Kinetic Modeling of Homogeneous Catalytic Processes R.V

Catalysis Today 66 (2001) 371–380

Kinetic modeling of homogeneous catalytic processes R.V. Chaudhari∗, A. Seayad, S. Jayasree Homogeneous Catalysis Division, National Chemical Laboratory, Dr. Homi Bhabha Road, Pune 411 008, India

Abstract Homogeneous catalysis by soluble metal complexes is gaining considerable attention due to their unique applications and features like high activity and selectivity. In this paper, a brief review of kinetic modeling in homogeneous catalysis has been presented. Approaches using empirical as well as molecular level rate models have been discussed. Special features relevant to asymmetric catalysis and multiple rate controlling steps have also been addressed. A case study on kinetics of carbonylation of 1-(4-iso-butylphenyl)ethanol using a homogeneous palladium catalyst has been discussed. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Homogeneous catalysis; Kinetics; Rate equation; Hydrogenation; Hydroformylation; Carbonylation; 1-(4-iso-Butylphenyl)ethanol; Ibuprofen

1. Introduction emerging applications in fine chemicals and pharma- ceuticals are particularly promising due to increased Kinetic modeling of catalytic reactions is one of the competition along with a need for selective, effi- key aspects investigated in order to understand the cient and environmentally acceptable processes. An- rate behavior of catalytic reactions [1–10] as well as other important feature is their high selectivity for reaction mechanism [5–7]. A knowledge of intrinsic the synthesis of biologically active molecules with reaction kinetics (a scale independent property) and asymmetric centers [16]. Since, most of the new development of rate equations is most essential as a drug molecules are expected to be optically active part of reaction engineering studies aimed to evolve isomers, homogeneous catalysis has a bright future strategy for reactor design. While, the subject of kine- in pharmaceutical industry. Homogeneous catalysis tic modeling has been well investigated for heteroge- has so far been investigated with the perspective of neous catalysis [8–10], only limited information is reaction mechanism, in which the role of catalysts, available on this aspect in homogeneous catalysis ligands, co-catalysts and nature of catalytically active [1–7]. species have been studied [11–15]. While, a num- Homogeneous catalysts consisting of soluble tran- ber of examples illustrate systematic studies of in sition metal complexes have several important ap- situ spectroscopic analysis of catalytic reaction in- plications in chemical industry for both bulk com- termediates leading to description of catalytic cycles modity as well as specialty products [11–15]. Some on a molecular level [17–19], correlation of these important examples are listed in Table 1. The newly with kinetic data and development of rate equations has received limited attention. In this paper, the cur- ∗ Corresponding author. Tel.: +91-20-589-3163; rent state of development on kinetic modeling in fax: +91-20-589-3260. homogeneous catalysis has been presented with a E-mail address: [email protected] (R.V. Chaudhari). specific case study on kinetics of carbonylation of

