Subcritical Solvent Effects on a Parallel Diels ... - ACS Publications

Ind. Eng. Chem. Res. 1999, 38, 855-864

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APPLIED CHEMISTRY Subcritical Solvent Effects on a Parallel Diels-Alder Reaction Network J. Todd Reaves and Christopher B. Roberts* Department of Chemical Engineering, Auburn University, 230 Ross Hall, Auburn, Alabama 36849

The effect of pressure on the measured bimolecular rate constants of a parallel Diels-Alder reaction network in subcritical propane at 80 °C is determined. The network consists of maleic anhydride reacting simultaneously with isoprene and 1,3-cyclohexadiene. A phase behavior observation is made for each reaction to ensure the homogeneity of the system. Ratios of the bimolecular rate constants measured simultaneously in the parallel reaction network are compared to the ratios obtained when the two reactions are carried out independently. Also, a comparison of the experimental pressure effect for each independent reaction and the reaction network to predictions of the thermodynamic pressure effect using transition-state theory and the Peng-Robinson equation of state is made. Furthermore, an attempt is made to correlate the normalized rate constants of the individual reactions with the density of the solution. The results of the investigations are interpreted in the context of local reactant concentrations about the maleic anhydride and solvent-solute/cosolvent-solute interactions. Background As a result of the public’s increasing environmental awareness, research focused on developing processes that utilize less toxic organic solvents has flourished in the past 10 years. Much of this solvent replacement research has examined the possibility of using supercritical (SCF) and slightly subcritical fluids (including CO2, propane, ethane, and ethylene) as extraction and reaction solvents.1-4 Using supercritical and subcritical fluids as solvents can influence reaction systems in several ways. One is through the ability to dramatically change the densitydependent bulk properties (i.e., dielectric constant, solubility, and diffusivity) of these compressible fluids with small perturbations in temperature or pressure. SCF density-dependent bulk properties have been shown to dramatically affect reacting systems in many instances including variable solvent strength, enhancement of reactant solubilities, facilitation of product separation, and the thermodynamic pressure effect on rate constants.5-7 While the bulk properties of compressed fluids influence the behavior of reactions in these media, it has also been recognized that the fundamental molecular level interactions between all species in solution must be understood.8-13 Several investigations,14-30 including early solvatochromic and bathochromic studies,31-35 have shown that local densities and local concentrations of cosolvents around dilute solutes in a SCF can be significantly different than those of the bulk. Studies of bimolecular reactions in SCF solvents have shown that these local environments can impact reactivity by manipulating local reactant concentrations at the reaction site.8-10 * To whom correspondence should be addressed. Phone: (334) 844-2036. Fax: (334) 844-2063. E-mail: croberts@ eng.auburn.edu.

These local environments are primarily controlled by short-range molecular level interactions between species in solution and differ from the long-range correlations that lead to large partial molar properties in the near and supercritical regime.36 Solvatochromic studies have shown that local concentration enhancements can occur in both binary liquid solvents and subcritical fluid/ cosolvent mixtures.37,38 This suggests that the local reactant environment at conditions far removed from the critical regime could influence reactivity. Unfortunately, this has not been illustrated in subcritical, compressible fluids (T < Tc). Diels-Alder reactions have been widely used to explore the solvent effects on reactions in supercritical fluid mixtures.9,39-50 This class of reactions is employed because of its well-understood, irreversible second-order kinetics and well-characterized transition state. The effect of SCF solvents on the selectivity of parallel Diels-Alder reactions has been explored; however, the studies focused only on the regioselectivity of single reactions.39,40,47 For example, Kim and Johnston40 studied the effect of pressure on the endo/exo-selectivity of the methylacrylate and cyclopentadiene reaction in scCO2 and found that the selectivity results correlated with solvatochromic polarity scales. These selectivity experiments39,40,47 show that the regioselectivity of Diels-Alder reactions can be influenced by the solvent strength of SCFs. However, parallel reaction networks in which two dienes compete to react with one solute were not explored. The examination of a parallel reaction network in which one solute reacts simultaneously with two competing diene cosolvents is important since the system behavior may give further insight into the impact that local reactant concentrations can have on reactivity through the competition of the two dienes. This paper presents two investigations of Diels-Alder reactivity in subcritical propane (Tc ) 369.8 K, Pc ) 42.5 bar). In the first investigation, the Diels-Alder reaction

10.1021/ie980474v CCC: $18.00 © 1999 American Chemical Society Published on Web 01/23/1999

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Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999

Figure 1. Diels-Alder reaction between maleic anhydride and isoprene.

