Ind. Eng. Chem. Res. 1996, 35, 645-652
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KINETICS, CATALYSIS, AND REACTION ENGINEERING General Kinetic Model for Liquid-Liquid Phase-Transfer-Catalyzed Reactions† A. Bhattacharya‡ Chemical Engineering Division, National Chemical Laboratory, Pune 411008, India
A simple and fairly general kinetic model framework for analyzing the rate data for phasetransfer catalysis reactions has been developed. The model does not a priori assume extractive equilibrium and applies equally well to cases where the pseudo steady state with respect to the active catalytic species in one of the phases is not maintained. Within this framework, complex multistep reactions of comparable rates in both phases along with interphase mass-transfer resistance, if and when present, can be considered. The model was applied to interpret published kinetic data for a number of phase-transfer and inverse phase-transfer catalysis reactions. The model is likely to be useful in rationalizing published or new kinetic data from a general and unified framework and will contribute to the design and development of reactors carrying out phase-transfer catalysis reactions of industrial importance. Introduction Reactions between two substances which exist in two mutually insoluble phases are normally too slow to be of much practical importance. This is so mainly because of the intrinsically low mutual solubility of the reactants in the opposite phases, even if other factors important in interphase mass transfer (such as interfacial area) are taken care of by using high agitation rates. Traditionally, such reactions were carried out by dissolving the reactants in polar aprotic solvents. However, this method has several disadvantages for industrial process development: the solvents are expensive, are sometimes difficult to remove, and are definitely an environmental hazard in large-scale operations. Moreover, in some alkylations with ambident ions, side reactions may be promoted by the solvent. Chemists have found that (Bra¨ndstro¨m and Gustavii, 1969; Makosza and Wawrzyniewicz, 1969; Starks, 1971) a very effective and economical way of enhancing the rate of such a reaction is to add a small catalytic quantity of another substance which can transport the reactant across the phase boundary in a form that has greater solubility in the target phase. In the original context of its discovery, the term phase-transfer catalysis (PTC) was taken to mean reactions between ionic compounds and organic, waterinsoluble, substances in solvents of low polarity, wherein onium salts or other complexing agents accelerate the reaction by solubilizing the anions of the reacting salt into the organic medium in the form of an ion pair. The main advantages of this synthetic procedure are enhancement of the reaction rate even at fairly moderate temperature and high conversion. There is also no need for expensive anhydrous or aprotic solvents and use is made of easily available catalysts and reactants. Other advantages claimed are occurrence of reactions that would not otherwise proceed and improved product selectivity through suppression of side reactions. † ‡
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The concept of phase-transfer catalysis has now become more broad-based, including extraction of cations or even neutral molecules from one phase into another (usually the organic phase) with the help of a catalyst. The cations could be derived from aqueous salts, acids, or bases. The catalysts range from onium salts, crown ethers, alkali-metal salts, or similar chelated salts. A large number of reactions of varied categories, such as alkylation, arylation, condensation, elimination, and polymerization, have seen application of the PTC technique (Dehmlow and Dehmlow, 1993; Starks et al., 1994). Extensions of the basic PTC technique to organometallic PTC applications, e.g., carbonylation of halides to carboxylic acids by using Co2(CO)8 (Alper, 1981), have been growing rapidly. Finally, although still not numerous, examples of “inverse” phase-transfer-catalyzed extraction of species into the water phase carried out (Mathias and Vaidya, 1986; Fife and Xin, 1987) with partially water-soluble pyridines or derivatives which form complexes with the organic substrate are reported. Aryl anhydrides (e.g., benzoyl benzoate, acetate) can be produced with good selectivity from acid chlorides by this process. Industrial applications of PTC reactions, especially in the fine chemicals area (pharmaceuticals, agrichemicals, etc.), are growing. Several examples of industrialscale processes using phase-transfer catalysis have been cited in the literature (Freedman, 1986). Among the most important applications are processes for making benzylpenicillins and for other drugs derived by O- and N-alkylation of various heterocycles, processes for making synthetic pyrethroids like cypermethrin and other analogues, and reactions of alkyl chlorides with nitriles, for example. It is generally agreed that, under the normal operation of the PTC processes in the laboratory, the reaction rates remain unaffected by the stirring rate above a certain minimum value, probably necessary to break up the concentration gradients on both sides of the interface. Dehmlow and Dehmlow (1993) summarized a number of examples from the published literature which confirm the above conclusion. While this may not be © 1996 American Chemical Society
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universally true in all situations, in the kinetic and mechanistic studies above conditions are usually found to hold true. Therefore, it is the rate model that becomes the focus of the investigation rather than the hydrodynamic or transport parameters. The basic mechanism of phase-transfer catalysis along with its variations under neutral, alkaline, or other conditions has been extensively studied and has been summarized among others by Dehmlow and Dehmlow (1993) and by Starks, Liotta, and Alper (1994). In spite of the diversity of the reaction conditions and possible mechanisms involved, the kinetic observations made in a large number of reactions have apparently been rationalized by an approach pioneered by Starks. Let us represent a basic PTC reaction mechanism consisting of the following steps: ORG.