homogeneous catalytic reactions is complex even if Nomenclature only a single reaction is involved, since the catalytic Bl concentration of IBPE in the liquid cycle consists of several stoichiometric reactions. phase at time t When a co-catalyst or a promoter is used, additional B0 initial concentration of IBPE in steps are associated with the catalytic cycle either to the liquid phase form the active catalytic species around which the Dl concentration of IBS in the liquid principal catalytic cycle operates or to form an active phase at time t substrate. The reactions may also involve one or more El concentration of IBPCl in the liquid gas phase reactants or biphasic systems with catalyst phase at time t and reactants/products present in different phases. ki rate constants These multi-phase catalytic gas–liquid reactions need min k−1 mac dissociation rate constant for the consideration of interphase mass transfer steps in minor diastereomer addition to the overall catalytic reactions. Thus, ho- maj k1 mac binding rate constant for the mogeneous catalytic reactions can be categorized as major diastereomer follows: min k1 mac binding rate constant for the minor diastereomer 1. Single or multi-step reactions with only one cata- maj lytic component: the examples of this class are k2 rate constant for the H2 addition step forthe major diastereomer found in hydrogenation of olefins using RhCl- min (PPh3)3, hydroformylation of olefins using k2 rate constant for the H2 addition step for the minor diastereomer HRh(CO)(PPh3)3, oligomerization of ethylene Ki equilibrium or empirical constants using Ni complex catalyst, etc. maj 2. Single or multi-step reactions with multi-component K1 mac binding equilibrium constant for the major diastereomer catalyst systems (catalyst/co-catalyst/promoter): min the examples of this category include the Wacker K1 mac binding equilibrium constant for the minor diastereomer process for oxidation of ethylene to acetaldehyde m, n, p reaction orders as given in Eq. (6) using PdCl2/CuCl2 and molecular oxygen. During conversion of ethylene to acetaldehyde, Pd2+ is PCO partial pressure of CO 0 P partial pressure of C H reduced to Pd and the co-catalyst CuCl2 has a C2H4 2 4 role to re-oxidize Pd0 to the active Pd2+ [20]. Also Pl concentration of carbonylated products (IBN + IPPA) in the the molecular oxygen has a role to re-oxidize the liquid phase at time t reduced co-catalyst and hence is only indirectly involved in catalysis. The re-oxidation is required ri rate of the reaction to be faster than main oxidation reaction for the riso rate of formation of the iso-isomer catalytic cycle to operate efficiently. Another im- rn rate of formation of the n-isomer portant example is the carbonylation of methanol rR-product rate of formation of the R-product to acetic acid using Rh complex with HI as a pro- rS-product rate of formation of the S-product [X] concentration of the species X moter. In this case, the promoter HI converts the substrate methanol to CH3I, an active substrate 1-(4-iso-butylphenyl)ethanol (IBPE) using homo- for carbonylation and the catalytic reaction pro- geneous Pd complex catalyst. ceeds only when Rh complex with HI promoter is used. Several examples with even more complex catalysis are known in homogeneous catalysis, a 2. Kinetic models in homogeneous catalysis common feature in which the overall reaction is catalytic with regeneration of principle catalyst, As a first step in kinetic modeling, it is important to co-catalyst as well as the promoter (as applicable). consider the reaction pathways and catalytic reaction 3. Reactions involving two or more gas phase mechanism for any given system. The mechanism of reactants with catalyst in solution with one or R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380 373

Table 1 Applications of homogeneous catalysis in industry [11–15] No. Process Catalyst Company

1 Oxidation of ethylene to acetaldehyde PdCl2/CuCl2 Wacker–Werke 2 Hydrocyanation of butadiene to adipic acid Ni complex Du Pont 3 Asymmetric hydrogenation of acetamido cinnamic acid [Rh(diene)(solvent)]+/dipamp Monsanto (3-methoxy-4-acetoxy derivative) (l-dopa process) 4 Hydroformylation of propene to butyraldehyde NaCo(CO)4 BASF HCo(CO)3PBu3 Shell HRh(CO)(PPh3)3 Union Carbide Rh/TPPTS Ruhrchemie–Rhone–Poulenc 5 Hydroformylation of diacetoxybutene to 1-methyl- HRh(CO)(PPh3)3 Hoffmann–La Roche 4-acetoxy butanal (vitamin A intermediate) Rh catalyst BASF 6 Carbonylation of methanol to acetic acid Rh/iodide Monsanto Co2(CO)8 BASF Ir/iodide BP Chemicals 7 Carbonylation of methyl acetate to acetic anhydride Rh/MeI Halcon Rh/MeI Eastman Chemical 8 Carbonylation of ethylene to propionic acid Ni(OCOC2H5)2 BASF 9 Carbonylation of butadiene to adipic acid Co2(CO)8/pyridine BASF 10 Carbonylation of IBPE to ibuprofen PdCl2(PPh3)2/HCl Hoechst–Celanese 11 Carbonylation of propyne to MMA Pd(OAc)2/2-PyPPh2 Shell 12 Oxidative carbonylation of methanol to dimethyl carbonate PdCl2–CuCl2 Assoreni 13 Co-polymerization of CO and ethylene to polyketones Pd(OAc)2/dppp/TsOH Shell 14 Amidocarbonylation of benzaldehyde to phenylglycene PdBr2(PPh3)2 15 Hydroaminomethylation of oleﬁns to primary amines [Rh(COD)Cl]2 16 Heck arylation of ethylene with 2-bromo-6-methoxy Palladacycles Hoechst AG naphthalene