Figure 3. Parallel Diels-Alder reaction network in which maleic anhydride reacts with isoprene and 1,3-cyclohexadiene. Figure 2. Diels-Alder reaction between maleic anhydride and 1,3-cyclohexadiene.

of maleic anhydride with isoprene (Figure 1) and of maleic anhydride with 1,3-cyclohexadiene (1,3-CHD) (Figure 2) are studied independently at 80 °C. The experimental conditions are such that the maleic anhydride is a dilute solute reactant and the isoprene (or 1,3-CHD) is a reacting cosolvent. The bimolecular rate constants of the two reactions are measured as a function of pressure and a comparison is made to the predictions of the thermodynamic pressure effect using transition-state theory and the Peng-Robinson equation of state. Also, an attempt is made to correlate the normalized rate constants of the individual reactions with the density of the solution.46 In the second investigation, the effect of pressure on the measured bimolecular rate constants of a parallel Diels-Alder reaction network (Figure 3) in subcritical propane is observed. The network consisted of maleic anhydride (dilute solute) reacting simultaneously with both isoprene and 1,3-CHD at 80 °C. The pressure effect on the ratios of the individual bimolecular rate constants (kisp/k1,3CHD) are compared to the pressure effect on the ratios obtained when the two reactions are carried out simultaneously in the parallel reaction network. In addition, the individual reactions and the parallel reaction network are carried out in chloroform, ethyl acetate, and hexane at 35 °C and ambient pressure and the results are compared to those obtained in subcritical propane. Experimental Section Materials. Maleic anhydride (99%, Aldrich) was stored in a vacuum desiccator and freshly ground for each experimental run. Isoprene and 1,3-cyclohexadiene (97+%, Fluka) were stored over molecular sieves and used as received. Propane (99+%, BOC Gases), ethyl acetate (99.9%, Fisher), chloroform (99+%, Fisher), and hexane (99+%, Fisher) were used as received. The use of liquid propane at high temperatures and pressures is extremely dangerous and must be done with care. Propane is highly flammable and presents a significant danger for explosion. Vessels should always be grounded and have sufficient ventilation whenever propane is being discharged. Rate Constant Measurements. The reaction was carried out in a 200 mL, 316 stainless steel reactor

designed to handle pressures up to 300 bar (Figure 4). The temperature of the reactor was controlled to (0.1 °C using an Omega 6071A controller with a resistance temperature device (RTD) and heating tape. Pressure in the reactor was monitored to within (0.9 bar using a PSI-TRONIX digital gauge. Solvent was delivered to the reactor using an Isco high-pressure syringe pump equipped with a water jacket to control the solvent temperature. The reactor contents were agitated using a stir plate and Teflon stir bar. The reactions in propane were carried out at T ) 80.0 °C (Tr ) 0.95) and pressures ranging from 90 to 152 bar (Pr ) 2.12-3.58). The initial maleic anhydride concentration was ≈3.0 × 10-4 mole fraction in all runs. The isoprene and 1,3-CHD bulk concentrations were ≈0.005 mole fraction each in all runs. To initiate the reaction, the appropriate amounts of each reactant were loaded into separate compartments in the vessel such that they were segregated until the solvent was rapidly delivered using the Isco syringe pump. The appropriate amount of solvent was added in order to reach a desired pressure at the reaction temperature. With the temperature of the cooling jacket and the pressure indicated on the Isco syringe pump, the density of the solvent was calculated by using the pure component equation of state for propane.51 The mass of solvent delivered was then calculated using the density and the differential volume displaced into the reactor as indicated on the Isco syringe pump. After an initial mixing period, four to five samples were taken from the reactor using a 0.25 mL sample chamber connected to the center of the reactor during the course of the reaction. The contents of the sample chamber were slowly bubbled through 2 mL of ethyl acetate, flushed with an additional 2 mL of ethyl acetate, and then collected in sample vials for GC analysis. Even though the volume of the sample chamber is quite small compared to that of the reactor, a small amount of solvent was delivered to the reactor after each sample removal to maintain the desired reactor pressure. Calculation of the change in the bulk concentrations in the reactor both before and after the sampling showed that this technique changed the bulk concentrations by less than 1% of the initial concentration. Maleic anhydride concentrations in the collected samples were determined using a Varian 3300 GC with FID. Ratios of the maleic anhydride area response to that of naphthalene (inert, internal standard) were used

Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 857

Figure 4. Experimental apparatus for high-pressure kinetic measurements.

