vlume f the system [Smth96, Sand99, O cn05]: S = maxmum fr equlbrum at cnstant M, U, and V G = mnmum fr equlbrum at cnstant M, T, and p (2.1) A = mnmum fr equlbrum at cnstant M, T, and V Fr a nn-reactve clsed system, a cmbned statement f the frst and secnd laws f thermdynamcs s [Prau99]: du = TdS pdv (2.2) If the system s pen, e.g., cnnected t anther system, a change n cmpstn must be taken nt accunt as expressed n the fllwng equatn: du = TdS pdv + N c = 1 μ dn (2.3) r n anther arrangement: 1 ds = du + T p T dv 1 T N c = 1 μ (2.4) dn where μ s the chemcal ptental (equal t the partal mlar Gbbs free energy) f cmpnent, n s the mle number f cmpnent and N c s the number f cmpnents n the system Phase Equlbrum n a Tw-Phase Clsed System Wthn a nn-reactve clsed system cnsstng f tw phases, each f the ndvdual phases s an pen system because f the pssble exchange wth the ther phase. Equatn (2.4) may therefre be wrtten fr each phase:

18 2.1 Phase Equlbra 9 ds I 1 = I T du I p + T I I dv I 1 I T N c = 1 μ dn (2.5a) I I ds II 1 = T II du II p + T II II dv II 1 T II N c = 1 μ dn (2.5b) II II where superscrpts I and II dentfy the phases. Cnsderng a clsed, adabatc cnstant-vlume system, the equlbrum crtern s S = maxmum subject t the cnstrants f cnstant U, V, and ttal number f mles f each cmpnents n. Thus, the fllwng equatn must hld at equlbrum: I II ds = ds + ds = 0 (2.6) Snce the ttal nternal energy, ttal vlume, and the number f mles f each cmpnent are fxed, ne can have II I du = du dv dv dn II I = = 1,, N c (2.7) II = dn I Substtutng Eq. (2.7) nt Eqs. (2.5a-b), Eq. (2.6) can be rewrtten as fllws: I II N 1 1 c I I p p I μ ds = du + dv I II I II I T T T T = 1 T II μ II T I dn = 0 (2.8) The cndtns fr equlbrum are that the dfferentals f the entrpy wth respect t all I I I varatns f the ndependent and uncnstraned varables (here du, dv and dn ) are zer. Therefre, the fllwng cndtns must be met n rder fr ds t be zer: 1) 2) 3) I II T = T (2.9a) I II p = p (2.9b) μ = μ = 1,, N c (2.9c) I II

19 10 Chapter 2 Theretcal Aspects In ther wrds, fr phase equlbrum t exst n a clsed, nn-reactve multcmpnent system at cnstant energy and vlume, the temperature, the pressure and the chemcal ptental f each cmpnent must be the same n each phase. Alternatvely, the basc relatn cnnectng the Gbbs free energy t the temperature and pressure can be expressed as n equatn (2.10) fr any clsed system, and as n equatn (2.11) fr any pen system. dg = Vdp SdT (2.10) N c dg = Vdp SdT + μ (2.11) 1 = dn Equatn (2.11) can be wrtten fr each f the ndvdual phases n a clsed system cnsstng f tw phases as belw: dg I I = V dp I I S dt I + N c = 1 μ dn (2.12a) I I dg II = V II dp II S II dt II + N c = 1 μ dn (2.12b) II II Cnsderng a clsed system at cnstant temperature and pressure, the cndtns fr phase equlbrum can be derved frm the equlbrum crtern that G shuld be a mnmum, and the dfferental f G fr the system s therefre equal t zer. I II dg = dg + dg = 0 (2.13) Substtutng Eqs. (2.12a-b) nt Eq. (2.13) yelds N c N c I I II II dg = Vdp SdT + μ dn + μ dn = 0 (2.14) = 1 = 1 Snce the temperature and pressure are cnstant, the changes dp and dt are equal t zer. Hwever, n a clsed system nt undergng chemcal reactn, the number f mles f each cmpnent s cnstant. Thus, mass cnversatn f each speces fr the clsed system requres that

20 2.1 Phase Equlbra 11 dn II = dn = 1,, N c (2.15) I Substtutn f Eq. (2.15) nt Eq. (2.14) shws that at equlbrum N c = 1 I II I ( μ ) dn = 0 dg = μ (2.16) Settng the dervatve f the Gbbs free energy wth respect t each f ts ndependent I varables (here the mle numbers n ) equal t zer yelds μ = μ = 1,, N c (2.17) I II Thus, t s agan fund that the equalty f chemcal ptentals s a necessary cndtn fr the exstence f phase equlbrum fr systems subject t a varety f cnstrants. These analyses fr equlbrum f tw-phase systems can easly be generalzed t multphase systems. The result fr a ϕ -phase system s I II μ = μ = L μ = 1,, N c (2.18) = ϕ Phase Equlbrum n a Slvent Plymer System In exchange resns, whch are defned as nsluble plymers cntanng charged grups r ns that can be exchanged fr charged grups r ns present n a surrundng slutn, have been wdely used n physcal and chemcal prcesses [Wll99]. In partcular, a resn based n a mcrprus styrene-dvnylbenzene cplymer, whch s functnalzed by the sulphurc acd type (SO 3 H) wll be used as a catalyst n ths wrk (see mre detals n Sectn 3.2). An understandng f the crrespndng phase equlbra n such a plymer s mprtant. The dervatn f quanttatve relatns that descrbe phase equlbrum fr a plymer n cntact wth a slvent mxture s ntrduced belw. Ths has been extensvely descrbed n the artcle f San et al., 2004 [San04] and n the publshed dssertatn f T. San, 2005 [San05]. Man parts are revsed belw. Cnsder a system wheren a crss-lnked elastc plymer phase s n cntact wth a surrundng lqud phase. When a crss-lnked elastc plymer cmes nt cntact wth a lqud, t can swell untl an equlbrum s reached [Flry53]. Chemcal speces can parttn between the plymer and surrundng lqud. In ths wrk, nly the dstrbutn f

21 12 Chapter 2 Theretcal Aspects neutral lqud cmpnents, but nt nc speces between a lqud phase and the plymer phase s dscussed. The term phase equlbrum here des nt refer t the equlbrum f phase transfrmatn, but t the equlbrum dstrbutn f chemcal speces between the tw phases n cntact. The system n ths case s cnsdered t cnsst f a hmgeneus plymer slutn, a hmgeneus surrundng lqud phase, and an elastc structure. The plymer phase behaves lke a bulk lqud phase encaged n an elastc structure where the rle f the structure s smlar t that f a sempermeable membrane n an smtc equlbrum. The structure dscussed here s elastc and therefre the energy f that structure depends n the vlume f the plymer phase [Maur96]. As ntrduced n the prevus sectn, a cmbned statement f the frst and secnd laws f thermdynamcs s expressed as n Eq. (2.2) fr a reversble prcess n a clsed system. du = TdS pdv (2.2) Any extensve state functn f the system s the sum f cntrbutns frm all hmgeneus phases. Dentng respectvely the lqud phase surrundng the plymer, the plymer phase (r the sld phase ) and the elastc structure by L, S and el, ne can wrte the fllwng extensve state functns f the system: du + L S el = du + du du (2.19a) dv + L S el = dv + dv dv (2.19b) ds + L S el = ds + ds ds (2.19c) In the classcal thery f rubber elastcty, defrmatn f the elastc structure des nt nvlve changes n the nternal energy r vlume f the elastc structure, but nly changes n ts cnfguratnal entrpy ([Flry53], p. 451). Thus, el du = 0 (2.20a) el dv = 0 (2.20b) At fxed temperature, the elastc behavr f the structure s nfluenced nly by the vlume f the sld phase. It shuld be nted that pressure p n Eq. (2.2) s the external pressure whch s equal t p L. Frm Eqs. (2.19b) and (2.20b), ne can then wrte:

22 2.1 Phase Equlbra 13 L L S pdv = p ( dv + dv ) (2.21) Intrducng Eqs. (2.19), (2.20) and (2.21) nt Eq. (2.2) leads t L L L L S L S S el du + p dv TdS + du + p dv TdS TdS = 0 (2.22) Snce temperature T and external pressure p L are cnstant, the dfferental f the Gbbs free energy fr the lqud and sld phase can be expressed as dg L L L L L = du + p dv TdS (2.23a) dg S S S S S S S = du + p dv + V dp TdS (2.23b) Thus, Eq. (2.22) can be rearranged t gve L S S S S el ( p p ) dv V dp TdS = 0 L S dg + dg + (2.24) At cnstant temperature T and external pressure p L, Eq. (2.24) can be smplfed t L S S S L el [ G + G V ( p p ) TS ] = 0 d (2.25) S S S The Gbbs free energy f the sld phase G ( T p, n ) are temperature T, pressure p S and mle numbers n S 1, S L S replaced by G ( T p, n ),, wheren the ndependent varables S n 2, etc. dented by n S, can be, because f the cnstant external pressure p L. Fr ths end, ne can derve the fllwng relatn [Eq. (2.26)] fr a change f pressure frm p L t p S n the sld phase at cnstant temperature and mle numbers, wth an assumptn that the sld phase s ncmpressble when T and p L are cnstant. G S S S S L S S S L ( T p, n ) = G ( T, p, n ) + V ( p p ), (2.26) Substtutng Eq. (2.26) nt Eq. (2.25) yelds (n L s a vectr f mle numbers L n 1, L n 2, ): L L L S L S el [ G ( T, p, n ) + G ( T, p, n ) TS ] = 0 d (2.27) It s tld by Eq. (2.27) that at equlbrum, fr a reversble change at cnstant temperature T, and external pressure p L, the sum f the Gbbs free energy f the lqud phase, G L, and