QY + RX
a
RY + QX
d
AQ.
Q+Y– + X–
b c
Y– + Q+X–
This shows extraction of the nucleophilic anion Y- into the organic phase after forming an ion pair with the quaternary ammonium cation Q+ and the reaction of the ion pairs with the organic substrate RX in a displacement reaction, following which the replaced anion is transported back as an ion pair Q+X- to the aqueous phase. It is pertinent to point out here that, in general, the exchange of anions between the organic and the aqueous phases does not necessarily require a concomitant partition of the catalyst cation, i.e., Q+, in the aqueous phase. Under conditions of intense agitation in a batch reactor, if one may assume that the phases are in instant equilibrium with each other, the following extractive equilibrium can be said to be operative (i.e., steps b, c, and d are rapid): QXorg. + Yaq. h Xaq. + QYorg.
General Kinetic Model Model Assumptions. The model to be presented below is subject to the following assumptions: 1. Reaction steps are represented by bimolecular irreversible or reversible reactions governed by rate equations such as
ri ) ki(
The rate of the overall reaction is then controlled by that of the rate-limiting step, namely, the displacement reaction in the organic phase. It is easy to show that under these conditions the overall rate is that of a pseudo-first-order reaction (Starks and Owens, 1973; Dehmlow and Dehmlow, 1993), namely,
ln(CoRX/CRX0) ) -kCQX0t
the equilibrium approach is likely to become cumbersome and impractical if not restrictive. In a general approach, one may allow multiple reactions with comparable rates if the experimental data so indicate. Also, a general formulation should be easily extendible to include the mass-transfer resistances in one or both of the phases (again, if the observed data warrants it). Finally, a general kinetic model will predict the dynamic buildup/decay of the concentration of certain key intermediates, which when confirmed against observed behavior, would lead to a better understanding of the kinetics and the mechanism involved. With the above ideas in mind, an attempt has been made in the present work to provide a simple kinetic model for phase-transfer-catalyzed liquid-liquid reactions (extension to include mass-transfer resistances is shown in the appendix). This model has been shown to be adaptable for studying a number of PTC reactions for which mechanisms and limited conversion-time data have been reported in the literature. With a validated general kinetic model such as this, it is hoped that available, if scanty, kinetic data for a wider variety of PTC reaction schemes than shown here can be rationalized and interpreted. Application of the batch reactor model is also likely to contribute to the improved understanding of the effects of various process and operating parameters important for conducting these reactions and, hopefully, would lead to a better design and scaleup of reactors to carry out the same.
(1)
provided that the quaternary cation is almost exclusively partitioned into the organic phase and that the product to reactant anion ratio in the aqueous phase is essentially constant. These two conditions ensure that the effective concentration of the ion pair Q+Y- in the organic phase remains constant for most of the reaction period. In general, these conditions may seem restrictive, but the remarkable thing is that, in most of the experimental conversion-time data on PTC reactions, this observation has been repeatedly made. One is, therefore, tempted to generalize Starks’ equilibrium approach to more diverse reaction systems than for which it was derived originally. In the array of PTC reaction categories some of which were referred to earlier in this section, one commonly encounters multiple reaction steps in both phases that may be individually irreversible or reversible. These may constitute a consecutive-competitive mechanistic sequence. Also involved are the transport of the ion pairs across the phase boundary. A straightforward generalization of
∏j Cj - ∏l Cl/Ki)
ri ) ki
∏j Cj
(reversible)
(irreversible)
(2a) (2b)
2. The quaternary ammonium cation bearing species, denoted as QY and QX, are assumed to be distributed between the two phases as
MQX ) CoQX/CaQX,
MQY ) CoQY/CaQY
(3)
3. The partition coefficients are not affected by the changes in the phase composition. 4. A total of two liquid phasessone organic and one aqueoussis considered. 5. Interphase mass-transfer resistances are negligible. 6. The phase volumes remain unchanged during the reaction. 7. The phase-transfer catalyst in its original form is assumed to be added to one or the other of the liquid phases. 8. Batch isothermal reactor operation is being considered. Model Equations. In a typical phase-transfer catalytic reaction experiment, except for the cation Q+ bearing species, all other species would be normally restricted to one or the other phase. This is reflected in the separate mass balance equations written below for the different categories of species found in the
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organic (denoted by the superscript “o”) and in the aqueous (denoted by the superscript “a”) phases.