to monitor the solute concentration in the reactor. The concentration of the reaction products were determined by taking the ratio of each reaction product area response to that of naphthalene. The molar concentration of naphthalene used was at least 19 times less than that of the reactant maleic anhydride. Experiments were performed to verify that naphthalene did not react with either the isoprene or 1,3-CHD at the reaction conditions studied. The reactions were carried out in the same manner in ethyl acetate, chloroform, and hexane at 35 °C and atmospheric pressure. A series of control studies were performed to verify that the samples taken using this method were representative of the reactor contents. Several experiments were performed in the absence of the dienes, and the maleic anhydride concentration was sampled for consistency using different sampling intervals and sampling rates. These experiments were conducted at 80 °C and 92 bar in subcritical propane. The measured concentrations differed by less than 2% from one another in each run. These studies showed that the sampling method is consistent and that the maleic anhydride solubility is not influenced by the sampling method. Phase Behavior Studies. To properly analyze the kinetics of reaction systems in supercritical or subcritical fluids, the homogeneity of the system must be verified.47 That is, the system must be one phase. To test the homogeneity of the system, two experiments

were performed. First, kinetic experiments were carried out at the lower propane densities studied with varying diene concentrations between 0.003 and 0.007 mole fraction. The resulting bimolecular rate constants agreed to within 3% from one another in all cases. This suggests that the reaction system is homogeneous in this cosolvent concentration range. Also, on the basis of the control experiments, we estimate the experimental error in the measurements to be (5%. In the second experiment the reaction was carried out in a high-pressure view cell to observe the phase behavior of the individual reactions and the reaction network in propane. The purpose of the experiment was not to determine the exact location of the phase transition from one phase to two phases in the system. Rather, the objective was to observe whether or not the mixture was a single homogeneous phase when the solvent and reactants are loaded into the view cell in the same concentrations as those used in the kinetic experiments. The experiments were performed at pressures lower than those in the kinetic studies to ensure that a single phase was present. The view cell apparatus consisted of a 42.2 mL, 316 stainless steel Jerguson sight gage model 13R32. The temperature of the view cell was controlled to within (0.1 °C using an Omega 6071A controller with an RTD and heating tape. Pressure was measured to within (0.7 bar using a pressure transducer (Omega, model PX945-10). The pressure transducer was calibrated

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Table 1. Results of the Phase Behavior Observations for the Three Reaction Systems Studied at 80 °C in Subcritical Propane T (K) P (bar) xdiene,total MA and isoprene MA and 1,3-cyclohexadiene parallel network

xMA

phases

353 353

69 69

0.008 0.008

3.40 × 10-4 3.40 × 10-4

1 1

353

69

0.016

3.40 × 10-4

1

using a Heise digital, pressure indicator (901A). Solvent was delivered to the view cell using an Isco highpressure syringe pump equipped with a water jacket to control the solvent temperature as described earlier. The view cell contents were agitated using a stir plate and Teflon stir bar. To initiate the reaction in the view cell, the appropriate amounts of each reactant were loaded into the view cell and the propane was then rapidly delivered using the Isco syringe pump. The appropriate amount of propane was added in order to reach a desired pressure at the reaction temperature. The results of the phase behavior experiments are shown in Table 1. Each of the reactions were observed at 353 K and 69 bar. The maleic anhydride concentration used in all runs was 3.4 × 10-4 mole fraction. The diene concentrations for the individual reactions were 0.008 mole fraction. For the network, the total diene concentration was 0.016 mole fraction. In both cases, these concentrations were 60% greater than those used in the kinetic experiments. For each reaction system, one phase was observed. These results suggest that the kinetic data measured at higher pressures and with lower diene concentrations was obtained in the onephase regime.

Figure 5. Kinetic plot for maleic anhydride and isoprene at 80 °C and 150 bar in subcritical propane: (9) kinetic data points; (s) best fit trendline.

Results and Discussion Single-Reaction Investigation. In the first investigation, the reactions between maleic anhydride + isoprene and maleic anhydride + 1,3-CHD are firstorder with respect to both the maleic anhydride and the diene, and therefore, second-order overall. However, the reactions were carried out such that the kinetics would be pseudo-first-order. That is, the diene concentration was kept in large excess and, therefore, roughly constant during the reaction. The initial maleic anhydride concentration was ≈3.0 × 10-4 mole fraction in all runs, and the diene bulk concentration was ≈0.005 mole fraction in all runs. The observed pseudo-first-order rate constant was calculated from the slope obtained from the plot of the natural log of maleic anhydride concentration versus time. The bimolecular rate constant was obtained by dividing the observed rate constant by the bulk isoprene concentration in the reactor. This is shown in eqs 1-3. If A + B f P, then,

RATE ) -

dCA ) kbiCACB ) kobsCA dt

-ln

(1)

CA ) kobs CA0

(2)

kobs CB

(3)

kbi )

where CA is the concentration of maleic anhydride, CB is the concentration of the diene, kbi is the bimolecular