23 14 Chapter 2 Theretcal Aspects that f the sld phase, G S, mnus the prduct f temperature T and the entrpy f the elastc structure, S el, reaches a mnmum value. The effect f the elastc respnse f the plymer structure can be expressed n terms f mre easly measured quanttes than. The stress n a crss-lnked plymer structure el ds due t a defrmatn by an external frce s btaned frm the classcal thery f rubber elastcty. The nmnal stress f an unswllen crss-lnked plymer structure (.e., tensle frce per unt area f unswllen undefrmed sample) under unaxal defrmatn s cmputed as n Eq. (2.28) [Flry53], where τ s the nmnal stress, W s the wrk f defrmatn, V S, s the vlume f the unswllen undefrmed sample, and α s the defrmatn factr. Exact and nexact dfferentals are dented wth d and δ, respectvely. S el 1 δw T ds τ = = (2.28) S, S, V dα V dα The true stress that ppses further swellng f a swllen sphercal crss-lnked plymer netwrk (.e., tensle frce per unt area f swllen sample) s calculated usng Eq. (2.29). The true stress, whch s dented wth π sw, can be nterpreted as an addtnal pressure exerted n the sld phase, and s termed as swellng pressure [Flry53]. As a result, the pressure f the sld phase s the sum f the pressure f the lqud phase and the swellng pressure [Eq. (2.30)]. π S el T ds = (2.29) 2 S 3α V dα sw, p S L = p + π sw (2.30) The factr 3α 2 n the dmnatr f Eq. (2.29) rgnates frm the sphercal gemetry and 2 S, S the assumptn f strpc swellng. Snce 3α d αv = dv, the change n the cnfguratnal entrpy f the elastc structure can be expressed n terms f the swellng pressure and the vlume f the sld phase as fllws [San04]: ds el π dv T S sw = (2.31) S Eq. (2.27) can nw be rewrtten t gve L L L S L S S [ G ( T, p, n ) + G ( T, p, n ) + V ] = 0 d π (2.32) ws

24 2.1 Phase Equlbra 15 Applyng the Gbbs-Duhem equatn at cnstant temperature T, cnstant external pressure p L results n dg dg L S Nc L L L L L L ( T p, n ) = ( T, p, n ) dn, μ (2.33a) = 1 Nc L S S L S S ( T p, n ) = ( T, p, n ) dn, μ (2.33b) = 1 The ttal vlume f the sld phase s the sum f the partal mlar vlumes, V m,, as expressed n Eq. (2.34). V S N = c = 1 S n Vm, (2.34) Snce mass balances are dn L = dn = 1,, N c (2.35) S substtutn f Eqs. ( ) nt Eq. (2.32) gves Nc L L L S L S L [ ( T, p, n ) μ ( T, p, n ) π swvm, ] dn = 0 = 1 μ (2.36) Therefre, at cnstant temperature T and external pressure p L, the crtern fr phase equlbrum s L L L S L S ( T, p, n ) μ ( T, p, n ) π swvm, μ = + = 1,, N c (2.37) The relatn f chemcal ptental μ n each phase wth actvty a (the actvty a s defned and dscussed later n Sectn 2.4) s gven n Eq. (2.38), where μ s the chemcal ptental at the standard state. ( T, p, n) = μ ( T, p) + RT ln a ( T, p n) μ = 1,, N c (2.38), Wth an assumptn that the standard chemcal ptental f cmpnent s the same n bth phases, Eq. (2.37) can be expressed n terms f actvtes as belw:

25 16 Chapter 2 Theretcal Aspects ln L L S L S ( T, p, n ) ln a ( T, p, n ) + π swvm L a, = = 1,, N c (2.39) As dscussed earler, the secnd term n the rght-hand sde f Eqs. (2.37) and (2.39) gves the nfluence f the ncrease f pressure frm the lqud phase, p L, t that f the sld phase, p S. A determnatn f the parttnng f cmpnent between a lqud and a sld phase at equlbrum s very mprtant. In realty, t s dffcult t expermentally determne the prtn f a cmpnent n the sld phase. It can be alternatvely determned frm the measurable prtn f the cmpnent n the lqud phase usng an equlbrum functn. At a gven temperature ths equlbrum functn s called adsrptn stherm. A bref ntrductn f adsrptn stherms s gven n the fllwng sectn Adsrptn Equlbra A smple and straghtfrward pssblty t express the equlbrum between a lqud phase and a sld phase s t ntrduce adsrptn stherms. In the case f adsrptn frm lqud slutns, at a gven cncentratn f a cmpnent n the lqud phase, sme prtn f the cmpnent s parttnng ut f the lqud phase nt the sld phase, and sme prtn s desrbng and re-enterng the lqud phase. As cmpnent cncentratns n the lqud phase change, the relatve amunts f cmpnent that are adsrbng and desrbng wll change. The relatnshp between the ladng f a cmpnent n the sld phase (desgnated by q ) and ts cncentratn n the lqud phase (desgnated by c ) at equlbrum s referred as the adsrptn stherm. Adsrptn stherms generally exhbt ne f several characterstc shapes, dependng n the srptn mechansm [Ruth84, D98]. The thermdynamc apprach t the study f equlbrum can be appled t adsrptn equlbra as just t any ther phase equlbrum. Hence ne can use the equlbrum crtern that the chemcal ptental n the adsrbed phase s equal t the chemcal ptental n the lqud phase [Myers65, Radke72]: μ = μ = 1,, N c (2.40) S L where S dentes the adsrbed phase ( sld phase), and L dentes the lqud phase. The theretcal apprach t the nvestgatn f lqud-sld equlbra s mre cmplex and much less advanced than the study f gas-sld equlbra. Numerus mdels, whch were

26 2.1 Phase Equlbra 17 frst develped t descrbe the adsrptn behavr f cmpnents n gas-sld systems, have been extended t lqud-sld systems. A few shuld be mentned here Lnear Adsrptn Istherms The smplest expressn f equlbrum adsrptn s the lnear stherm (see Fg. 2.1a), whch s vald fr the cmpnent that s present n the lqud phase at lw cncentratns. The lnear relatn between the flud phase cncentratn, c, and ts ladng n the sld phase, q, s descrbed by Henry s law: q = K c = 1,,N c (2.41) Henry ceffcent, K, s the adsrptn cnstant, whch s ndependent t ther cmpnents Nn-lnear Adsrptn Istherms At hgh lqud phase cncentratns, the adsrptn stherm s n lnger lnear (see Fg. 2.1b). The mst cmmn mdel descrbng adsrptn behavr n lqud-sld systems s the Langmur stherm: q ( c ) = q b c s 1+ bc = 1,,N, c (2.42) where q s, s the saturatn capacty f the sld phase fr cmpnent, b s the stherm ceffcent f pure cmpnent, whch have t be determned expermentally. At lw lqud phase cncentratn the term 1+ b c 1, s that the Langmur stherm fr ths case reduces t the lnear frm, r Henry s law frm Eq. (2.41). The Langmur stherm fr pure-cmpnent adsrptn can readly be extended t a multcmpnent system. In ths case, the Langmur stherm accunts fr the cmpettve nteractns f the cmpnents wth the sld phase. Fr a N c -cmpnent system, the Langmur stherm hlds q ( c ) = q s, 1+ b c N c j = 1 b c j j = 1,,N c (2.43)

27 18 Chapter 2 Theretcal Aspects a) b) Ladng q Ladng q Cncentratn c Cncentratn c Fgure 2.1. (a) Lnear adsrptn stherm, and (b) Nnlnear adsrptn stherm Eqs. ( ) can be als expressed usng actvtes a L and a S nstead f c and q. Mre nfrmatn regardng actvty f a cmpnent n slutn s gven n Sectn Heat f Adsrptn The heat f adsrptn prvdes a drect measure f the strength f the bndng between adsrbed mlecules and the surface f the adsrbent. Physcal adsrptn frm the gas phase s nvarably exthermc [Ruth84]. Ths s generally true als fr adsrptn frm the lqud phase, as may be shwn by a smple thermdynamc argument. Snce the adsrbed mlecule has at mst tw degrees f translatnal freedm n the surface and snce the ratnal freedm f the adsrbed speces must always be less then that f the lqud phase mlecule, the entrpy change n adsrptn ( S = S ads S lqud ) s necessarly negatve. In rder fr sgnfcant adsrptn t ccur spntaneusly, the Gbbs free energy change n adsrptn ( G) must als be negatve. Frm G = H T S fllws that H s negatve, and adsrptn s exthermc. Hwever, unlke adsrptn frm the gas phase, the argument s less cgent and exceptns are pssble n the case f adsrptn frm the lqud phase. One f the basc quanttes n adsrptn studes s the ssterc heat, whch s the rat f the nfntesmal change n the adsrbate enthalpy t the nfntesmal change n the amunt f adsrbed [D98]. The Clausus Clapeyrn equatn relates the ssterc heat f adsrptn t the temperature dependence f the adsrptn stherm as shwn belw [Smth96]:

28 2.1 Phase Equlbra 19 ln p T q ΔH = RT st 2 (2.44) where Δ H st s the ssterc heat f adsrptn f a pure gas at an adsrbate ladng f q and temperature T. The crrespndng equlbrum gas phase pressure s p. The Clausus Clapeyrn equatn n ths frm s true nly fr the case that the bulk gas phase s cnsdered deal and the adsrbed phase vlume s neglected. Hwever, t can generally be als appled fr adsrptn frm the deal lqud phase. In that case, p n Eq. (2.44) can be replaced by the equlbrum cncentratn n the lqud phase c (see, e.g., [Sat87]). lnc T q ΔH = RT st 2 (2.45) The temperature dependence f the adsrptn equlbrum cnstant, K, shuld fllw a van t Hff equatn [Ruth84]: d ln K dt ΔH ads = (2.46) 2 RT where Δ H ads s the heat f adsrptn. The assumptns f dentcal stes wth n nteractns between adsrbed mlecules mply that the heat f adsrptn s ndependent f cverage. It fllws by dfferentatn f Eq. (2.41) that the ssterc heat f adsrptn, Δ H st, s the same as the heat f adsrptn, Δ H ads : ln c T q = ΔH RT st 2 d ln K = dt = ΔH RT ads 2 (2.47) The magntude f the heat f adsrptn can ften be used t dstngush between physcal adsrptn and chemsrptn. Fr chemsrptn, Δ H st magntudes usually range frm 60 t 170 kj/ml. Fr physcal adsrptn, the values are typcally smaller [Smth96].