dCoj
No
) dt
νijroi ∑ i)1
(4)
for a species j that exclusively remains in the organic phase;
dCaj
Na
) dt
νijrai ∑ i)1
(5)
for a species j that exclusively remains in the aqueous phase. No and Na are the total number of reaction steps in the organic and aqueous phases, respectively. νij is the stoichiometric coefficient (-ν for consumption and +ν for the production of the jth species by the ith reaction). For the species which are transported across the 1-1 interface from one phase to the other (e.g., Q+ ion bearing species), the following mass balance will typically hold true:
o1
dCoj + dt
a1
dCaj
No
) dt
∑ i)1
Na
νijroi
+
νijrai ∑ i)1
(6)
Initially, it is possible to specify the concentration of the species j restricted to either phase,
t ) 0,
o Coj ) Cj0 ,
a Caj ) Cj0
(7)
For the catalytic species (such as QY or QX) the initial conditions can be written as:
t ) 0,
o the catalyst equal to o1CQ0 was added to the organic phase, the Q-balance at any instant of time will require that the following relation hold true:
CoA ) 0
a al CQ0 ) ol CoQ + al CaQ
(8) (9a)
o ol CQ0 ) ol CoQ + al CaQ + ol CoA + al CaA
(11)
When all the pertinent thermodynamic parameters (e.g., partition coefficients), rate constants, and operating parameters such as the phase holdup and the initial species concentrations were specified, these equations could be easily solved by a standard Runge-Kutta fourth-order method, and in all cases the Q-balance was scrupulously maintained. Model Applications. The above model was applied to three different PTC reaction schemes, studies on which have been published in the literature that reported batch reactor conversion-time data. In what follows, the results of these specific applications have been discussed. The actual model equations pertinent to all three schemes can be derived easily from the general equations given in the previous section. However, the advantage of the general formulation is that it can also be programmed on a personal computer and the results for specific cases produced. Case A: Synthesis of 2,4,6-Tribromophenyl Allyl Ether. This reaction was studied by Wang and Yang (1990). The organic phase reactant is allyl bromide dissolved in chlorobenzene, while the nucleophile comes from 2,4,6-tribromophenol dissolved in an aqueous solution, with KOH providing the requisite level of alkalinity. With excess KOH, complete formation of 2,4,6-tribromopotassium phenoxide (ArOK) in the aqueous phase should occur. The SN2 substitution reaction can then be represented as follows: Organic phase CH2CHCH2Br + Br3(C6H2)O–Bu4N+ (RX)
(ArOQ)
Bu4N+Br– + Br3(C6H2)OCH2CHCH2 (QX)
(RY)
Aqueous phase
or o ol CQ0
)
ol CoQ
+
al CaQ
(9b)
Condition (9a) or (9b) will hold good depending on whether the catalyst is originally added to the aqueous or the organic phase, and the equations reflect the fact of its instantaneous distribution between the two phases. The subscript Q denotes the original form of the catalyst, and A denotes its active form in which it has transported the nucleophile from the aqueous to the organic phase (e.g., in the typical reaction scheme shown in the introduction, Q is QX and A is QY). Finally, Q and A in the organic phase are assumed to be in equilibrium with the corresponding species in the aqueous phase:
CoQ ) MQCaQ
(10a)
CoA ) MACaA
(10b)
The above is a complete set of equations representing the dynamic behavior of all the pertinent species concentrations in either phase. Although not a part of the model equations, a good check on the calculation results is provided by a balance on the Q+ ion (Qbalance) in all the forms in which it is found in both phases. For example, for the same typical PTC reaction scheme shown above, if initially an amount (molar) of
K+Br– + Br3(C6H2)O–Bu4N+
Bu4N+Br– + Br3(C6H2)O–K+
(K+X–)
(Q+X–)
(ArO–Q+)
(ArO–K+)
The phase-transfer catalyst, tetrabutylammonium bromide, originally dissolved in the aqueous phase, converts the phenoxide anion into an active intermediate tetran-butylammonium 2,4,6-tribromophenoxide (ArO-Q+) that is far more lipophilic than the original nucleophile. Once in the organic phase, the species ArOQ readily reacts with allyl bromide. Wang and Yang (1990) studied the effect of agitation speed on the reaction rate, which leveled off beyond 400 rpm or so. Observed conversion-time data were presented as -ln(1 - X) vs time plots (where X is the fractional conversion of allyl bromide, RX). It can be seen from Figures 2 and 3 of their paper that, for any given temperature (e.g., 50 °C), after an extremely short initial period of stabilization, the system approaches an extractive equilibrium condition, wherein the organic phase concentration of ArOQ becomes invariant with time. As a result of the larger rate of the aqueous phase ion exchange (than the intrinsically slow substitution reaction in the organic phase) and also due to the higher lipophilicity of ArOQ, the organic phase reaction becomes the rate-controlling step in the overall process. The rate of the overall reaction then can be represented by a pseudo-first-order reaction, with the effective rate constant being directly proportional to CQX0.