Figure 6. Pressure dependence on the maleic anhydride and isoprene bimolecular rate constant at 80 °C in subcritical propane: (b) measured bimolecular rate constants; (s) thermodynamic pressure effect calculation from transition-state theory.

rate constant, kobs is the pseudo-first-order rate constant, and t is the time. Per convention, the bimolecular rate constant was calculated on the basis of the bulk concentration of the diene (cosolvent). However, if the local concentration of cosolvent is different than that of the bulk about the maleic anhydride, then an overestimation or underestimation may be borne out in the calculated bimolecular rate constant. Therefore, to properly interpret the measured rate data, we must take into account both the thermodynamic pressure effect on the bimolecular rate constant and any local reactant concentration influence on the rate. Figure 5 shows an example of the plots used to determine the observed pseudo-first-order rate constants. Figure 6 gives the pressure dependence of the maleic anhydride and isoprene bimolecular rate constants in subcritical propane at 80 °C. The measured rate constants remain statistically constant from 25.1 h-1 (mole fraction units) at 152 bar to 24.9 h-1 at ≈138 bar. However, at pressures below 138 bar the measured rate constants (based on the bulk isoprene concentration) begin to then increase to 28.5 h-1 at ≈90 bar. This observed pressure effect on the bimolecular rate constants in subcritical propane is remarkably different from that observed by Paulaitis and Alexander 41 in


supercritical CO2. Paulaitis and Alexander found that the bimolecular rate constant for the reaction increased with increasing reaction pressure. This result was verified in a recent paper using pseudo-first-order kinetics.52 Interestingly, the pressure effect on the rate constants in subcritical propane is similar to that seen in supercritical propane with a very similar Diels-Alder reaction. In the study by Knutson et al.,9 opposite pressure effects between the experimental rate constants and predictions (thermodynamic pressure effect) were attributed to enhanced local concentrations of the reacting cosolvent (2,3-dimethylbutadiene) about the dilute reacting solute (maleic anhydride). The pressure effect on the rate constant observed in this paper is also similar to that observed by Brennecke, Chateauneuf, and coworkers in their laser flash photolysis (LFP) studies of the reactions of triplet benzophenone with 2-propanol and 1,4-cyclohexadiene in SCFs.8a,b Furthermore, a very similar pressure effect was observed for the esterification reaction of phthalic anhydride and ethanol in SCF CO2.8d The unique pressure effects in these studies were also attributed to enhanced local concentrations of the cosolvent about a dilute solute in the SCF solutions. The pressure dependence of the bimolecular rate constant for the maleic anhydride and 1,3-CHD reaction in subcritical propane is given in Figure 7. As the pressure is decreased from 148 to 90 bar the bimolecular rate constant decreases from 24.8 to 21.2 h-1 in mole fraction units. Also note that the rate constants for both reactions at high pressure are similar. This pressure effect behavior is counter to that seen with the isoprene reaction in the same solvent and at the same temperature. The pressure effect behavior is, however, similar to that seen by Roberts et al.8c in their studies of the reaction of triplet benzophenone with a nonattractive cosolvent (O2) in SCF solvents. Thermodynamic Pressure Effect Analysis. Several investigators 8,9 have used transition-state theory to estimate the thermodynamic pressure effect on bimolecular rate constants in order to evaluate kinetic data in supercritical solvents. Transition-state theory53 assumes a reaction model in which there is a thermodynamic equilibrium between the reactants and a transition state. According to transition-state theory, the thermodynamic pressure effect54 on the mole fraction based bimolecular rate constants is given by the reaction activation volume as shown in eqs 4 and 5:

- ∆v* ) T RT

(

)

(4)

∆v* ) vj TS - vj A - vj B

(5)

∂ ln kbi,x ∂P

where kbi,x is the bimolecular rate constant in mole fraction units, P is the pressure, T is the temperature, ∆v* is the activation volume for the bimolecular reaction, vj TS is the partial molar volume of the transition state, vj A is the partial molar volume of the maleic anhydride, and vj B is the partial molar volume of the diene. An estimate of the thermodynamic pressure effect can be made by estimating the difference in the partial molar volumes of the transition state and reactants by using an equation of state. For simplicity, the PengRobinson equation of state55 with standard mixing rules was employed here. The Peng-Robinson equation is

Figure 7. Pressure dependence on the maleic anhydride and 1,3cyclohexadiene bimolecular rate constant at 80 °C in subcritical propane: (b) measured bimolecular rate constants; (s) thermodynamic pressure effect calculation from transition-state theory. Table 2. Critical Parameters Used in the Thermodynamic Pressure Effect Calculations Using the Peng-Robinson Equation of State component

Tc (K)