29 20 Chapter 2 Theretcal Aspects 2.2 Chemcal Reactn Equlbra In ths sectn the equlbrum cmpstn f reactng systems s cnsdered. Equatn 2.1 als prvdes a means f dentfyng the equlbrum state when chemcal reactns ccur. The crtern fr equlbrum n a clsed system at cnstant temperature T and pressure p s als that the Gbbs free energy f the system attans ts mnmum value. Hence t fllws at the equlbrum state, that dg = 0 (2.48) T, p Equatn 2.11 gves the basc relatn cnnectng the Gbbs free energy t the temperature, pressure and cmpstn changes fr a sngle phase system: N c dg = Vdp SdT + μ (2.11) 1 = dn Sngle Reactns Cnsder the case f a sngle chemcal reactn ccurrng n a sngle phase n a clsed system at cnstant temperature and pressure. The mle number f cmpnent, n, present at any tme can be calculated frm the ntal mle number, mass balance: n, accrdng t the fllwng n = + ν ξ = 1,,N c (2.49) n where ξ dentes the extent f reactn; and ν s the stchmetrc ceffcent fr cmpnent (pstve fr prducts and negatve fr reactants). Takng the dfferental f Eq. (2.49) yelds the relatn between a dfferental change n the number f mles f a reactng cmpnent and a dfferental change f the extent f reactn: dn = ν dξ = 1,,N c (2.50) Substtutn f Eq. (2.50) nt Eq. (2.11) gves dg = Vdp SdT + N c = 1 ν μ dξ (2.51)

30 2.2 Chemcal Reactn Equlbra 21 At cnstant temperature and pressure, Eq. (2.51) becmes N = c μ ξ, p = 1 dg T ν d (2.52) Cmbnatn f Eqs. (2.48) and (2.52), the cndtn f chemcal reactn equlbrum can be wrtten N c = 1 ν μ = 0 (2.53) Equatn 2.53 shws that, fr a chemcal reactn at cnstant temperature T and pressure p, the net chemcal ptental f the reactants (weghted by the stchmetrc ceffcents) must be equal t the net chemcal ptental f the prducts at equlbrum. The fllwng equatn shws the relatn f the chemcal ptental f a cmpnent n slutn t that f the cmpnent n ts standard state, whch s characterzed by temperature T and pressure p. f μ ( p, T ) = μ ( p, T ) + RT ln = 1,,N c (2.54) f where f s the fugacty f cmpnent n slutn, f s the fugacty f cmpnent n ts standard state. The rat f f s called the actvty a f cmpnent n slutn (see Sectn 2.4 fr mre detals): f a = 1,,N c (2.55) f Equatn (2.54) then becmes μ = μ + RT ln a = 1,,N c (2.56) Elmnatn f μ n Eq. (2.53) by Eq. (2.56) gves the fllwng relatn fr the equlbrum state f a chemcal reactn:

31 22 Chapter 2 Theretcal Aspects N c = 1 ( μ + RT ln a ) = 0 ν (2.57) r N c N c ν μ + RT ln a = 0 (2.58) = 1 = 1 ν The standard chemcal ptental μ f cmpnent crrespnds t the standard Gbbs free energy f ts frmatn Δ. Thus, G f, Nc Nc μ = = 1 = 1 f, ( T ) ΔG ( T ) ν ν ΔG (2.59) r wth Δ G r beng the standard Gbbs free energy change f reactn. It s the dfferent between the Gbbs free energes f frmatn f the prducts and reactants (weghted by ther stchmetrc ceffcents) when each s n ts standard state as a pure substance at the system temperature and at a fxed pressure. Thus, the value f Δ G r s fxed fr a gven reactn nce the temperature s establshed, and s ndependent f the equlbrum pressure and cmpstn [Smth96]. Extensve tabulatns f values f the Gbbs free energes f frmatn fr cmmn cmpunds n the standard state, Δ, can be fund n handbks and n mst thermdynamcs texts. (see, e.g., [Stull69], [Red87], [Barn89], [Perry99] and [CRC05]). G f, Cmbnng Eqs. (2.58) and (2.59) gves r ΔG ΔG r r N c ν ( T ) + RT ln ln a = 0 = 1 N c ν ( T ) + RT ln a = 0 = 1 (2.60) (2.61) The prduct n the secnd term n the left hand sde f Eq. (2.61) s typcally called the equlbrum cnstant K a : N K a a = c = 1 ν (2.62)

32 2.2 Chemcal Reactn Equlbra 23 Frm Eqs. (2.61) and (2.62) ne can derve r r ( T ) = RT ln Ka Δ G (2.63) ( T ) ΔGr Ka = exp (2.64) RT Accrdng t the defntn f the actvty ceffcent [see Eq. (2.116) n Sectn 2.4], Eq. (2.62) can be rewrtten as N c = 1 ( ) K a = γ x ν (2.65) In the case f deal slutn, all actvtes γ are unty, and the reactn equlbrum cnstant can be expressed als n terms f mle fractns, x, r cncentratns, c, at equlbrum: N = c ν K x x = 1 N = c ν K c c = 1 (2.66) (2.67) Multple Reactns Fr the case that there are several chemcal reactns ccurrng n a sngle phase n a clsed system at cnstant temperature and pressure, the mass balance f cmpnent s n = n + N R j = 1 ν ξ = 1,, N c (2.68) j j where N R s the number f ndependent reactns j; ν j s the stchmetrc ceffcent f cmpnent fr reactn j; and ξ j s the extent f reactn j. Snce the stchmetrc ceffcents are cnstant, dfferentatn f Eq. (2.68) gves N = R dn ν dξ = 1,,N c (2.69) j = 1 j j

33 24 Chapter 2 Theretcal Aspects Substtutng Eq. (2.69) nt Eq. (2.11) yelds dg = Vdp SdT + N c N R = 1 j= 1 ν μ dξ (2.70) j j At cnstant temperature and pressure, Eq. (2.70) becmes N = c N R jμ ξ, p j = 1 j = 1 dg T ν d (2.71) The cndtn fr chemcal equlbrum n ths multreactn system s that dg = 0 [Eq. (2.1)] fr all varatns cnsstent wth stchmetry at cnstant temperature, pressure and ttal mass. Fr the present case, ths mples G ξ j T, p, ξ k j = 0 j = 1,,N R (2.72) Thus G ξ j T, p, ξ k j N c = 0 = ν μ j = 1,,N R (2.73) = 1 j As dscussed abve fr the case f a sngle reactn, a separate equlbrum cnstant s evaluated fr each reactn n the present case. Eq. (2.62) then becmes N = c ν j, j = 1 K a a j = 1,,N R (2.74) In the case f deal slutn, Eqs. (2.66) and (2.67) becme N = c ν j, j = 1 K x x N = c ν j, j = 1 K c c j = 1,,N R (2.75) j = 1,,N R (2.76)

34 2.2 Chemcal Reactn Equlbra 25 In the next sectn, a few aspects regardng the calculatn f equlbrum cmpstns f systems cntanng an actve multcmpnent mxture and an n-exchange resn are gven Calculatn f Equlbrum Cmpstns Recent advances n equlbrum analyss permt the rapd calculatn f the equlbrum cmpstn f a cmplex reactng mxture [Smth82]. There are tw basc appraches fr cmputng chemcal equlbra. In the frst ne, the equlbrum cnstants f chemcal reactns and the mass balance equatns are emplyed t determne equlbrum cmpstn. The secnd apprach s based n mnmzatn f the Gbbs free energy wth the mass balances f the elements as cnstrants. The frst apprach was used n ths wrk. Several chemcal reactns ccurrng smultaneusly n a system cntanng a slvent mxture and an n-exchange resn are cnsdered. As descrbed n Sectn 2.2.2, the equlbrum state fr multple reactns ccurrng n a sngle phase system at cnstant temperature and pressure s dentfed by fndng the state fr whch N c = 1 ν μ = 0 j = 1,,N R (2.73) j subject t the mle balances n = n + N R j = 1 ν ξ = 1,, N c (2.68) j j Hwever, fr multple reactns ccurrng n a lqud sld phase system, the crrespndng mle balances can be frmulated as fllws: n L N R = n + j =1 ν ξ n = 1,, N c (2.77) j j S where agan superscrpts L and S dente the lqud and sld phases, respectvely; n s the S ttal mle number f cmpnent n the system, and n s the amunt present n the sld phase.

35 26 Chapter 2 Theretcal Aspects Recallng Eq. (2.74), ne can wrte the equlbrum cnstant expressns fr each f N R reactns n the lqud phase as fllws: N c ( ) j L L K a, j = a j = 1,,N R (2.78) = 1 ν S The mle number f cmpnent n the sld phase, n, s a functn f the lqud phase cmpstn accrdng t the adsrptn stherm (Sectn 2.1.3). The actvty f cmpnent n the lqud phase s als a functn f the lqud phase cmpstn. Therefre, wth the mass balance shwn n Eq. (2.77), the actvty f cmpnent n the lqud phase s a functn f the N R unknwn extents f reactn ξ j. Equatn (2.78) tgether wth Eq. (2.77) represents a nnlnear system f algebrac equatns wth the unknwn ξ j. The cmpstns f the lqud phase and the sld phase as well n the smultaneus phase and chemcal equlbrum system can be cmputed by fndng the rts ξ j (e.g., Newtn Raphsn methd). In rder t start teratve cmputatns, ntal apprxmatns fr the rts are needed. The methd cnverges when the ntal apprxmatns are suffcently clse t the true rts, but may dverge when the ntal apprxmatns are far frm the true rts. Thus, fndng ntal apprxmatns suffcently clse t the true rts t acheve cnvergence s mst mprtant. If the adsrptn equlbrum functns are decupled and lnear,.e., q = K c = 1,, N c (2.79) then the mle number f cmpnent n the sld phase, S n, can be cmputed as S L V = Kn = 1,, N L c (2.80) V S S n KcV = where V L and V S dente the vlume f the surrundng lqud and sld phase, respectvely. Defnng the vlume fractn f the lqud phase (the lqud fractn) as L, V ε = (2.81) L, S V + V