more catalyst components, the examples of which (e.g. based on Langmuir–Hinshelwood mechanism) are found in hydroformylation, oxidative carbony- is observed except that in homogeneous catalysis lation and copolymerization, etc. the mechanisms considered involve molecular level 4. Biphasic reactions with or without gas phase description of the catalytic intermediate species. For reactants and catalyst being soluble in one of the some cases, like hydroformylation, even though the phases, the examples of which are hydroformy- catalytic cycle is reasonably well established, the lation, carbonylation, hydrogenation, etc. using rate equations used are empirical due to complexities water soluble metal complex catalysts and phase such as substrate inhibition with CO and also olefins. transfer catalytic reactions. However, it would be more appropriate to develop rate equations based on a molecular level and corre- Due to the various complexities involved as indi- late the observed trends with the mechanism. Salient cated in the examples shown above, the kinetics of features of the kinetic studies for a few examples are such reactions are often represented by non-linear rate discussed below. equations, some purely empirical and some derived Hydrogenation of olefins using homogeneous catal- based on a mechanism. A summary of kinetic studies ysis is an excellent example to illustrate the molecular in homogeneous catalysis is presented in Table 2. It level approach to kinetic modeling as the mechanism can be noted that the mathematical forms of rate equa- of these reactions has been well established. Osborn tions used range from simple power law types to hy- et al. [21] studied kinetics of hydrogenation of cyclo- perbolic forms to those derived based on mechanisms hexene using RhCl(PPh3)3 catalyst and proposed a already established. In some cases, a close analogy rate equation assuming a reaction mechanism in which to the rate equations used in heterogeneous catalysis parallel steps to activate olefins and hydrogen are 374 R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380

Table 2 A summary of kinetic studies in homogenous catalysis No. Reaction Catalyst Rate equation

1 Carbonylation of methanol RhCl3/HI r = k[Rh][CH3I], zero order with CO and methanol k[catalyst]t [I]t [MeOH] RhCl3/HI [25] r = [water] + K1[CH3OH]t + K2[I]t [CH3COOH] k[CO][substrate] iso r = NiCl2/ -quinoline [26] 2 (1 + K1[CO])(1 + K2[substrate])(1 + K3[water])

2 Carbonylation of styrene PdCl2(PPh3)2 [27–32] See Eqs. (7)–(10) ( + K )2 r = kPCO 1 1[styrene] [catalyst][water] Pd(OAc)2/PPh3/TsOH [33] 2 (1 + K2PCO)(1 + K3[water]) kK1[H2][substrate][catalyst] 3 Hydrogenation of cyclohexene RhCl(PPh3)2 [21] r = 1 + K1[H2] + K2[substrate] r = kK1[H2][substrate][catalyst] 4 Hydrogenation of allyl alcohol RhCl(PPh3)3 [22] 2 1 + K1[substrate] + K1K2[substrate] + [PPh3]/K3 + 5 Asymmetric hydrogenation [Rh(dipamp)S2] [36] See Eqs. (1)–(5) of mac k[substrate][catalyst][H ] 6 Hydroformylation of propylene HCo(CO) [39] r = 2 4 [CO] 0.55 0.75 0.87 k[H2] [CO][catalyst] [substrate] rn = 7 Hydroformylation of propylene Co2(CO)8 [40] 2 (1 + K1[CO]) k 0.32 0.62 r = [H2] [CO][catalyst] [substrate] iso 2 (1 + K2[CO])