Pc (bar)

acentric factor

CO2 propanea isoprenea 1,3-cyclohexadieneb,c maleic anhydrideb,c isoprene transition stateb,c 1,3-CHD transition stateb,c

304 370 484 568 720 851 764

73.8 42.5 38.5 45.4 59.9 36.1 31.9

0.225 0.152 0.164 0.215 0.453 0.582 0.705

a

a Appendix A. See ref 56. b T and P from the Joback modificac c tion of Lyderson’s method. See ref 56, p 12. c Acentric factor from ref 56, p 23.

given in eq 6:

P)

a(T) RT v - b v(v + b) + b(v - b)

(6)

where v is the molar volume, a ) 0.45724R2Tc2Pc-2, and b ) 0.07780RTcPc-1. Since directly calculating the partial molar volume is difficult, the triple product rule was used to obtain the partial molar volume from the pressure explicit equation as shown in eq 7:

vj i )

( ) ∂(nv) ∂ni

) P,T,nj

( ) ( ) ∂P ∂ni

T,nv,nj

∂P ∂(nv)

(7)

T,n

The details of the calculation of the partial molar volume are given elsewhere.8d Critical properties of all components are listed in Table 2.56 In the absence of further information, the binary interaction parameters (kij’s) are set equal to zero and the transition-state critical parameters were modeled as those of the product.57 The predicted pressure effect on the rate constant (∂ ln kbi,x/∂P)T was numerically integrated to predict the trend in the bimolecular rate constant with pressure for direct comparison with the experimentally measured bimolecular rate constants. The predicted bimolecular rate constant at high pressure is assigned the value of the experimental bimolecular rate constant at the same high pressure. Please note that the purpose of these calculations is not to predict the absolute value of the bimolecular rate constant. The calculation is only used

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to predict the rate of change of the bimolecular rate constant with a change in pressure. As stated before, Figure 6 presents the effect of pressure on the measured bimolecular rate constants for the maleic anhydride and isoprene reaction in subcritical propane. The solid line represents the predicted thermodynamic pressure effect from transitionstate theory using the Peng-Robinson equation of state. The prediction from the thermodynamic pressure effect calculation shows a slight decrease in the rate constant with a decrease in pressure over the entire range studied. This is expected since at 80 °C the subcritical propane is fairly noncompressible and, therefore, the partial molar volumes are not expected to change dramatically. The prediction also agrees with kinetic studies of maleic anhydride and isoprene in liquid ethyl acetate at high pressure.58 However, the effect of pressure on the experimentally measured bimolecular rate constants in subcritical propane is dramatically different from both the thermodynamic pressure effect prediction and those in compressed ethyl acetate. The measured rate constant remains relatively unchanged from 25.1 h-1 (mole fraction units) at 152 bar to 24.9 h-1 at ≈138 bar. Yet, at pressures below 138 bar the measured rate constant (based on the bulk isoprene concentration) begins to increase to 28.5 h-1 at ≈90 bar. Knutson et al.9 also observed this opposite behavior between measured rate constants and predictions of the thermodynamic pressure effect for the Diels-Alder reaction of maleic anhydride and 2,3-dimethylbutadiene in supercritical propane at 100 °C. This behavior was explained in terms of enhanced local concentration of the cosolvent about the dilute solute in SCF propane. A possible explanation of the results presented here in subcritical propane is that the reaction rate is augmented because an enhanced local concentration of isoprene about the maleic anhydride in the reaction mixture. This would result in an apparent overestimation of the measured rate constant in propane. This is important since short-range molecular interactions seem to be influencing the pressure effect in subcritical propane, 20 °C below the critical point of the solvent. Figure 7 shows the comparison between the measured bimolecular rate constants for the maleic anhydride and 1,3-CHD reaction and those predicted by the thermodynamic pressure effect. The measured bimolecular rate constants follow the trend of the thermodynamic pressure effect over the entire pressure range studied. This is significantly different from the maleic anhydride reaction with isoprene at the same reaction conditions and in the same solvent. One plausible explanation of these results involves the relative size and rigidity of the 1,3-CHD molecule compared to that of isoprene. Since Diels-Alder chemistry is highly dependent on the orientation of the molecules prior to the reaction taking place, these considerations could be a factor. The isoprene molecule can apparently pack or orient itself more efficiently about the maleic anhydride than the 1,3-CHD molecule and therefore a local concentration enhancement may be the result. Density Analysis of the Bimolecular Rate Constant. While the presentation and interpretation of high-pressure kinetics is often done as a function of pressure as the independent variable, another approach is to present and interpret kinetic data as a function of density.59 In a recent study by Weinstein et al.,46 it was illustrated that the mole fraction based rate constants