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Table 1. Comparison of the Model Predictions of the Effect of Bromophenol to Allyl Bromide Mole Ratio on Kobs with Experimental Dataa (Wang and Yang, 1990) mole ratio of bromophenol/allyl bromide 1.044 1.305 1.567 1.828
103Kobs (min-1) model experiment 10.32 11.25 11.83 12.18
10.20 11.00 11.95 12.25
a 9.072 × 10-3 mol of tribromophenol; 6.213 × 10-4 mol of tetrabutylammonium bromide; mole ratio of KOH to tribromophenol, 1.970; 50 mL of H2O/50 mL of chlorobenzene, 50 °C.
Table 2. Comparison of the Model Predictions of the o Effect of Bromophenol to Bu4N+Br- Mole Ratio on CArOQ with Experimental Dataa (Wang and Yang, 1990) mole ratio of bromophenol/Bu4N+Br29.2 14.6 9.73 7.3 5.84
o 102CArOQ (M) model experiment
0.526 1.04 1.54 2.01 2.45
0.480 1.04 1.53 2.02 2.61
a 9.072 × 10-3 mol of tribromophenol; 1.785 × 10-2 mol of KOH; mole ratio of tribromophenol to allyl bromide, 0.788; 50 mL of H2O/ 50 mL of chlorobenzene, 50 °C.
While Starks’ equilibrium formulation of the batch PTC reaction kinetics is ideally suited to this classical case, one could use this example to test the more general kinetic model formulated in this paper. For instance, consider the conditions of some of the experimental runs as reported in Table 1 of Wang and Yang (1990), namely, 9.0772 × 10-3 mol of 2,4,6tribromophenol, 6.213 × 10-4 mol of tetra-n-butylammonium bromide, and a mole ratio of KOH to bromophenol of 1.970, in a 50 mL of chlorobenzene-50 mL of H2O two-phase mixture, at a stirring rate of over 800 rpm. The apparent first-order rate constant Kobs calculated by the present model compares favorably with the experimental data as shown in Table 1, for a number of mole ratios of bromophenol to allyl bromide. Similarly, from another set of experimental runs, reported in Figure 7 of Wang and Yang (1990), showing the effect of the initial concentration of Bu4N+Br- (i.e., CQX0) on the concentration of ArOQ in the organic phase, i.e., CoArOQ, it is clear that the pseudo-steady-state values of this concentration are maintained only during the earlier part of the reaction period (time < 30 or 40 min) for most CQX0 values. In Table 2, the model predictions of pseudo-steady-state values CoArOQ have been compared with those reported by Wang and Yang (1990) in their paper (p 525). The predictions seem to be quite accurate. Since our work is not meant to be a detailed kinetic study of any particular system, we have made no effort to fit the model parameters exactly, except that these were chosen consistent with the known facts (e.g., a high value of MArOQ and the rate constant of the aqueous phase reaction being much higher than that of the organic phase reaction). Nonetheless, the general kinetic model can be potentially used to interpret experimental kinetic data, especially for more complex kinetic models. The effect of KOH concentration in the aqueous phase cannot be predicted by the simple scheme above wherein the potassium phenoxide is assumed to be produced by an irreversible reaction and is taken to be available in excess. In actual practice, under conditions of lower alkali concentrations, the effective concentration of
Figure 1. Effect of initial Bu4N+Br- on the AROQ concentration profile (predicted by the present model using parameters as for Table 2).