8 Hydroformylation of HRhCO(PPh3)3 [41–43] See Eq. (6) 1-hexene, allyl alcohol, vinyl acetate

9 Hydroformylation of HRhCO(PPh3)3 [44] See Eq. (7) 1-decene, styrene k (P / ) 1 C2H4 [PPh3] 10 Hydroformylation of ethylene Rh(acac)(CO)2/PPh3 [47] TOF = 1 + K1(PCO/[PPh3]) + K2([PPh3]/PCO) k r = [H2][CO][catalyst][substrate] 11 Hydroformylation of 1-octene [RhCl(1,5-COD)]2/TPPTS [51] 2 (1 + K1[CO]) (1 + K2[H2]) k[H ]0.48[catalyst]0.84[octene]0.5 p r = 2 12 Hydroformylation under HRh(CO)[ -CF3C6H4)3]3 [52] 2.2 1 + K1[CO] supercritical CO2 k[substrate][catalyst] 13 Oxidation of cyclohexane Mn(OAc)2 [34] r = K1 + K2[catalyst] k[PhI][oleﬁn]2[Me N][catalyst] 14 Heck coupling of Pd(OAc) /PPh [35] r = 3 2 3 ( + K 2)( + K 4)( + K )3 iodobenzene and 1 1[oleﬁn] 1 2[Me3N] 1 3[catalyst] × ( + K ) methyl acrylate 1 4[PPh3]

considered. Wadkar and Chaudhari [22] showed that alcohol using RuCl2(PPh3)3 catalyst have also been for substrates like allyl alcohol, substrate inhibition is reported and rate equations proposed [2,23,24]. observed and proposed a rate equation with modiﬁed A kinetic analysis of enantioselective hydrogenation reaction mechanism. Similar studies on hydrogena- of methyl-(Z)-␣-acetamidocinnamate (mac) has been tion of cyclohexene, maleic acid, acrylamide and allyl studied by Landis and Halpern [36] and rate equations R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380 375

min min were proposed considering a molecular level mech- k2 k1 [Rh][H2] rS = (4) -product maj min min anism to demonstrate the role of kinetics on enan- K1 (k−1 + k2 [H2]) tioselectivity. Their kinetic studies showed that the predominant stereo isomer (S)-N-acetylphenylalanine Case 3. Association of substrate (mac) as the rate- methyl ester was derived from the minor less stable determining step: + catalytic intermediate [Rh(dipamp)(mac)] by virtue maj min r = k1 [Rh]tot[mac] + k1 [Rh]tot[mac] (5) of its much higher reactivity towards H2. The enantioselectivity was found to decrease with increase in H2 Other important aspect of kinetics of asymmetric pressure. The observed variation in enantioselectivity catalysis concerning non-linear effects [37] on enan- with H2 pressure has been explained considering dif- tioselectivity occurring due to the association of chiral ferent rate-determining steps at lower and higher H2 ligands inside or outside the catalytic cycle and con- pressures. At lower H2 pressures, oxidative addition version dependent [38] enantioselectivity have also of H2 is the rate-determining step for both the isomers. been addressed. With increasing H2 pressure, oxidative addition of H2 Kinetic modeling of hydroformylation of propy- competes with the dissociation of substrate, mac. Since lene and cyclohexene was studied by Natta et al. [39] min maj k2 k2 , such competition starts at a lower pres- using co-carbonyl catalyst. The reaction was found to sure for the minor diastereomer than for the major di- be first order with olefin, catalyst and hydrogen but astereomer. In this regime, the rate-determining step negative order dependent with CO. Gholap et al. [40] for major diastereomer is still the H2 addition step, reported rate equations to represent kinetics of forma- while rate of minor diastereomer pathway is given by a tion of both n- and iso-butyraldehyde in co-carbonyl steady state rate equation. Thus, the rate corresponding catalyzed hydroformylation of propylene. Deshpande to the major diastereomer pathway, which contributed and Chaudhari [41–43] investigated detailed kinetics only a small fraction of the total product remains first of hydroformylation of 1-hexene, allyl alcohol and order in H2 pressure and the rate of minor diastere- vinyl acetate using HRh(CO)(PPh3)3 catalyst and omer pathway becomes independent of the H2 pres- proposed the following form of rate equations: sure. Hence, as the H pressure is increased, the total 2 k m reaction rate is expected to level off and the enantios- r = [H2] [CO][catalyst][substrate] ( + K )n( + K )p (6) electivity to decrease. At higher H2 pressure, the ox- 1 1[substrate] 1 2[CO] idative addition step becomes faster than the substrate The important observations were a strong substrate binding steps and the reaction rate and enantioselec- inhibition with respect to CO and a mild substrate tivity are determined by the substrate (mac) associa- inhibition with respect to olefins and requirement of tion step and independent of H2 concentration. The a critical catalyst concentration. However, in all these rate equations proposed for the three cases are: cases, the rate models proposed were empirical in Case 1. Oxidative addition of H2 as the rate-deter- spite of a reasonably well-understood mechanism for mining step for both the stereo isomers: hydroformylation. In recent investigations, Divekar maj maj k2 K1 [H2][Rh]tot et al. [44] and Nair et al. [45] derived rate equa- rR = (1) -product maj min tions considering a molecular level approach based K1 + K1 on the mechanism proposed by Evans et al. [46] k minK min 2 1 [H2][Rh]tot for HRh(CO)(PPh3)3 catalyzed hydroformylation of rS = (2) -product maj min K1 + K1 1-decene and styrene, respectively. The rate model derived assuming oxidative addition of hydrogen to Case 2. Oxidative addition of H for R-isomer and a 2 Rh-acyl species as the rate-determining step was steady state rate equation for the S-isomer: K r = kK1 2[H2][CO][catalyst][substrate] 2 3 (7) 1 + K2[CO] + K1K2[CO][substrate] + K1K2K3[CO] [substrate] + K1K2K3K4[CO] [substrate] This model predicted the negative order dependence maj rR-product = k2 [Rh][H2] (3) with CO, a unique feature of kinetics of olefin hydro- 376 R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380