36 2.2 Chemcal Reactn Equlbra 27 where V L, s the ttal vlume f the lqud ncludng the vlume f lquds n the sld phase, Eq. (2.80) can be rearranged wth the assumptn that the densty f the lqud phase s cnstant: n S L, L 1 ε V = Kn = 1,, N L c (2.82) ε V By substtutng S n frm Eq. (2.82) nt Eq. (2.77), ne can wrte r n n L L 1 ε V N R L, L = n + ν jξ j Kn L j = 1 ε V N R n + ν jξ j j = 1 = 1 ε V 1+ K ε V L, L = 1,, N c (2.83) = 1,, N c (2.84) The vlume f the lqud phase V L can be estmated as fllws f deal mxng s assumed, where V m, are the mlar vlume f cmpnent : V L = V L, N c = 1 n V S m, = 1,, N c (2.85) The sum n the rght-hand sde f Eq. (2.85) s the ttal vlume f the cmpnents stred n the sld phase, whch can be expressed n mre detals [last term f Eq. (2.86)] by S substtutng n frm Eq. (2.82). V L = V L, 1 ε V ε V L, L N c = 1 K n V L m, = 1,, N c (2.86) L Substtutng n frm Eq. (2.84) nt Eqs. (2.78) and (2.86) yelds a system f (N R +1) L nnlnear equatns nvlvng varables ξ j and V whch can be expressed as fllws: k (, V L ) = 0 F ξ j = 1,, N R ; k = 1,, N R +1 (2.87) j If ε s set equal t 1 fr a sngle phase lqud system, the nnlnear equatns whch need t be slved reduce t

37 28 Chapter 2 Theretcal Aspects j ( ) = 0 F ξ j = 1,, N R (2.88) j Heat f Reactn Every chemcal prcess s asscated wth sme type f heat effect. The heat f reactn s defned as the amunt f heat that must be added r remved durng a chemcal reactn n rder t keep all f the substances present at the same temperature. If the pressure n the vessel cntanng the reactng system s kept at a cnstant value, the measured heat f reactn als represents the change n enthalpy, Δ H r. Tabulatn f all pssble heat effects fr all pssble reactns s mpssble. Therefre, the heat effects fr reactns carred ut n any cndtns are calculated frm data fr reactns carred ut at certan standard cndtns. The standard heat f reactn s defned as the enthalpy change that ccurs by the chemcal reactn under the standard cndtns. Ths defntn f a standard heat f reactn can be expressed mathematcally by the fllwng equatn: N c ΔH r = ν H (2.89) = 1 where Δ H r s the standard reactn enthalpy, and H s the enthalpy f cmpnent n ts standard state. The standard enthalpy f a chemcal cmpund s equal t ts heat f frmatn plus the standard enthalpes f ts cnsttuent elements. The standard enthalpy f elements s establshed t be zer. Thus, the standard enthalpy f each cmpund s ts standard heat f frmatn, = ΔH, and Eq. (2.89) becmes H f, N c ΔH r = ν ΔH (2.90) = 1 f, Extensve tabulatns f values f the enthalpes f frmatn fr cmmn cmpunds at the standard state, Δ H f,, can be fund n handbks and n mst thermdynamcs texts. (see, e.g., [Stull69], [Red87], [Barn89], [Perry99] and [CRC05]). Fr standard reactns, all cmpnents are always at the standard pressure f 1 bar. Standard enthalpes are therefre functns f temperature nly:

38 2.2 Chemcal Reactn Equlbra 29 dh = c dt = 1,,N c (2.91) p Snce ν s a cnstant, frm Eq. (2.91) ne can wrte d N c = 1 N c ν H = ν c dt (2.92) = 1 p N c The term = 1 ν s the standard heat f reactn as defned by Eq. (2.89). Smlarly, the H standard heat capacty change f reactn can be defned as N c Δc p = ν c (2.93) = 1 p Usng these defntns, Eq. (2.92) becmes dδ H = Δc dt (2.94) r p Equatn (2.94) prvdes the temperature dependence f enthalpy f reactn. The ntegratn f Eq. (2.94) frm temperature T t T gves ( ) = Δ ( ) + T T H T Δ Δ H r r C pdt (2.95) T where Δ (T ) and Δ H ( r T ) are heats f reactn at temperature T and at reference H r temperature T respectvely Influence f Temperature n Reactn Equlbrum Cnstants The standard Gbbs free energy f reactn s cnsdered as a measure f the spntanety f a reactn. In turn, ths thermdynamc parameter measures a cmbnatn f changes n heat, wrk, and entrpy that ccur durng a reactn. The Gbbs free energy f reactn s defned as Δ G = ΔH TΔS (2.96) r r r

39 30 Chapter 2 Theretcal Aspects where Δ G r and Δ S r are the standard reactn enthalpy and entrpy, respectvely. By rearrangng Eq. (2.96) and usng the relatnshp n Eq. (2.63), ne can btan ΔH r ΔSr ln Ka = + (2.97) RT R Thus, f ne measures K a as a functn f temperature, a plt f lnk a versus 1/T shuld yeld a straght lne wth a slpe f ΔH R and an ntercept f Δ S R. Ths relatnshp can be expressed as a dfferental equatn descrbng the temperature dependence f the equlbrum cnstant K a : d ( ln K ) dt a ΔH r = (2.98) 2 RT As dscussed earler n Sectn 2.2.4, Δ H r s als a functn f temperature [Eq. (2.95)]. Hwever, fr small temperature dfferences, Δ H r s assumed t be cnstant, and then ΔH r 1 1 ln Ka( T ) = ln Ka( T ) (2.99) R T T Eq. (2.98) s knwn as the van t Hff equatn, and by perfrmng a van t Hff analyss, the reactn enthalpy and entrpy can be extracted. 2.3 Reactn Rates Brad knwledge regardng the knetcs f chemcal reactns can be fund n the lterature (fr example [Smth81], [Cnn90], [Leven99] and [Mss99]). In ths sectn, a shrt emprcal macrscpc descrptn f the rates f chemcal reactns s gven. The descrptn cncentrates n the defntn f reactn rates and n the develpment f a quanttatve analyss f the dependence f the reactn rates n the reactn cndtns, ncludng cncentratn f nvlved cmpnents and temperature. In fact, mst real reactrs need catalysts t speed up reactn,.e., t make reactn ccur at lwer temperatures r t attan a hgher selectvty t a partcular prduct. The catalysts can be hmgeneus r hetergeneus. Fr the hetergeneus systems, chemcal reactns can take place n all ndvdual phases. Therefre, the verall rate can be dependent n the rates n all ndvdual phases. In Sectn 2.3.1, the rates f chemcal reactns n a hmgeneus

40 2.3 Reactn Rates 31 sngle phase are ntrduced. Subsequently, a descrptn f the reactn rates n a hetergeneus system s gven (Sectn 2.3.2) Hmgeneus Systems The reactn rate s defned ether as the amunt f prduct prduced r the amunt f reactant cnsumed per unt vlume f the reactn phase per unt tme (see, e.g., [Schm98]). Fr a N R -reactn system n a hmgeneus phase, the rate f transfrmatn f cmpnent, verall r, n the system can be wrtten as verall N = R r ν r = 1,,N c (2.100) j j j where ν j s the stchmetrc ceffcent f cmpnent n reactn j, and r j s the rate f reactn j. The rate f a sngle reactn s typcally defned as 1 dn r = = 1,,N c (2.101) VRν dt In the abve equatn, V R s the sngle phase reactn vlume; n s the number f mles f cmpnent ; and N c s the number f cmpnents. The specfc numbers f mles f cmpnent n a batch reactr are smply the reactr vlume V R tmes the vlumetrc cncentratn c : n = V c = 1,,N c (2.102) R Wth ths, Eq. (2.101) becmes ( V c ) 1 d R r = V ν dt R 1 = V V ν R R dc dt + c dv dt R = 1,,N c (2.103) If vlume s cnstant, then Eq. (2.103) reduces t 1 dc r = = 1,,N c (2.104) ν dt

41 32 Chapter 2 Theretcal Aspects Pstulatng that the rate-cntrllng mechansm nvlves the cllsn r nteractn f a sngle mlecule f a reactant wth a sngle mlecule f the ther reactants, then the number f cllsn f thse mlecules s prprtnal t the rate f reactn [Mss99]. Hwever, n the case f deal slutn, at a gven temperature the number f cllsns s prprtnal t the cncentratn f reactants n the mxture. Thus, fr an rreversble reactn the rate f reactn can be descrbed as N r ( T ) ( ) r = k (2.105) c m where N r s the number f reactants; m s the rder f the reactn wth respect t the cmpnent. The rate cnstant k(t) s fund emprcally t be dependent n temperature as shwn n the fllwng Arrhenus equatn [Mss99]. k E = exp (2.106) RT ( ) A T k where E A s called the actvatn energy fr the reactn and k s called the pre-expnental factr. If the reactn s reversble, the rate can be wrtten as a dfference between the rate f the frward reactn r f and the rate f the backward reactn r b, N c c m f ( T ) ( c ) k ( T ) ( c ) N, b, r = r r = k (2.107) f b f b m wth m f, m b, = 2 1 = 2 1 ( ν ν ) ( ν + ν ) r N N 1, = k f c c m f m ( T ) ( c ) ( ) b c Kc r, (2.108) where k f and k b are the rate cnstants f the frward and backward reactns, respectvely. K c s the cncentratn-based reactn equlbrum cnstant [Eq. (2.67)].