CoArOQ becomes dependent on the initial alkalinity. This point will be discussed in greater detail in the following discussion of the model application to the synthesis of dialkoxymethane. The other point we wish to make on the kinetic modeling of PTC reactions is that, even in the seemingly straightforward reaction such as this, Wang and Yang (1990) presented data (their Figure 7) which clearly indicate that conditions may exist where the reaction need not be controlled solely by a reaction in the organic phase that is pseudo first order in the substrate concentration. It is to be noted that a quasi-stationary concentration of ArOQ in the organic phase arises only in the particular case where the rate of delivery of the nucleophile ArO- from the aqueous to the organic phase is almost exactly balanced by its consumption in the substitution reaction. When the consumption is the faster of the two rate processes, CoArOQ will fall as shown in Figure 1 (predicted by our model using the same parameters as used to compute results presented in Table 2). Hence, the signature straight line -ln(1 X) vs time plots are no longer obtained for the entire reaction period, the rate being reduced with time. The fact that the CoArOQ vs time profiles in Figure 1 do not match quantitatively (at longer times) with those of Figure 7 of Wang and Yang (1990), although the qualitative trends are quite similar, is due likely to additional factors such as possible mass-transfer resistance being important, which the present model ignores but can incorporate easily if required (see comments in the appendix). In other situations, ArOQ may accumulate in the organic phase and a reverse trend in the conversiontime plot will be obtained. The advantage of the present general model is that it has sufficient generality to take care of possible variations in the reaction scheme (additional reaction steps and variation of the relative values of the rate constants for the same in either phase, etc.) or to include mass-transfer resistances and specific phase equilibria if and when necessary. Case B: Synthesis of Dialkoxymethane. Wang and Chang (1994) have studied the kinetic and dynamic behavior of the reaction of dibromoethane in an organic solvent (say, chlorobenzene) with an aliphatic alcohol (e.g., 1-butanol, 1-heptanol) in a highly alkaline aqueous solution, in the presence of tetrabutylammonium bro-
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Figure 2. Effect of the initial alkalinity of the aqueous phase on the fraction of Q+ as QOR(organic).
mide (TBAB) as the phase-transfer catalyst. The reaction scheme can be represented as follows: Organic phase QOR + CH2Br2
CH2(OR)Br + QBr
QOR + CH2(OR)Br
CH2(OR)2 + QBr
Aqueous phase Br– + Q+ Q+OR– ROH + OH– K+
+
OH–
Q+
+
Q+Br–
OR–
OR– + H2O K+OH–
This scheme, in effect, generalizes the one for case A and is a good example of a case which should call for the use of the general kinetic model proposed in this work. As in scheme A, the original form of the catalyst (TBAB), QBr, is preferentially distributed into the aqueous phase, wherein it is possibly in a partially dissociated form. The nucleophile OR- is, unlike in scheme A, derived by an equilibrium limited reaction in the aqueous phase requiring a fairly high concentration of KOH. The active form of the catalyst, namely, tetrabutylammonium alkoxide (QOR), is highly lipophilic and is, in general, partially dissociated in the aqueous phase into Q+ and OR- ionic species. QOR (dissolved in the organic phase) converts the substrate dibromoethane, in a series of two competitive-consecutive substitution reaction steps, to the desired product, dialkoxymethane for the corresponding alcohol. Wang and Chang (1994) have presented for this system a plot of experimental conversion-time data (in the form of -ln(1 - X) vs time, the X denoting the fractional conversion of dibromoethane) at various initial KOH concentrations in the aqueous phase. They have also provided a corresponding plot of measured percent QOR in the organic phase against the initial alkalinity for various alcohols. For a typical case, such as 50 mL of chlorobenzene, 10 mL of H2O, 9.17 × 10-2 mol of 1-butanol, 2.76 × 10-2 mol of CH2Br2, and 3.10 × 10-3 mol of TBAB at 50 °C and 1020 rpm, Figure 2 shows a comparison of our model predictions with the experimental data on fraction QOR in the organic phase plotted against the initial KOH concentration. The
Figure 3. Predicted conversion of the alcohol vs time in the PTC synthesis of dialkoxymethane at various initial alkalinities (constant k1).