Figure 8. Normalized mole fraction based rate constants for the reaction of maleic anhydride and isoprene in subcritical propane at 80 °C: (b) ln[kx(T,F)/kx(T,F0)]; (s) ln(F/F0).

for the Diels-Alder reaction of ethyl acrylate and cyclopentadiene showed a linear dependence on density in scCO2. Using a typical Arrhenius rate expression they demonstrated that the density dependence on the rate is reflected primarily in the preexponential factor. Weinstein et al.46 also examined rate constant data for two other Diels-Alder reactions from the literature41,43 in this manner and showed the same density dependence in scCO2. In their paper the relationship between the normalized mole fraction based rate constant (kx), normalized concentration based rate constant (k), Gibbs free energy of reaction (∆G h *+), the continued product of activity coefficients (Kγ*), and the transmission coefficient (κ) was presented in the following expressions:

ln

( ) ( ) kx(T,F)

kx(T,F0)

) ln

κ(T,F) κ(T,F0)

(

)

h *+(T,F0) K* ∆G h *+(T,F) - ∆G γ (T,F) (8) - ln * RT Kγ (T,F0) ln

(

kx(T,F)

kx(T,F0)

) ( ) ln

) ()

k(T,F) F + ln F0 k(T,F0)

(9)

By plotting ln[kx(T,F)/kx(T,F0)] versus density, the researchers indicate that the ln(F/F0) term in eq 9 accounts for most of the density dependence of ln[kx(T,F)/kx(T,Fο)] for the three Diels-Alder reactions analyzed in scCO2 including the data from Paulaitis and Alexander for the reaction of maleic anhydride and isoprene.41 Figure 8 shows rate constant data for the maleic anhydride and isoprene reaction in subcritical propane analyzed in terms of density. The reference density and bimolecular rate constant used were 0.443 g/cm3 and 25.4 h-1, respectively. The behavior of ln[kx(T,F)/kx(T,F0)] versus density in subcritical propane does not correlate with ln(F/F0) as seen in the Weinstein et al.46 analysis of other Diels-Alder reactions in scCO2. At the lower densities studied, the plot of ln[kx(T,F)/kx(T,F0)] diverges from that of ln(F/F0). This counter behavior is similar to that observed by Knutson et al.9 who studied the similar Diels-Alder reaction of maleic anhydride and 2,3-dimethylbutadiene in supercritical propane. Their bimolecular rate constant data at 100 °C is analyzed


Figure 9. Normalized mole fraction based rate constants for the reaction of maleic anhydride and 2,3-dimethylbutadiene in supercritical propane at 100 °C: (b) ln[kx(T,F)/kx(T,F0)]; (s) ln(F/F0). Data from Knutson et al.9

further suggests the possible explanation presented earlier that the 1,3-CHD appears to be less efficient in its ability to orient itself about the maleic anhydride. Therefore, an increase in local diene concentration is not apparent in the 1,3-CHD reaction. Parallel Reaction Network Investigation. The effect of a second reacting cosolvent on a ground-state reaction in a subcritical fluid or SCF has not been explored in the literature. Knutson et al.9 did investigate the effect of adding a second nonreacting cosolvent (2,2,2-trifluoroethanol) on the reaction of maleic anhydride with 2,3-dimethyl-1,3-butadiene in supercritical propane. However, the authors concluded that the nonreacting cosolvent did not appreciably affect the solute-cosolvent interactions. In the second investigation the parallel reaction network in which maleic anhydride reacts simultaneously with isoprene and 1,3CHD is studied in subcritical propane at 80 °C. As before, both reactions are second-order overall, but the reactions are carried out with excess diene (cosolvent), making the kinetics pseudo-first-order with respect to the maleic anhydride. The reaction kinetics are, therefore, similar to those for the single-reaction studies as shown in eqs 10-16 below.

A + B f P (kbi1)

(10)

A + Z f R (kbi2)

(11)

RATE ) - ln

CA ) (kobs1 + kobs2)t CA0

(12)

R ) (kobs1 + kobs2)

(13)

dCP kobs1 ) )β dCR k 2

(14)

Rβ R and kobs2 ) β+1 β+1

(15)

kobs1 kobs2 and kbi2 ) CB CZ

(16)

obs

Figure 10. Normalized mole fraction based rate constants for the reaction of maleic anhydride and 1,3-CHD in subcritical propane at 80 °C: (b) ln[kx(T,F)/kx(T,F0)]: (s) ln(F/F0).