42 2.3 Reactn Rates 33 Alternatvely, the reactn rate can be expressed n terms f actvtes as n Eq. (2.109) n rder t take nt accunt the nn-dealtes f the slutn. K a s the actvty-based reactn equlbrum cnstant [Eq. (2.62)], and a s the actvty f cmpnent. N N 1, = k f c c m f m ( T ) ( a ) ( ) b a Ka r, (2.109) Hetergeneus Systems Fr hetergeneus systems, a study f the knetcs s mre cmplex than dealng wth hmgeneus systems. Specfcally, there are mre factrs t cnsder fr hetergeneus system. Fr nstance, fr a sld-catalyzed reactn, there can be fve basc steps n the sequence f mass transfer and reactn ver a sld catalyst [Harr03]: 1. Dffusn f reactants t the external surface f the catalyst and nt the pres 2. Adsrptn f ne r bth reactants n actve stes 3. Reactn n the surface between adsrbed speces r between surface speces and a reactant n the lqud phase 4. Desrptn f the prducts 5. Dffusn f prducts ut f the pres and nt the external lqud When the system s at steady state, all the steps n the sequence take place at the same rate. Hwever, the verall rate s ften cntrlled by ne step, whch s the slwest ne. In many cases, ths s the chemcal reactn. In ths wrk, the reactn n a system cnsstng f a sld catalyst and lqud reactants s cnsdered. Fr ths case, the reactn can ccur n bth lqud and sld phases. The verall rate f reactns, r verall, s the sum f the rates f the reactn takng place n the lqud phase, r hm, (frm nw n, called hmgeneus reactn) and the reactn takng place n the sld phase, r het, (frm nw n, called hetergeneus reactn). The hmgeneus reactns take place n the lqud phase wth the vlume fractn ε [Eq. (2.81)], the hetergeneus reactns take place n the sld phase wth the vlume fractn (1 ε ). At fxed temperature, r hm depends n the cmpnent cncentratns (c 1, c 2, etc. dented by c ), and r het depends n the speces ladngs n the catalyst (q 1, q 2, etc. dented by q ). It fllws fr the verall rate that het ( c ) + ( 1 ) r ( c q ) r verall hm = εr ε, (2.110)

43 34 Chapter 2 Theretcal Aspects Applcatn f the rate expressn f reversble reactns derved abve fr hmgeneus systems [Eq. (2.108)] can be extended t each phase n a hetergeneus system: and N hm 1 c c hm m f, m ( c ) = k ( ) ( ) ( ) b f T c c hm Kc r, c c het m f, m ( c q ) = ( ) ( ) ( ) b av k f T qav, q het av, Kc N (2.111), N N (2.112) het 1, r wth m f m, b, * * ( ν ν ) * * ( ν + ν ) 1 = 2 1 = 2 *) hm r het In the abve equatns, k hm f and k het f dente the rate cnstants, hm K c and het K c the equlbrum cnstants f the frward reactns n the lqud and sld phases, respectvely. q, s the average ladng f cmpnent n the sld phase. av In prncple, the ladng f a cmpnent n the sld phase depends n ts cncentratn n the lqud phase. Snce, n fact, t s dffcult t expermentally determne the ladng f a cmpnent n the sld phase, mdels must be develped t predct the ladngs as functns f the cncentratns n the lqud phase. The rate expressn f reactns n the sld phase can then be wrtten n terms f the lqud cncentratn. The relatnshp between the ladng f a cmpnent n the sld phase and ts cncentratn n the lqud phase at equlbrum s referred as the adsrptn stherm. Ths has been dscussed prevusly n Sectn In rder t take nt accunt the nn-dealtes f systems, the rate expressns shuld be wrtten n terms f actvtes. Fr ths end, the fllwng equatns (2.113) and (2.114) can be wrtten, where a L and a S dente actvtes n the lqud and sld phase, respectvely. r r N c N c L hm L m ( ) ( ) ( ) ( ) f, L m = b, a k f T a a hm Ka hm 1 N c N c S het S m ( ) ( ) ( ) ( ) f, S m = b, a k f T a a het Ka het 1 (2.113) (2.114)

44 2.4 Actvty and Actvty Ceffcents Actvty and Actvty Ceffcents In the abve sectns, several tmes actvty a the actvty ceffcents γ were ntrduced. Nw a mre detaled ntrductn abut actvty and dscussn f hw t calculate actvty ceffcents are presented. As basc references regardng actvty and actvty ceffcents, [Prau99], [Sand99] and [Neve02] are recmmended. The actvty f cmpnent n a mxture at sme temperature, pressure, and cmpstn s defned as the rat f the fugacty f cmpnent at these cndtns t ts fugacty n the standard state, that s a state at the same temperature as that f the mxture and at sme specfed cndtn f pressure and cmpstn [Prau99]: a ( T p, x) ( T, p, x) f, = 1,,N c (2.115) f ( T, p, x ) where p and x are, respectvely, an arbtrary but specfed pressure and cmpstn. The actvty ceffcent γ s the rat f the actvty f cmpnent t sme cnvenent measure f the cncentratn f cmpnent, usually the mle fractn: a γ = 1,,N c (2.116) x The fugacty f cmpnent n a lqud slutn, f, s defned n relatn wth the partal mlar Gbbs free energy f cmpnent by the equatn: g ( T ) + RT ln f = Γ = 1,,N c (2.117) where g s the partal mlar Gbbs free energy f cmpnent ; and Γ (T ), a functn f temperature, s the ntegratn cnstant at cnstant T. In the ther cntext, the fugacty f cmpnent n a lqud slutn s mst cnvenently related t the mle fractn x by: f = γ x f = 1,,N c (2.118) In an deal slutn at sme cnstant temperature and pressure, the fugacty f cmpnent s prprtnal t sme sutable measure f ts cncentratn, usually the mle fractn. It fllws that f = R x = 1,,N c (2.119)

45 36 Chapter 2 Theretcal Aspects where R s a prprtnalty cnstant dependent n temperature and pressure but ndependent f x. Based n the defntn f the fugacty [Eq. (2.117)], at cnstant temperature and pressure, fr a cmpnent n slutn, the fllwng relatn can be wrtten: g [ ln f f ] ( real) g(deal) = RT (real) ln = 1,,N c (2.120) (deal) By dfferentatn at cnstant T, p, and n j (j ) f the equatn defnng the excess Gbbs free energy, G E, G E G G (2.121) ( real slutn at T, p and x) (deal slutn at samet, p and x) the partal mlar excess Gbbs free energy s ntrduced: g E = g g = 1,,N c (2.122) ( real) (deal) Cmbnatn f Eqs. (2.120) and (2.122) yelds f E (real) g = RT ln = 1,,N c (2.123) f(deal) Substtutng Eq. (2.119) nt Eq. (2.123) gves g E f R x = RT ln = 1,,N c (2.124) If the standard fugacty f s set equal t R, then ne can have a f = γ x = = 1,,N c (2.125) R Fr an deal slutn f s equal t R x [Eq. (2.119)] and therefre, γ = 1 and a = x. Substtutng Eq. (2.125) nt Eq. (2.124) yelds g E = RT lnγ = 1,,N c (2.126)

46 2.4 Actvty and Actvty Ceffcents 37 Thus the mlar excess Gbbs free energy f a slutn can be expressed n relatn wth mle fractns and actvty ceffcents as fllws: g E = RT N c = 1 x lnγ (2.127) Many equatns have been prpsed fr the relatn between actvty ceffcents and mle fractns [Prau99]. UNIQUAC equatn frst gven by Abrams and Prausntz [Abram75] s ne f the mst relable equatns fr many practcal calculatns. The UNIQUAC equatn, whch s used n ths wrk, s ntrduced belw. Calculatn f actvty ceffcents usng UNIQUAC equatn The UNIQUAC equatn fr the excess Gbbs free energy g E cnssts f tw parts, a cmbnatral part g C that attempts t descrbe the dmnant entrpc cntrbutn, and a resdual part g R that s due prmarly t ntermlecular frces that are respnsble fr the enthalpy f mxng. The cmbnatral part s determned nly by the cmpstn and by the szes and shapes f the mlecules; t requres nly pure-cmpnent data. The resdual part, hwever, depends als n ntermlecular frces; the tw adjustable bnary parameters, therefre, appear nly n the resdual part. The UNIQUAC equatn s: E C g = g + g R (2.128) Fr a multcmpnent system hlds: g C = Nc N c u x ln + q x ln = 1 x 2 = 1 Φ Φ z θ (2.129) g R = N c N c u' q x ln = 1 j= 1 ' θ jτ j (2.130) where the crdnatn number z s set equal t 10 [Prau99]. Segment fractn, Φ, and area fractns, θ, and θ, are gven by: Φ N c j = 1 x r u x r u j j = 1,,N c (2.131)

47 38 Chapter 2 Theretcal Aspects and θ N c j= 1 x q u x q j u j u' ' xq θ N c = 1,,N c (2.132) u' x q j= 1 j j The parameters r u, q u, and q u are pure-cmpnent mlecular-structure cnstants dependng n mlecular sze and external surface areas. In the rgnal frmulatn, q u = q u. T btan better agreement fr systems cntanng water r lwer alchls, q u values fr water and alchls were adjusted emprcally by [Ander78] t gve an ptmum ft t a varety f systems cntanng these cmpnents. Fr alchls, the surface f nteractn q u s smaller than the gemetrc external surface q u, suggestng that ntermlecular attractn s dmnated by the OH grup (hydrgen bndng). Fr fluds ther than water and lwer alchls, q u = q u. Subscrpt dentfes agan speces, and j s a dummy ndex; all summatns are ver all speces. Nte that τ j τ j ; hwever, when = j, then τ = τ jj = 1. The nfluence f temperature n g E enters thrugh the nteractn parameters τ j f Eq. (2.130), whch are temperature dependent: a u = j τ j exp and T a u = j τ j exp, j = 1,,N c (2.133) T Parameters fr the UNIQUAC equatn are therefre values f u a j and u a j. An expressn fr ln γ s fund by applcatn f Eq. (2.134): E ( G / RT ) lnγ = n, j = 1,,N c (2.134) T, P, j t the UNIQUAC equatn fr g E fllwng equatns: [Eqs. (2.128)-(2.130)]. The result s gven by the ln γ = lnγ + lnγ = 1,,N c (2.135) C R

48 2.4 Actvty and Actvty Ceffcents 39 = = = = + Φ + Φ + Φ = c c c c N j N k kj k j j u u N j j j u N j j j u q q q l x x l q z x 1 1 ' ' ' ' 1 ' ' 1 ln ln 2 ln ln τ θ τ θ τ θ θ γ = 1,,N c (2.136) where n addtn t Eq. (2.136), ( ) ( ) 1 2 = u j u j u j j r q r z l j = 1,,N c (2.137) Agan subscrpt dentfes speces, and j and k are dummy ndces. An extensve cllectn f values fr the parameters u r, u q, u j a and u j a allwng the predctn f actvty ceffcents wth Eqs. ( ) s gven by Gmehlng et al., 2002 [Gmeh02].