formylation. Kiss et al. [47] also reported a mecha- idated independently by characterization of catalytic nistic model for kinetics of ethylene hydroformylation intermediates using in situ IR and NMR techniques using Rh(acac)(CO)2/PPh3 catalyst with unusual ob- [17]. A detailed review on the history of kinetics and servations of ﬁrst order with ethylene at higher PPh3 mechanism of methanol carbonylation has been given concentration and zero order at lower PPh3 concen- by Maitlis [17], which is one of the best examples of tration. The complex kinetics and change in reaction kinetics and mechanism investigated with excellent orders have been explained as a result of shift in correlation of observed kinetics with mechanism. rate-determining step under different conditions. Another important example of kinetic modeling Kinetics of biphasic hydroformylation of 1-octene in homogeneous catalysis is the carbonylation of [48], ethylene [49] and styrene using water soluble styrene using Pd(OAc)2/PPh3/TsOH in methanol [33] Rh–TPPTS [50] catalyst has also been studied and rate wherein an empirical rate equation was found suitable equations proposed. In contrast to the earlier reports to explain the kinetic trends. The rate of carbonylation using homogeneous catalysts, in this case, substrate varied linearly with catalyst and was zero order with inhibition with CO was not observed. This is due to respect to styrene up to a certain concentration beyond the lower range of dissolved CO concentrations as a which an unusual trend of increase in reaction rate was result of lower solubility in aqueous catalyst phase. observed. Water also showed a remarkable promoting The effect of co-solvent on kinetics of biphasic hy- effect on reaction rate up to a certain concentration. droformylation of 1-octene has been reported by Pur- Similarly, a detailed kinetic analysis of hydrocar- wanto and Delmas [51] for a catalyst prepared from boxylation of styrene to 2- and 3-phenyl propionic a precursor [Rh(COD)Cl]2 and TPPTS ligand. Due to acids has been reported by Noskov and coworkers enhancement of solubility of CO in the presence of [27–32] using PdCl2(PPh3)2 as a catalyst. Kinetic the co-solvent, ethanol, a substrate inhibition with CO rate models were developed to explain the effect of was observed as expected. different parameters on the rates of formation of iso In a recent study, Palo and Erkey [52] reported as well as linear acids, which determine the regiose- kinetics of hydroformylation of 1-octene in supercrit- lectivity. The following rate equations were proposed ical CO2 with HRh(CO)[p-CF3C6H4)3]3 as a catalyst which explained the combined effects of PCO and ◦ at 50 C and 273 bar pressure. The reaction order was H2O on the formation of individual isomers based on found to be 0.5 with H2 and 1-octene, 0.84 with a molecular approach: catalyst and a negative order with CO. The catalyst [H2O][Pd]0 solubility in supercritical CO2 is reported to be higher rn = + K 2P / + K 2 than that in organic solvents and the critical catalyst 1 1[H2O] CO [HCl] 2[H2O] concentration was not observed like the conventional K4PCO × K3 + (8) homogeneous catalysts [41–43]. The main advantage 1 + K5PCO of supercritical CO2 claimed is the higher solubility of H2, CO and catalyst, but for hydroformylation, P 2 the higher CO concentration is not desirable due to r = [H2O] CO [Pd]0 iso + K 2P / + K 2 rate inhibition with CO and hence it is necessary to 1  1[H2O] CO [HCl] 2[H2O]  optimize the H2/CO ratio for achieving higher rates in supercritical medium.  K K K  ×  4 5 + 6[H2O]  Carbonylation of methanol using Rh, Ir and Ni   (9) 1 + K5PCO ([HCl] + K7[H2O]) complex catalysts has been studied by Roth et al. × (1 + K8[H2O]) [53] as well as by Chaudhari and coworkers [26,54] and rate equations were proposed (see Table 2). The where Ki are the constants and PCO is the effective kinetics observed was indeed very simple for Rh/HI CO pressure. Other parameters, which affected the catalyst with a zero order with methanol and CO and n/iso ratio, were the concentrations of styrene and ﬁrst order with Rh and HI. This correlates with the PPh3. The rate of formation of n-isomer was zero or- mechanism assuming oxidative addition of CH3ItoRh der with respect to styrene and more than zero in the complex as the rate-determining step, which was val- case of iso-isomer. An increase in concentration of R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380 377