as a function of density and is presented here in Figure 9. The reference density and bimolecular rate constant used were 0.355 g/cm3 and 1.4 min-1, respectively. Again, ln[kx(T,F)/kx(T,F0)] correlates well with ln(F/F0) at densities of 0.43-0.33 g/cm3. However, at densities less than 0.33 g/cm3, the correlation diverges. These results are similar to those seen in the thermodynamic pressure effect analysis presented earlier. One possible explanation for the contrary rate constant behavior with density observed in supercritical and subcritical propane compared to that observed in scCO2 is the influence of enhanced local diene concentrations. If the local concentration of diene is different than that of the bulk about the maleic anhydride, then an overestimation of the bimolecular rate constant could result. Figure 10 represents the rate constant data for the maleic anhydride and 1,3-CHD reaction in subcritical propane analyzed in terms of density. The reference density and bimolecular rate constant used were 0.451 g/cm3 and 23 h-1, respectively. For this reaction, the behavior of ln[kx(T,F)/kx(T,F0)] versus density does correlate with ln(F/F0) as was seen in the Weinstein et al.46 analysis of other Diels-Alder reactions in scCO2. As with the isoprene reaction, these results are similar to those obtained from the thermodynamic pressure effect analysis. This agreement between the two analyses

kobs1 )

kbi1 )

where A is the maleic anhydride, B is the isoprene, Z is the 1,3-CHD, CA is the concentration of maleic anhydride, CB is the concentration of isoprene, CZ is the concentration of 1,3-CHD, CP is the concentration of the isoprene reaction product, CR is the concentration of the 1,3-CHD product, kbi1 is the bimolecular rate constant of the isoprene reaction, kbi2 is the bimolecular rate constant of the 1,3-CHD reaction, kobs1 is the pseudofirst-order rate constant of the isoprene reaction, kobs2 is the pseudo-first-order rate constant of the 1,3-CHD reaction, R is the sum of the observed pseudo-first-order rate constants, and β is the ratio of the pseudo-firstorder rate constants. There are two differences between the single-reaction and parallel reaction kinetics. First, the measured pseudo-first-order rate constant is a function of the individual pseudo-first-order rate constants. As before, this rate constant is taken from the slope of the line defined by eq 12. To calculate the individual pseudofirst-order rate constants, eq 14 is used which shows that a plot of the change in the concentration of the products is a constant and is equal to the ratio of the

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Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999 Table 3. Results of the Liquid Reaction Kinetic Studies at Atmospheric Pressure for the Three Reaction Systems Studied at 35 °C in Chloroform, Hexane, and Ethyl Acetate kISP,ind (h-1) kCHD,ind (h-1) (kISP/kCHD)ind kISP,net (h-1) kCHD,net (h-1) (kISP/kCHD)net

Figure 11. Kinetic plot for a parallel reaction network in propane at 80 °C and 116 bar: (9) [CHD adduct]/[ISP adduct]; (s) best fit trendline.

Figure 12. Pressure dependence on the product selectivity (kISP/ kCHD) of the parallel reaction network in which maleic anhydride reacts with isoprene and 1,3-cyclohexadiene simultaneously at 80 °C: (b) product selectivities of the reactions when they are carried out independently; (9) product selectivities of the parallel reaction network; (s) product selectivity prediction from transition-state theory and the thermodynamic pressure effect calculation.

individual pseudo-first-order rate constants. Once the pseudo-first-order rate constants are determined, they are divided by the bulk diene concentrations, per convention. Figure 11 shows a plot of the concentration change of the products for one of the runs at 80 °C and 116 bar. Figure 12 illustrates the pressure dependence of the product selectivities (kISP/kCHD) of the maleic anhydride + isoprene and maleic anhydride + 1,3-CHD reaction network in propane at 80 °C. As the pressure is decreased from 142 to 92 bar, the selectivities of the reactions run independently increase 25% from 1.03 to 1.28. This behavior is a consequence of the pressure dependence seen in Figures 6 and 7. In the maleic anhydride reaction with isoprene the bimolecular rate constant increases dramatically over this pressure range while the bimolecular reaction rate constant for the reaction with 1,3-CHD decreases slightly. The pressure dependence of the selectivities in the reaction network is much different. Over the same pressure range the selectivities for the network are relatively unchanged at ≈1.0. When the thermodynamic pressure effect prediction of the product selectivities for the network is plotted, the selectivities decrease 12% from 0.98 to 0.86. This calculation is essentially the same as that done for the