model predictions are remarkably accurate, considering the fact that the model makes several assumptions. Also, the major model parameters, such as the reaction rate constants and distribution and dissociation constants, are empirically fitted to the data for one alkali concentration and maintained the same for all other cases. The trend of variation of percent QOR (organic) with the initial alkalinity is, of course, well-known and is consistent with the mechanism wherein the aqueous phase concentration of OR- is limited by the reversible reaction between ROH and OH-. For the same set of data, conversion-time plots are generated as in Figure 3. While the pseudo-first-order behavior is shown as expected, there is, however, one significant difference in trends between the model predictions and the data presented by Wang and Chang in Figure 8 of their paper (1994). This difference relates to the fact that, although with an increasing initial OHconcentration the percent QOR (organic) reaches a saturation value, the observed rate of reaction does not seem to reach an asymptotic level as predicted by the model (Figure 3), as indeed, even by the so-called equilibrium model with which Wang and Chang (1994) have tried to interpret their results. Within the framework of this latter model, under conditions of pseudofirst-order rate behavior, the rate of the slow first substitution step (the rate-controlling one) in the organic phase becomes directly proportional to CoQOR. Since the latter reaches an asymptotically high level that is invariant with further increase in the initial alkalinity, the persistent increase in the reaction rate is not rationalized by the equilibrium model any better than the general kinetic model. It was qualitatively suggested by Wang and Chang (1994) that the increase in the reaction rate is probably due to the higher reactivity of the ion pairs Q+ORwhich are progressively less hydrated with increasing alkalinity, as these are transported from the aqueous to the organic phase. Such a desiccation effect of concentrated NaOH/KOH in PTC systems has been discussed thoroughly (say, by Landini et al., 1982) in the literature. Our general kinetic model does not incorporate such microdetails of specific reaction systems. However, the model can still be used in such a situation in the following way.
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Figure 4. Predicted conversion of the alcohol vs time in the PTC synthesis of dialkoxymethane at various initial alkalinities (variable k1).
In Table 1 of Wang and Chang (1994) the values of the so-called “intrinsic” rate constant k1 for the ratecontrolling step have been given at various values of initial KOH concentrations, obtained presumably from the observed pseudo-first-order rate constant and the measured/calculated value of CoQOR. The data of Wang and Chang in their Figure 8, then, can be closely predicted by our model (see Figure 4) by having k1 and KQOR ( ) KQX d d ), the dissociation equilibrium constants for QOR and QX, appropriately changed with the initial OH- concentration. Thus, as the intrinsic rate constant value increases (from 9.65 × 10-3 to 1.66 × 10-1 min-1 M-1), the QOR availability in the organic phase is sought to be maintained by the reduction in the dissociation of QOR in the aqueous phase. In effect what is being done to fit the experimental data is to increase the so-called extraction equilibrium constant [EQOR ) a a MQOR/KQOR ) CoQOR /(CQ +)/(COR-)] with the increase in d the alkalinity, as with less QOR available EQOR is likely to grow [see Figure 3 of Wang and Chang (1994)]. In this way, percent QOR in the organic phase is maintained at the asymptotic level of Figure 2 even with higher k1 values. This leads to increasing conversions even after CoQOR has reached the asymptotic level and does not increase any more with an increase in alkalinity. An equilibrium model based on the premise of complete dissociation of Q+X- and Q+OR- in the aqueous phase [which has been assumed by Wang and Chang (1994) in deriving their equilibrium model] is unlikely to explain the observed kinetic behavior. The present general model has adequate parameters so that it can fit the experimental data at least empirically. However, a more fundamental kinetic model that can correlate the progressive desiccation of the ion pair with the increasing alkali concentration is called for. Work in this direction is in progress in our laboratory and will be reported in a future communication. Case C: Synthesis of Acid Anhydrides by Inverse Phase-Transfer Catalysis. In the earlier examples, the catalytic cycle is driven by the continuous formation of a lipophilic ion pair of an anionic reactant with a lipophilic cation such as the tetraalkylammonium ion and the transport of this ion pair from the aqueous phase to the organic phase where the latter reacts