PPh3 decreased rate of formation of the iso-isomer to cycle. Thus, a critical oxygen/oxidant concentration a greater extent than that of n-isomer. The above rate exists below which the catalytic cycle will fail to equations (Eqs. (8) and (9)) were modiﬁed (Eqs. (10) operate. A detailed analysis of this aspect has been and (11)) to explain these effects. given by Bhattacharya and Chaudhari [56] for the Wacker process. [H2O][Pd]0 rn = + K 2P / + K 2 1 1[H2O] CO [HCl] 2[PPh3][H2O] K4PCO 3. Carbonylation of IBPE using × K3 + (10) 1 + K5PCO PdCl2(PPh3)2/TsOH/LiCl catalyst

Carbonylation of IBPE represents an example of [H O]P 2[Pd] r = 2 CO 0 a homogeneous catalytic reaction involving single iso + K 2P / + K 2 1 1[H2O] CO [HCl] 2[PPh3][H2O] reaction but three catalyst components. As a result, the reaction mechanism and catalytic cycle also involve  K K K   4 5 6[H2O][styrene]  series of elementary reaction steps. Kinetic modeling ×  +  1+K5PCO ([HCl] + K7[PPh3][H2O]) of this industrially important reaction [57–59] has ×([styrene] + K8[H2O]) been presented here as a detailed case study. The re- (11) action involves three important steps: (i) formation of the active substrate 1-(4-iso-butylphenyl)ethyl chlo- Liquid phase oxidation is an important class of ride (IBPCl) through 4-iso-butylstyrene (IBS) as an homogeneous catalytic reactions and a review of ki- intermediate, (ii) conversion of PdCl2(PPh3)2 to the netic modeling of such systems has been presented by active Pd(0) species, and (iii) catalytic carbonylation Mills and Chaudhari [55]. In some cases, oxidation of IBPCl (the main catalytic cycle) as shown in Fig. 1. involves redox mechanism in which re-oxidation is Several experiments were carried out in which required to be faster than other steps in the catalytic concentration–time proﬁles were observed at