49 40 Chapter 2 Theretcal Aspects

50 C H A P T E R 3 Mdel Reactns, Catalysts and Adsrbents In Chapter 2, man theretcal aspects f relevance fr the present wrk have been dscussed. Ths chapter ntrduces the mdel reactns nvestgated n ths wrk ncludng the catalysts used. Ths s fllwed by a sectn summarzng the expermental nvestgatns carred ut. 3.1 Mdel Reactns Hydrlyss f Esters In ths wrk, the hydrlyss f the fur carbxylate esters s studed,.e., the hydrlyss f methyl frmate, methyl acetate, ethyl frmate and ethyl acetate t the crrespndng carbxylc acds and alchls. There are several specfc analyses f sme f these reactns n the lterature (e. g., [Newl36], [Shah54], [Bell55], [Bala69], [Weth74], [Raja78], [Ch80a], [Ch80b], [Gt83], [Indu93], [Vlcu94], [Pöpk01], [Lde03] and [Yu04]). Typcally the hydrlyss f esters s slw at neutral ph, but faster at acdc r basc ph. Acds and bases can catalyze ester hydrlyss reactns. The fur reactns can be descrbed wth the fllwng stchmetrc equatns: 41

51 42 Chapter 3 Mdel Reactns, Catalysts and Adsrbents H + r OH - CH 3 -OOCH + H 2 O CH 3 OH + HCOOH (3.1a) H + r OH - CH 3 -OOCCH 3 + H 2 O CH 3 OH + CH 3 COOH (3.1b) H + r OH - C 2 H 5 -OOCH + H 2 O C 2 H 5 OH + HCOOH (3.1c) H + r OH - C 2 H 5 -OOCCH 3 + H 2 O C 2 H 5 OH + CH 3 COOH (3.1d) In rder t descrbe the fur smpler reactns n a systematc manner, the fllwng ndcatrs are used n ths wrk: CH 3 - Al 1 - (the methyl grup f alchl 1) C 2 H 5 - Al 2 - (the ethyl grup f alchl 2) -OOCH Ac 1 - (the frmate grup f acd 1) -OOCCH 3 Ac 2 - (the acetate grup f acd 2) CH 3 -OOCH Es 11 (ester f alchl 1 and acd 1) (3.2) CH 3 -OOCCH 3 Es 12 (ester f alchl 1 and acd 2) C 2 H 5 -OOCH Es 21 (ester f alchl 2 and acd 1) C 2 H 5 -OOCCH 3 Es 22 (ester f alchl 2 and acd 2) H 2 O W Usng the abve ntatns, the fur hydrlyss reactns f the fur esters can be descrbed n a scheme as shwn n Eq. (3.3): H + r OH - Es j + W Al + Ac j, j = 1, 2 (3.3) Belw, n sme cases, Es j, Al, and Ac j are smply dented by Es, Al, and Ac respectvely. Catalysts fr the reactns can be a mneral acd (e.g., HCl, H 2 SO 4, HNO 3 ) r a mneral base (e.g., NaOH, KOH) n the lqud frm. The catalyst can als be an acdc r basc nexchange resn. Fr example, catn-exchange resns based n styrene dvnylbenzene cplymers functnalzed by sulphurc acd grups (SO 3 H) have been frequently used (e.g., [Sard79], [Mazz79a-b], [Pöpk00], [Falk02], [Lde03] and [San04]).

52 3.1 Mdel Reactns 43 Lng chan esters are usually weakly plar. Therefre, they dsslve badly n water. Amng the fur esters mentned abve, the best and wrst slublty n water crrespnd t methyl frmate and ethyl acetate, respectvely (Table 3.1). Values f sme selected physcal parameters f the cmpnents relevant t the hydrlyss f the fur esters are lsted n Table 3.1. The standard enthalpes and standard Gbbs free energes f frmatn f many cmpunds fr the lqud and gas phase can be fund n the lterature (e.g., [Afee05], [Barn95], [CRC05], [Perry99] and [Stull69]). A summary f thse values fr the cmpunds nvlved t the reactns nvestgated s gven n Tables 3.2 and 3.3. Table 3.1. Selected physcal parameters f the cmpunds n the nvestgated reactns system frm [Merck05]. M ρ t,20 C blng 1013mbar, Slublty n water at 20 C Cmpund [g/ml] [g/cm 3 ] [ C] [g/l] [ml/ml] Es Es Es Es Al Al Ac Ac W The standard Gbbs free energy f frmatn f methyl frmate n the lqud phase can nt be fund drectly n the lterature. It can be calculated frm the standard Gbbs free energy f frmatn f methyl frmate n the gas phase and the partal vapr pressure ([Stull69], p. 134). The needed partal vapur pressure f methyl frmate s cmputed usng the Antne equatn and the ceffcents whch can be fund n the lterature (e.g., [Jaku92] and [Lange99]). The Antne equatn and the relevant ceffcents are ntrduced n Appendx A. The calculated value f the standard Gbbs free energy f frmatn f methyl frmate n the lqud phase s shwn n Table 3.3. Usng Eqs. (2.90) and (2.59) and the values frm [CRC05] and [Stull69] gven n Tables 3.2 and 3.3, the standard reactn enthalpes and the standard Gbbs free energes f hydrlyss f the fur esters n the lqud phase were respectvely calculated and are shwn

53 44 Chapter 3 Mdel Reactns, Catalysts and Adsrbents n Table 3.4. Fr ethyl frmate, the enthalpy values f frmatn n the lqud phase fund n tw varus surces are sgnfcantly dfferent (see Table 3.2). Therefre, the standard reactn enthalpy f the hydrlyss f methyl frmate calculated usng the values frm these tw surces are als sgnfcantly dfferent. Partcularly, t wll be kj/ml f the value frm [Stull69] s used and kj/ml f the value frm [Hne74] s used. In fact, the hydrlyss f ethyl frmate s endthermal, thus the value frm [Hne74] s mre relable and used n ths wrk (Table 3.4). Table 3.2. Standard enthalpes f frmatn f the cmpunds nvlved t the nvestgated reactns frm several dfferent surces. Δ H f,, T = 25 C [kj/ml] Cmpund [CRC05] [Stull69] [Perry99] [Hne74] Es 11 (lqud) Es 11 (gas) Es 12 (lqud) Es 12 (gas) Es 21 (lqud) Es 21 (gas) Es 22 (lqud) Es 22 (gas) Al 1 (lqud) Al 1 (gas) Al 2 (lqud) Al 2 (gas) Ac 1 (lqud) Ac 1 (gas) Ac 2 (lqud) Ac 2 (gas) W (lqud) W (gas)

54 3.1 Mdel Reactns 45 Table 3.3. Standard Gbbs free energes f frmatn f the cmpunds nvlved t the nvestgated reactns frm several dfferent surces. Δ G f,, T = 25 C [kj/ml] Cmpund [CRC05] [Stull69] [Perry99] Calculated Es 11 (lqud) Es 11 (gas) Es 12 (lqud) Es 12 (gas) Es 21 (lqud) Es 21 (gas) Es 22 (lqud) Es 22 (gas) Al 1 (lqud) Al 1 (gas) Al 2 (lqud) Al 2 (gas) Ac 1 (lqud) Ac 1 (gas) Ac 2 (lqud) Ac 2 (gas) W (lqud) W (gas) Table 3.4. Standard enthalpes Δ H r and standard Gbbs free energes Δ G r f hydrlyss f the fur esters n the lqud phase frm dfferent surces. T = 25 C. Δ H r [kj/ml] Δ G r [kj/ml] Reactant Eq. (2.90) Lterature Eq. (2.59) Es [Reut89] Es [Sng98] * Es Es [Yu04] * *) Esterfcatn reactns nvestgated.

55 46 Chapter 3 Mdel Reactns, Catalysts and Adsrbents UNIQUAC Parameters In Sectn 2.4 the UNIQUAC mdel, whch s used n ths wrk t calculate the actvty ceffcents n the lqud phase, has been ntrduced. The values f pure-cmpnent and nteractn parameters used n the UNIQUAC mdel fr the relevant cmpnents were fund n the lterature [Gmeh02] and are lsted Tables 3.5 and 3.6. Table 3.5. Values f UNIQUAC pure-cmpnent parameters [Gmeh02], Eqs. ( ). N. Cmpnent u r u q 1 Es Es Es Es Al Al Ac Ac W Table 3.6. Values f UNIQUAC bnary parameters u a j, u a j [Gmeh02], Eqs. ( ). Es 11 Es 12 Es 21 Es 22 Al 1 Al 2 Ac 1 Ac 2 W Es * * * * Es Es 21 * * * * Es 22 * * Al * Al * Ac * * * * Ac 2 * * W * * *) Mssng data.

56 3.1 Mdel Reactns 47 Acd Base Equlbrum As dscussed abve, acds and bases can accelerate the hydrlyss f esters. Thus, the H + n dsscated frm acds and alchls whch are the prducts f the hydrlyss prcess shuld be cnsdered. The catalyss f ths knd f H + n the hydrlyss prcess s knwn as autcatalyss. Table 3.7 lsts the dsscatn (nzatn) cnstants f frmc acd, acetc acd, methanl, ethanl and water. All data apply t dlute aqueus slutns and are presented as values f pk Ac, whch s defned as the negatve f the lgarthm f the equlbrum cnstant K Ac fr the fllwng dsscatn reactns: HCOOH HCOO - + H + CH 3 COOH CH 3 COO - + H + CH 3 OH CH 3 O - + H + C 2 H 5 OH C 2 H 5 O - + H + H 2 O OH - + H + (3.5) (3.6) (3.7) (3.8) (3.9) Table 3.7. Dsscatn cnstants (pk ac values) f several nvestgated cmpunds [Eqs. ( )] at 25 C frm [CRC05]. Cmpund Temperature [ C] pk Ac [-] Ac Ac Al Al W The pk Ac values n Table 3.7 shw that frmc acd and acetc acd are weak acds. Frmc acd s the strngest unsubsttuted fatty acd. Its acdty s abut ten tmes lager than that f acetc acd. The acdc strengths f methanl and ethanl are almst the same and extremely small Chemcal Reactn Equlbra Applyng Eqs. (2.67) and (2.62) presented earler, the equlbrum cnstants f hydrlyss f the fur esters n the lqud phase can be expressed as shwn belw Eqs. (3.10) and (3.11) fr the deal and nn-deal lqud mxture, respectvely. In these expressns, Es j, Al, and Ac j are smply expressed as Es, Al, and Ac.