effectively with a second reactant dissolved therein. In an upcoming synthetic procedure, termed “inverse phase transfer catalysis (IPTC)” (Mathias and Vaidya, 1986; Kuo and Jwo, 1992) the organic phase reactant is converted, by means of a reagent (such as pyridine 1-oxide) partially soluble in the organic phase, into an ionic intermediate that is transported into the aqueous phase for reaction with the anionic reactant to produce the desired product. For instance, carboxylic acid anhydrides, important intermediates for the synthesis of esters, amides, etc., can be synthesized by IPTC techniques. The reaction of an acid chloride (RCOCL) with the carboxylate ions (R′COO-) catalyzed by pyridine 1-oxide (PNO) is likely to proceed through an intermediate 1-(acyloxy)pyridinium chloride formed in the organic phase. This is believed to be preferentially water soluble and sufficiently stable so that it distributes to the aqueous phase and reacts with the carboxylate ion to produce the acid anhydride. The latter being more soluble in the organic phase, the product of the reaction is eventually isolated from the organic phase. The pertinent reaction scheme can be written as follows: Organic phase RCOCl + PNO
RCO
O
N+PCl–
Aqueous phase M+Cl– + RCO O
OCR′ + PNO
RCO O
N+PCl– + R′COO–M+
Kuo and Jwo (1992) have studied the pyridine 1-oxide catalyzed substitution reaction of benzoyl chloride and benzoate ion in a water/dichloromethane two-phase reaction system. Wang and Ou (1994) have studied a similar reaction for the acetate ion in the aqueous phase and with a number of organic phase solvents of varying polarity. The observed kinetic data were presented by the latter authors in the standard -ln(1 - X) vs time plots under various conditions, where X is the fractional conversion of the acid chloride. They have further plotted Kobs (calculated from the slope of these plots) against the initial concentration of PNO taken in the aqueous phase, (PNO)i,aq. (see their Figure 7 and Table 3). We applied our model to case (b) in their Figure 7, wherein the reaction was conducted at 18 °C in a 50 mL of H2O/50 mL of CH2Cl2 two-phase medium, with [PhCOCl]i,org. ) 1.0 × 10-2 M, [CH3COONa]i,aq. ) 0.5 M, and with [PNO]i,aq. varying between 2 × 10-4 and 6 × 10-4 M. In this case, the original form of the catalyst, i.e., pyridine 1-oxide is known to be only sparingly soluble in CH2Cl2 (Kuo and Jwo, 1992). On the other hand, the catalytic intermediate 1-(acyloxy)pyridinium chloride can be taken to be almost wholly distributed to the aqueous phase. On this premise, our model predicts the values of Kobs as 48.48, 91.98, and 132.99, which are practically the same as those reported by Wang and Ou in the second row of Table 3 in their paper (1994). In the same way, for the IPTC reaction system where CH3COONa is replaced by sodium benzoate, PhCOONa, keeping the same concentrations as above, Kobs data have been reported by Kuo and Jwo (1992) in their Table 1. For the entry numbers 15, 14, and 8 in this table, Kobs values predicted by our model are 1.03, 1.82, and 2.47, which match very closely with those reported. In both Kuo and Jwo (1992) and Wang and Ou (1994) the slope of the linear plot of Kobs vs (PNO)i,aq. has been estimated. If we disregard the much smaller intercept, we get the slope kc as defined by the following equation:
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 651
Kobs ) kc(PNO)i,aq.
(12)
Furthermore, Kuo and Jwo (1992) have found, by a simple mechanistic analysis for the experimental conditions in their paper, that (written in the nomenclature of the present paper):
kc ) k1/(1 + 1/MPNO)
(13)
Greek Letters
On the other hand, our general model, under conditions where the organic phase reaction is rate controlling, can be shown to yield the following result: o Kobs ) k1[CPNO /(PNO)i,aq.](PNO)i,aq.
M ) partition coefficient for the quaternary ammonium cation bearing (phase distributable) species N ) total number of reaction steps in a given phase r ) net rate of a reaction step within a given PTC reaction scheme t ) time, min X ) fractional conversion of the limiting reactant in the rate-controlling reaction step in the organic phase
(14)
ν ) stoichiometric coefficients for a given PTC reaction scheme µ ) coefficients as defined for eqs A.3 and A.4 of the appendix 1 ) fractional phase holdup Subscripts
This in effect means that o CPNO /(PNO)i,aq. ) 1/(1 + 1/MPNO)
(15)
That is, the small fraction of PNO to be found in the organic phase, which effectively controls the overall reaction rate, must be shown to be equal to the righthand side, which is a function of the distribution coefficient for PNO. All our model calculations for both the IPTC systems indeed satisfied the above condition closely, which is a good indication of the accuracy of our model.