Fig. 1. Proposed mechanistic pathway for carbonylation of IBPE (B). 378 R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380

dP different concentrations of IBPE, water, PdCl2(PPh3)2, l = r7 = k7C7[H2O] (19) TsOH/LiCl, CO pressure and temperatures. The aver- dt age rate of carbonylation was found to vary with ﬁrst with initial conditions order dependence with concentration of water, of the order 0.8 with CO, 0.7 with IBPE and 0.43 with respect at t = 0,Bl = B0,Dl = El = Pl = 0, to catalyst concentration. Even though the empirical C = C and C = C = C = 0 (20) rate model predicted [60] the concentration–time data 1 0 4 5 7 well for certain conditions, a more appropriate method where k1, k2, k3, k4, k5, k6 and k7 represent the would be that considering a molecular level approach. rate constants, B0 the initial concentration of IBPE, Since, the average rate of carbonylation shows depen- Bl, Dl, El and Pl the concentrations of IBPE, IBS, dence on several parameters, deriving a rate model IBPCl and total amount of carbonylated products assuming any one of the steps as rate-determining [2-(4-iso-butylphenyl)propionic acid (IBN)+3-(4-iso- step would not explain all the observed trends. In this butylphenyl)propionic acid (3-IPPA)], respectively, case, a dynamic analysis incorporating the variation C0 the initial concentration of the catalyst, and C1, of concentrations of all the catalytic species as well C4, C5, and C7 the concentrations of various catalytic as reaction intermediates with time would be most species as shown in Fig. 1. suitable as it would allow consideration of more than The differential equations (12)–(19) were solved by one step as rate limiting. An attempt has been made using the initial conditions (Eq. (20)) and guess values to interpret the concentration–time data for carbony- for the rate parameters using a fourth order Runge– lation of IBPE using a dynamic approach for one Kutta method. A comparison of the experimental and speciﬁc case as demonstrated below. predicted concentration–time data for a standard ex- The rate of change of concentration of IBPE (B), periment using the dynamic model is shown in Fig. 2. IBS (D), IBPCl (E) and the carbonylation products The values of rate constants determined for a set (F+G) as well as the catalytic intermediates (as shown 3 of conditions given in Fig. 2 are: k1 = 0.00745 (m / in Fig. 1) with time in a semi-batch reactor can be 2 −1 3 2 −1 kmol) s , k2 = 0.0125 (m /kmol) s , k3 = represented as follows:

dB + − l = r = k [B ][H ] (12) dt 1 1 l dD + l = r − r + r = k [B ][H ] dt 1 2 3 1 l + − + −k2[Dl][H ][Cl ] + k3[El][H ] (13) dE + − l = r − r − r = k [D ][H ][Cl ] dt 2 3 4 2 l + −k3[El][H ] − k4[El][C4] (14) dC − 1 = r = k [C ][CO][H O] (15) dt 6 5 1 2 dC 4 = r − r + r = k [C ][CO][H O] dt 5 4 7 5 1 2 −k4[El][C4] + k7[C7][H2O] (16) Fig. 2. Comparison of experimental and predicted concentration– C d 5 = r − r = k E C − k C time proﬁles using the dynamic model. Reaction conditions: t 4 6 4[ l][ 4] 6[ 5][CO] (17) IBPE, 1.123 kmol/m3; TsOH/LiCl (1:1), 0.121 kmol/m3; d −3 3 PCO, 5.4 MPa; PdCl2(PPh3)2,1.121 × 10 kmol/m ; PPh3, − − dC7 2.242 × 10 3 kmol/m3; water, 2.67 kmol/m3; MEK, 1.95 × 10 5 = r − r = k [C ][CO] − k C [H O] (18) 3 dt 6 7 6 5 7 7 2 m ; T, 388 K. R.V. Chaudhari et al. / Catalysis Today 66 (2001) 371–380 379

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