57 48 Chapter 3 Mdel Reactns, Catalysts and Adsrbents r c c Al Ac K c = (3.10) cescw a a Al Ac K a = (3.11) aesaw If the cncentratn f the ester s small, then durng the reactn the cncentratn f water wll be reasnably cnstant near that f pure water (55 ml/l). The rate f reactn can then be expressed n terms f vlumetrc cncentratns as fllws: = md c AlcAc r k c 1 Es (3.12) md Kc Therefre, n can ntrduce a mdfed equlbrum cnstant smetmes used n the lterature: c c md Al Ac K c = = ces K c c W (3.13) If the standard Gbbs free energes f reactn are knwn, the reactn equlbrum cnstants at 25 C can be cmputed as shwn earler n Eq. (2.64). Wth the values f the standard Gbbs free energes f reactn Δ G r shwn n Table 3.4, the thermdynamc reactn equlbrum cnstants f the fur ester hydrlyss reactns n the lqud phase at the standard temperature (25 C) were calculated usng Eq. (2.64). The reactn equlbrum cnstants at dfferent temperatures were estmated usng the ntegrated frm f the van t Hff equatn [Eq. (2.99)]. The btaned results are shwn n Table 3.8. Besde the calculatn frm the thermdynamc data, the reactn equlbrum cnstants can als be expermentally determned. The chemcal equlbra f hydrlyss r synthess f the fur esters have been studed and reprted n the lterature (e.g., [Schu39], [Weth74], [Falk99], [Du99], [Hwa04] and [Stye06]). The chemcal equlbrum f the methyl frmate hydrlyss was expermentally analysed n the wrk f Schultz [Schu39]. It was fund that the reactn equlbrum cnstant fr the methyl frmate hydrlyss depends n the water/ester rat. Wth a water/methyl frmate mlar rat f 1, the reactn equlbrum cnstant s 0.14, but wth a mlar rat f 15, t s 0.24.

58 3.1 Mdel Reactns 49 Table 3.8. Reactn equlbrum cnstants f hydrlyss f the fur esters n the lqud phase at the standard temperature (25 C) calculated frm the values f the standard Gbbs free energes f reactn Δ G r [Eq. (2.64)], and at ther temperatures estmated usng the ntegrated frm f the van t Hff equatn [Eq. (2.99)]. K a [Eq. (2.64)] Reactant 25 C 35 C 45 C 55 C Es Es Es Es In the wrk f Wetherld [Weth74], the chemcal equlbrum f the methyl frmate hydrlyss wth varus cncentratns f hydrchlrc acd at the temperature range f 22 t 24 C was expermentally nvestgated. In hs wrk, the values f the reactn md equlbrum cnstant f the methyl frmate hydrlyss were gven as values f K c [Eq. (3.13)]. T be able t cmpare t the ther values gven by ther wrks, thse values frm [Weth74] were cnverted t K c and are lsted n Table 3.9. Table 3.9. Equlbrum cnstants K c and [Weth74]. c HCl [ml/l] K c [Eq. (3.10)] [-] md K c f the methyl frmate hydrlyss frm md K c [Eq. (3.13)] [ml/l] Falk et al. (1999) als estmated the reactn equlbrum cnstant f the methyl frmate hydrlyss at 25 C frm the equlbrum cmpstn. A value f K c = 0.12 was btaned n relatvely gd agreement wth the value gven by Wetherld et al. (1974). Fr the methyl acetate hydrlyss, the equlbrum cnstant, K c, value range f was estmated by Du et al. (1999). In the ther wrk, Hwale et al. (2004) fund the value f K c between 0.14 and 0.2. Stye (2006) shwed the reactn equlbrum cnstant f the ethyl acetate esterfcatn at 40 C t be It can be cnverted t the equlbrum cnstant f the reverse reactn,

59 50 Chapter 3 Mdel Reactns, Catalysts and Adsrbents ethyl acetate hydrlyss, as defned K hydrlyss = 1/K esterfcatn. Thus, the equlbrum cnstant f ethyl acetate hydrlyss K c at 40 C s The data avalable n the lterature are stll nt fully satsfyng. It s ne f purpses f ths wrk t enlarge the regardng data set. 3.2 Catalysts and Adsrbents As dscussed earler, the hydrlyss f esters s slw at neutral ph, but accelerated at acdc ph. Therefre, acds can catalyze the ester hydrlyss reactn. The catalyst f the reactn can be a mneral acd (e.g., HCl, H 2 SO 4, and HNO 3 ) n the lqud frm. Lqud acds are rather rarely used n practce, snce the separatn f acds frm the mxture after the reactn s cstly. An alternatve that can be effcently utlzed s the applcatn f hetergeneus catalyss by an acd n the sld frm. Ths s a catn-exchange resn. Typcal representatves f ths resn grup are cmmercally avalable catn-exchange resns that are ffered by, fr example, Dw Chemcal Cmpany (Dwex), Bayer (Lewatt), Rhm and Haas (Amberlyst), Degussa (Delxan). These resns have been ften used by many researchers as a catalysts and adsrbents (e.g., [Mazz79a-b], [Pöpk00], [Falk02], [Lde03] and [San04]). In ths wrk, tw batches f the strngly acdc catn-exchange resn Dwex 50W-X8 (Dw Chemcal Cmpany) were manly used. Ths resn s based n a mcrprus styrene-dvnylbenzene cplymer functnalzed by the sulphurc acd type (SO 3 H). It acts as bth adsrbent and catalyst. The dfference between the tw batches was essentally the range f partcle szes. The catalyst wth the smaller partcle sze (Cat1) was already used extensvely n ther nvestgatns [Falk99, Falk02]. The secnd (Cat2) was purchased prr t the study dscussed here. Several physcal and chemcal prpertes f the catalysts are lsted n Table In addtn, n sme experments a mneral acd hydrchlrc acd was als used as a hmgeneus catalyst.

60 3.3 Summary and Outlne f Expermental Prgram 51 Table Physcal and chemcal prpertes f the tw catalysts. Catalyst characterstc Cat1 Cat2 Partcle sze, μm Type Dwex 50W-X8 Crss-lnk densty, wt-% 8.0 Actve grup sulfnc acd Matrx styrene-dvnylbenzene Inc frm H + Bulk densty, kg/m Feature ld (already 5 years n use) Newly acqured 3.3 Summary and Outlne f Expermental Prgram There are exstng data n the lterature regardng the fur hydrlyss reactns cnsdered. Hwever, there are several ncnsstences and mprtant data are mssng. Wth the expermental nvestgatns perfrmed durng ths wrk, new data shuld be acqured t enlarge the database related t these hydrlyss reactns. Tward that end, n partcular knetc parameters f the fur hydrlyss reactns n the lqud and sld phases shuld be estmated. The phase equlbra f the relevant cmpnents n the lqud resn system, and the chemcal equlbra f the hydrlyss f the fur esters shuld als be examned. In rder t acheve these gals, expermental studes perfrmed n a reactn calrmeter are prpsed. Frm these calrmetrc experments, the heat flws due t reactn and, therefre, the reactn rates and enthalpes can be determned. In parallel, several ther set ups as a cnventnal batch reactr and a equlbratn equpment shuld als be used t cllect mre data necessary. A descrptn f the equpments used and the expermental prcedures s gven n Chapter 5. Befre, because calrmetry s used ntensvely, n the cmng chapter bascs f calrmetrc technques are ntrduced (Chapter 4).

61 52 Chapter 3 Mdel Reactns, Catalysts and Adsrbents

62 C H A P T E R 4 Calrmetrc Technques In rder t acheve the gals f the wrk, several expermental methds were appled. In partcular, thermdynamc and knetc data were cllected by perfrmng experments n a reactn calrmeter. Ths chapter gves a basc descrptn f the calrmetrc technques. The partcular reactn calrmeter and ther equpments used n ths wrk tgether wth prcedures t cllect the data are explaned n the next chapter. Ths chapter als ntrduces the mdels descrbng the reactn calrmeter appled n ths study. 4.1 Reactn Calrmetry Reactn calrmetry s a sutable tl fr the purpse f knetc and thermdynamc screenng n early stages f prcess develpment. A revew n the prncples and the develpment f dfferent types f reactn calrmeters s presented by [Beck68], [Karl87a], [Land96] and [Regen97]. A cmprehensve vervew n dfferent calrmetrc prncples and ther applcatn n research and cmmercal devces s gven by [Pastré00]. A rather general vervew abut calrmetry s gven by [Hemm84] and [Günth06]. A unque technque fr the smultaneus determnatn f knetc and thermdynamc parameters s calrmetry [LeBl96]. Calrmetry, n the bradest sense, means the quanttatve measurement f energy exchanged n the frm f heat durng a reactn f any type. By cntrast, thermal analyss s cncerned nly wth the measurement and recrdng f temperature-nduced changes r temperature dfferences. Snce almst chemcal reactns and many physcal changes (e.g., defrmatn, phase transfrmatns) are asscated wth the uptake r release f heat, the quanttatve nvestgatn f heat 53

63 54 Chapter 4 Calrmetrc Technques exchange s a relatvely smple and unversal methd fr characterzng partcular prcesses bth n an verall sense and wth respect t tme [Günth06]. Nevertheless, nly n recent decades has calrmetry emerged frm the labratres f a few thermdynamcsts and specalsts t becme a wdespread, cnvenent analytcal methd. The develpment f cmmercal calrmeters snce the 1950s has led t rapd dssemnatn and applcatn f the methd even beynd the bunds f unverstes. Reactn calrmetry was wdely appled t nvestgate thermdynamc and knetc parameters f chemcal reactns [Beck68], [Regen83], [Land94], [LeBl96], [Semp98], [Pastré00], [Pastré01], [Ball00], [Ball02], [Ubrch99], [Dyer02], and [Stapp02]. Hwever, fr cmplex reactn systems the heat sgnal f chemcal reactns tself s nt enugh t pen a way t knetc parameters. Then ther analytcal technques are requred Methds f Calrmetry As nted abve, heat that s released r cnsumed by a prcess cannt be measured drectly. Unlke materal quanttes such as amunt f substance, whch can be determned wth a balance, r the vlume f a lqud, whch can be establshed wth a lter measure, the quantty f heat must be measured ndrectly thrugh ts effect n a substance whse temperature ether rases r lwers. The fundamental equatn requred t analyze experments s the relatnshp between heat exchanged and a crrespndng temperature change: ( T ) T Δ Q = cp Δ (4.1) where Δ Q s the exchanged heat, Δ T s the bserved temperature change, and c p (T) s an verall heat capacty. Fr temperature changes that are nt t large, the heat effect s drectly prprtnal. Hwever, f the temperature change exceeds a few Kelvn, knwledge f the temperature functn f the partcular heat capacty n questn s requred n rder t quantfy the heat effect n the bass f a measured temperature dfference. The relatnshp gven abve s drectly appled n the standard calrmetrc methds fr determnng the heats f certan prcesses: A) ether temperature s held cnstant by apprprate cmpensatn fr the heat effect, and the requred cmpensatn pwer s