A ) active form of the phase-transfer catalyst (say, ArOQ) aq. ) belonging to the aqueous phase i ) ith reaction step i,aq. ) belonging to the aqueous phase at t ) 0 i,org. ) belonging to the organic phase at t ) 0 j ) jth species j0 ) jth species at t ) 0 l ) lth species org. ) belonging to the organic phase Q ) original form of phase-transfer catalyst (say, QBr) Q0 ) original form in which the catalyst is added to either phase at t ) 0 Superscripts
Concluding Remarks In this paper, it has been shown that a simple, but sufficiently general, kinetic model can be easily developed and applied to interpret published kinetic data for a number of common liquid-liquid PTC and IPTC reaction systems. This model is not limited by the assumption of extractive equilibrium, popularly used in the existing literature, and is equally applicable to cases where pseudo steady state is not maintained with respect to a phase-transfer catalytic species in one of the phases. The model can be easily extended to include the mass-transfer resistances in either phase, if required. Finally, the model can be used to rationalize observed kinetic data and estimate the parameters involved. In summary, the present model is useful in studying a number of types of PTC reaction mechanisms (some of which were discussed above; others will be dealt with in future contributions) and can enhance our understanding of the kinetics of such systems. This will help in the design and scaleup of reactors for industrial PTC reactions. Nomenclature all ) liquid-liquid interfacial area per unit volume of dispersion, cm-1 C ) concentration, M CRX0 ) concentration of RX at t ) 0, M CQX0 ) concentration of QX at t ) 0, M ) dissociation constant for QOR, M KQOR d ) dissociation constant for QX, M KQX d Kobs ) apparent or pseudo-first-order rate constant, min-1 K ) equilibrium constant for a reversible reaction step, if present, within a given PTC reaction scheme k ) rate constant for a reaction step within a given PTC reaction scheme k1 ) rate constant for the rate-controlling reaction step in the organic phase in the synthesis of dialkoxymethane, M-1 min-1 kL ) mass-transfer coefficient, cm min-1
o ) refers to the organic phase a ) refers to the aqueous phase
Appendix. Extension of the Kinetic Model to Include Mass-Transfer Effects If item no. 5 in the list of model assumptions, namely, the absence of interphase mass-transfer resistance, is removed, some of the model equations will have to be modified. For the species j which exclusively remain in either the organic or the aqueous phase, the equations remain unaltered, i.e.,
dCoj
No
) dt
νijroi ∑ i)1
(A.1)
and
dCaj
Na
) dt
νijrai ∑ i)1
(A.2)
For the Q+-ion bearing species the balance equations can be written in the following compact form for the organic phase,
dCoj
No
) dt
νijroi + µoMjkLjall(Caj - Coj /Mj) ∑ i)1
(A.3)
where µoMj ) 1 for j ) A, i.e., the active form of the catalyst (e.g., QY in the typical PTC reaction scheme discussed in the Introduction section) and µoMj ) Mj for j ) Q, i.e., the original form of the catalyst (e.g., QX in the same scheme). Similarly for the aqueous phase,
dCaj
Na
) dt
νijrai + µaMjkLjall(Coj - MjCaj ) ∑ i)1
(A.4)
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Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996
where µaMj ) (ol /al )/Mj for j ) A and µaMj ) (ol /al ) for j ) Q. As in the kinetic model the initial concentration of the species j restricted to either phase can be specified as
t ) 0,
o Coj ) Cj0 ,
a Caj ) Cj0
(A.5)
For the species Q and A the following initial conditions can be written (assuming that the catalyst is originally dissolved in the aqueous phase):
t ) 0,
CoA ) 0,
CaA ) 0,
CoQ ) 0,
a CaQ ) CQ0
(A.6) The Q-balance holds as usual, i.e., a ) ol CoQ + al CaQ + ol CoA + al CaA al CQ0
(A.7)
When all the pertinent thermodynamic, kinetic, and transport parameters as well as the operating parameters like phase holdups and the initial species concentrations are specified, the above equations can be easily solved by any standard ODE solver with sufficient accuracy, keeping a check on the results against the overall Q-balance given by eq A.7. The above general equations can be applied to all the reaction schemes dealt with in this paper. These can also be applied to other more complex reaction schemes (with minor extensions if necessary). However, there are very few published experimental conversion-time data on liquid-liquid PTC reactions where the masstransfer effect has been demonstrated. One notable study is that by Wang and Yang (1991) in the case of the synthesis of 2,4,6-tribromophenyl ether, where they had presented a special case of the above general equations. For the specified values of the distribution and the kinetic constants and the mass-transfer coefficients estimated in that work, they solved the equations and simulated their own experimental data published earlier (Wang and Yang, 1990). Thus, for specific systems where mass transfer is known to play a role, the kinetic model needs to be and can be extended to reflect that effect. The advantage of a general formulation presented here is that for individual schemes a reformulation of the equations will not be required.
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Received for review August 2, 1995 Accepted December 1, 1995X IE950483T
Literature Cited Alper, H. Phase Transfer Catalysis in Organometallic Chemistry. Adv. Organomet. Chem. 1981, 19, 183.
X Abstract published in Advance ACS Abstracts, February 1, 1996.