n-hexane

ethyl acetate

chloroform

2.50 3.47 0.72 2.60 3.51 0.74

4.53 5.02 0.90 4.69 5.10 0.92

21.50 32.40 0.66 21.20 30.50 0.70

single-reaction investigation, the only difference being the inclusion of the second diene and adduct into the calculation of the partial molar volumes using the Peng-Robinson equation of state. The results obtained from the reaction network show that the product selectivities of the reaction network and those from the independent reactions clearly diverge as the pressure (i.e., density) is lowered. The presence of the second diene, 1,3-CHD, seems to be impeding the local reactant concentration enhancement of isoprene in the reaction sphere when the two reactions are run simultaneously. The selectivity predictions from the thermodynamic pressure effect indicate that the selectivities should decrease similarly to what is seen in the independent reaction calculations. This is expected since the calculation cannot take into account local concentration differences. The reaction network results are interesting since we may be observing the effect of local concentrations on the measured reaction rate without having to rely on the thermodynamic pressure effect calculation or the density correlations of Weinstein et al.46 In short, these results provide further qualitative experimental evidence of local cosolvent concentration enhancement in compressible fluids. This would be important since the primary way in which researchers have been able to show that local reactant concentrations affect measured reaction rates is by comparing the experimental bimolecular rate constants to those predicted by the thermodynamic pressure effect using transition-state theory. Ideally, we would prefer to not rely on this method because of the qualitative nature of the prediction. Also, the method can only be applied to reactions in which the structure of the transition state is well-known, since the critical properties of the transition state must be calculated. In the case of Diels-Alder reactions, though, we believe the thermodynamic pressure effect calculation from transition-state theory provides a good qualitative prediction of the pressure effect since it is well-known that the transition state of a Diels-Alder reaction is similar to that of the product. This is a consequence of the Diels-Alder reaction undergoing a concerted mechanism.57 Reaction Network in Conventional Liquid Solvents. To determine whether the reaction network results obtained in subcritical propane were atypical of liquid solvents, the same reactions were carried out in liquid ethyl acetate, hexane, and chloroform at atmospheric pressure and 35 °C. The results of those studies are presented in Table 3. As the solvent strength is increased from hexane through chloroform, the rate constant for the maleic anhydride and isoprene reaction increases from 2.5 to 21.5 h-1. The same behavior is observed for the maleic anhydride and 1,3-CHD reaction. The rate constant increases from 3.47 to 32.4 h-1. Only one literature value was available for comparison


for these reactions in these particular solvents. The rate constant measured for the maleic anhydride reaction with isoprene in ethyl acetate (4.53 h-1) agreed with the measurement of Grieger and Eckert58 to within 1%. More importantly, the bimolecular rate constants obtained by carrying out the reactions in the parallel reaction network were well within the experimental error of the bimolecular rate constants obtained from carrying out the reactions independently. This result is much different from what was observed in subcritical propane where the kISP/kCHD ratio obtained from the individual reactions and the reaction network was a function of the solvent pressure at a constant temperature. Also, in the liquid solvents studied the 1,3-CHD rate constant was always larger than the isoprene rate constant. However, in subcritical propane the isoprene rate constant was larger than the 1,3-CHD rate constant over the pressure range observed. The reaction network results in liquid solvents compared to the results obtained in subcritical propane once again suggests the possibility that local cosolvent concentration enhancements may be influencing the reaction network in subcritical propane as was previously reported in supercritical propane for a single reaction. Conclusions In this study two different investigations of reactivity in supercritical and subcritical fluids were made. In the first investigation, the Diels-Alder reactions of maleic anhydride with both isoprene and 1,3-cyclohexadiene were studied independently at 80 °C in propane. The bimolecular rate constants for the maleic anhydride and 1,3-CHD reaction followed the trend of the thermodynamic pressure effect in subcritical propane and showed a linear dependence on density when the rate constants were normalized. The maleic anhydride and isoprene reaction studied in subcritical propane produced markedly different behavior. Differences between the pressure effect on measured rate constants and the thermodynamic predictions were observed at lower pressures. Also, the normalized rate constants for the reaction did not show a linear dependence with density at the lower densities studied. One possible explanation for this behavior is that the local concentration of isoprene around the reacting maleic anhydride is significant in subcritical propane. Furthermore, this study indicated that the relative strengths of the interactions between solute, cosolvent, and solvent influence the degree of preferential solvation in some reaction mixtures far from the critical region. In the second investigation the parallel reaction network in which maleic anhydride reacts simultaneously with isoprene and 1,3-CHD was studied in subcritical propane at 80 °C. The results obtained from the reaction network show that the product selectivities of the reaction network and those from the independent reactions clearly diverge as the reaction pressure is lowered. These results obtained in subcritical propane differed from the results obtained in conventional liquid solvents. In hexane, ethyl acetate, and chloroform the product selectivities obtained from the reaction network were the same as those obtained from carrying out the reactions independently. In the subcritical propane, the presence of the 1,3CHD seemed to be inhibiting isoprene’s ability to experience a local concentration enhancement in the

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Received for review July 24, 1998 Revised manuscript received September 11, 1998 Accepted September 15, 1998 IE980474V

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