64 4.1 Reactn Calrmetry 55 measured, r B) a temperature change s measured and used t calculate the crrespndng value fr the exchanged heat [Günth06]. A) Cmpensatn fr Thermal Effects In the frst methd f heat measurement, temperature changes n the calrmeter cntents are avded by supplyng r wthdrawng heat n the amunt (but ppste n sgn) asscated wth the prcess under nvestgatn. Electrcal energy s used t prvde ths cmpensatn, ether by ntrductn n the frm f Jule heatng r dsspatn thrugh the Pelter effect [Nlss82]. A cmbnatn apprach s als pssble, wth an apprprate cnstant level f clng and smultaneus cntrlled electrcal heatng. The requred amunt f cmpensatn pwer can be prvded wth a hgh degree f precsn. The methd f cmpensatn s advantageus, snce t permts measurements t be carred ut under quas-sthermal cndtns, thereby avdng heat lss frm the calrmeter t the surrundngs by heat transprt prcesses. Furthermre, there s n need fr calbrated temperature measurements. B) Measurement f a Temperature Dfference In ths alternatve methd f heat measurement, whch s ndrect, a measured temperature dfference s used t calculate the amunt f heat exchanged. A dstnctn can be made between tempral and spatal temperature-dfference measurements. In tempral temperature-dfference measurement, the temperature f the calrmeter cntent s measured befre and after a prcess, and a crrespndng heat s calculated n the bass f equatn (4.1). In the spatal methd, a temperature dfference between tw pnts wthn the calrmeter (r between the calrmeter cntent and the surrundngs) s the quantty f nterest. In ths case, the bass fr nterpretatn s frm Furer's law f heat cnductn: ( T ) A ΔT Q & = U (4.2) W W where Q & s the heat flw rate, U W (T) s the ceffcent f thermal cnductvty, A W s the crss-sectn area, and ΔT s agan the temperature dfference. Ths expressn shws that the heat flw rate thrugh a heat-cnductng materal s prprtnal t the crrespndng temperature dfference. If the temperature dfference s recrded as a functn f tme, then fr a gven thermal cnductvty ne acqures a

65 56 Chapter 4 Calrmetrc Technques measure f the crrespndng heat flw rate, whch can be ntegrated t gve a ttal amunt f heat related t the prcess bserved. The technque tself s very smple, but the result wll be crrect nly f the measured temperature dfference accurately reflects the ttal heat flw rate and n heat s lst thrugh undetected heat leaks Basc Reactn Calrmeter Types Dfferng wth respect t measurng prncple, mde f peratn, and general cnstructn, there are dfferent calrmetrc technques, such as DSC (Dfferental Scannng Calrmetry), Mcr Calrmetry, Bmb Calrmetry, Slutn Calrmetry, ARC (Acceleratng Rate Calrmetry), and Reactn Calrmetry [Hemm84]. As n reactn calrmetry the system s typcally nvestgated under cndtns that are smlar t the nrmal prductn reactr, t s the apprprate technque fr the purpse f reactn ptmzatn. Ths sectn wll nt dscuss thermal analyss devces such as DSC (Dfferental Scannng Calrmeter) r ther mcr calrmetrc devces, but wll fcus n reactn calrmeter. Mst f the exstng reactn calrmeters use a duble-jacketed vessel as a reactr. A lqud used as heat transfer agent s pumped thrugh the duble jacket f the reactr n a clsed crculatn system. Ths keeps the temperature f the reactr cntents, T r, at the set temperature (see Fgure 2.2). Such devces can be classfed accrdng t ther measurement and cntrl prncples nt three categres: I) Heat-Flw, II) Pwer- Cmpensatn, and III) Heat-Balance reactn calrmeters [Land96]. They are brefly descrbed n the fllwng subsectns. I) Heat-Flw Reactn Calrmeter The temperature f the reactr cntents (T r ) s cntrlled by varyng the temperature f the heat exchange lqud (T j ). The heat flw thrugh the reactr wall (Q & ) s determned by measurng the dfference between the temperature f the reactr cntents and the jacket temperature. In rder t cnvert ths temperature sgnal nt a heat-flw sgnal, a heattransfer ceffcent has t be determned usng a calbratn heater. T allw a fast cntrl f the T r, the flw rate f the heat exchange lqud thrugh the jacket shuld be hgh. Mst f the cmmercally used reactn calrmeters are based n the Heat-Flw prncple, such as the RC1 frm Mettler Tled used n ths wrk (see Sectn 5.1.1). A detaled calculatn f the cmplete heat-flw balance s gven n Sectn

66 4.1 Reactn Calrmetry 57 II) Pwer-Cmpensatn Reactn Calrmeter The temperature f the reactr cntents (T r ) s cntrlled by varyng the pwer f a cmpensatn heater nserted drectly nt the reactr cntents. As wth an electrcal heater, clng s nt pssble, the cmpensatn heater always mantans a cnstant temperature dfference between the reactr jacket and the reactr cntents. Thus clng s acheved by reducng the pwer f the cmpensatn heater. The heat flw frm the reactr cntents thrugh the wall t the jacket s typcally nt determned because the reactn pwer s drectly vsble n the pwer cnsumptn f the cmpensatn heater. The jacket temperature (T j ) s kept cnstant by an external crystat. The Pwer-Cmpensatn prncple was frst mplemented by Andersen ([Ander66] and [Ander69]) and was further develped by [Köhl72], [Hent79] and [Schld81]. [Pll01] and [Pastré01] reprted a small scale Pwer-Cmpensatn calrmeter. A cmmercal Pwer-Cmpensatn calrmeter s the AutMate [Smm00] and the Smular (cmbned wth Heat Flw [Sngh97]) frm [HEL]. III) Heat-Balance Reactn Calrmeter The temperature f the reactr cntents (T r ) s cntrlled by varyng the temperature f the heat exchange lqud (Tj). The heat flw thrugh the reactr wall (Q & ) s determned by measurng the dfference between the jacket nlet (T j, IN) and utlet temperature (T j, OUT ) and the mass flw f the heat exchange lqud. Tgether wth the heat capacty f the heat exchange lqud, the heat-flw sgnal s drectly determned wthut calbratn. The Heat- Balance prncple was frst mplemented by [Meek68]. Cmmercal versns are the RM200 frm [Chems], SysCal 2000 Seres frm [Systag] and the ZM-1 frm [Zetn] Operatn Mdes Dependng n hw calrmeters are perated, dfferent peratn mdes can be dstngushed: sthermal, sperblc, adabatc and temperature prgrammed. As shwn n Table 4.1 and prevus dscussn (Sectn 4.1.1), the sthermal peratn mde s suppsed t be the easest n applcatn because n heat accumulatn by the reactr cntents has t be cnsdered. Therefre, n temperature-dependent heat capactes such as a functn f T r f the reactn mxture as well as f the reactr nserts (e.g., strrer, sensrs, baffles ) are requred. Hwever, n realty due t the nn-dealtes f the cntrl crcuts f the calrmeters and the prncples f heat flw, the reactn temperature cannt be cntrlled strctly sthermal. Because mst chemcal and physcal changes takng place

67 58 Chapter 4 Calrmetrc Technques durng a reactn step depend n the temperature, the evaluatn f the measured data wll be smpler f sthermal cndtns are fulflled [Karl87a, Schle97]. Table 4.1 Dfferent mdes f peratn f a reactn calrmeter. Operatn mde Isthermal Isperblc Adabatc Temperature prgrammed Prncple Cnstant T r by varyng T j r usng an electrc cmpensatn heater Cnstant jacket temperature T j Cntnuus readjustment f T j t be equal t T r Lnear heatng t a fnal temperature In the present wrk, calrmetrc measurements were carred ut under sthermal cndtns Cntrbutns t Heat Balance Fr the fllwng dscussns, deal sthermal cntrllng f the reactn temperature T r wll be assumed. Therefre, n Fgure 4.2 n heat accumulatn terms f the reactn mxture and the reactr nserts are ndcated. Hwever, ths assumptn des nt hld fr all applcatns f calrmetry. The task f a reactn calrmeter s t measure the ttal heat prductn r cnsumptn Q & tt durng a chemcal reactn. Generally, a heat effect due t any knd f physcal prcess ccurrng n the vessel s ncluded. Fr the sthermal cndtn, the ttal heat Q & tt s the heat flw thrugh the reactr wall Q & wall. Ths ttal heat flw Q & tt Q& wall can be expressed fr steady state cndtns as fllws: Q & Q& = Q& + Q& + Q& + Q& Q& Q& + Q& +... (4.3) tt wall chem mx phase str ds lss c where Q & chem s the heat flw due t chemcal reactns, Q & mx s the heat flw ccurrng due t nn deal mxng f dfferent fluds, Q & phase s the heat flw due t pssble phase change prcesses, Q & str s the heat flw resultng related t energy nput by the strrer, Q & ds s the heat flw caused by the dsng f reactants, Q & lss s the heat flw lst t the surrundngs, and Q & c s the heat flw frm the calbratn heater. Further pssble nfluences whch can

68 4.1 Reactn Calrmetry 59 als cntrbute the effect t the ttal heat flw (e.g., radatn, frctn, ) are nt cnsdered. Fr a sngle reactn, the mst relevant reactn heat flw can be expressed as fllws: Q & = V rδh (4.4) chem R r where V R s the vlume f the reactn mxture, r s the reactn rate, and reactn enthalpy. Δ H r s the Q & str Q & c Q & lss Q & ds Q & chem. Q & mx Q & phase Fgure 4.2. Man heat flws that have t be cnsdered n a reactn calrmeter runnng at sthermal cndtns. The heat evlved by the strrer Q & str can be descrbed by [Zgg93]: Q & = Neρ n d (4.5) str r 3 S 5 R where Ne s the Newtn number, ρ r s the densty f the reactn mxture, n S s the reversns per secnd f the strrer, and d R s the dameter f the strrer.