Ind. Eng. Chem. Res. 2004, 43, 8141-8147
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APPLIED CHEMISTRY Decomposition and Oxidation of Aliphatic Nitro Compounds in Supercritical Water V. Anikeev,*,† A. Yermakova,† and M. Goto‡ Boreskov Institute of Catalysis, SB RAS, Novosibirsk, Russia, and Department of Applied Chemistry and Biochemistry, Kumamoto University, Kumamoto 860-8555, Japan
Decomposition and oxidation of nitromethane, nitroethane, and 1-nitropropane in supercritical water (SCW) near the critical point have been studied in a flow reactor. It was found that the rate of aliphatic nitro compounds decomposition in SCW decreased with an increase in the number of carbon atoms, while the rate of their oxidation increased with an increase in the carbon number. Experimental data on the decomposition of the studied nitro compounds showed that the apparent rate constants, calculated on the assumption of first-order reaction, increased exponentially with an increase in the pressure at constant temperature. The transition-state theory has been applied to simulate the effect of pressure on the rate constants. Some ideas on the nature of the activation complex have been suggested. The calculated values of the activation volumes in the decomposition reactions of nitromethane, nitroethane, and 1-nitropropane in SCW were similar, which suggested the same nature of the activation complex in all three cases. 1. Introduction Numerous literature data devoted to the advantages of supercritical fluids for the performance of a wide range of chemical reactions are now available, especially for the conversion of organic nitro compounds.1-3 The latter attracts particular attention because of strict requirements for the utilization of explosives, rocket fuel components, and their production wastes, municipal wastes, and other substances containing C-NO2, -ONO2, N-NO2, CH-N, and some other groups. However, notwithstanding the urgency of studies in this field, analysis of the available literature reveals the deficit of works on the conversion of nitro compounds in supercritical water (SCW). Nitromethane (NM), nitroethane (NE), and 1-nitropropane (NP) were selected as the models for studies of aliphatic nitrogenated compounds and wastes. The oxidation reactions are preferred for the processing of various substances and wastes, including organic nitro compounds, in SCW.1,4-6 Air or oxygen is used as an oxidant. Oxidation in SCW provides complete (99.99%) and rapid conversion of chemical substances into nitrogen and carbon dioxide. However, the studies on the decomposition of these compounds in SCW without an oxidizer (i.e., hydrothermal reactions) are very important both for understanding fundamental regularities of the reaction mechanism and kinetics and for solving practical tasks. One of the important features of the chemical reactions occurring under supercritical conditions is the * To whom correspondence should be addressed. Fax: +7 383 239 74 47. E-mail:
[email protected]. † Boreskov Institute of Catalysis. ‡ Kumamoto University. E-mail: mgoto@ gpo.kumamoto-u.ac.jp.
dependence of the reaction rate on pressure/density.7-9 Under increasing pressure (fluid density), some chemical reactions in supercritical fluids proceed faster10-12 while others slow13,14 or exhibit extreme rate constants.12,15 Diverse effects of the pressure on the reaction rate constant relate both to the nature/properties of the supercritical solvent and to specific solute-solvent interactions at the molecular level. The effect of the pressure on the rate and selectivity of the chemical reaction in SCW is often attributed to the catalytic action of H3O+ and OH- ions, whose concentration changes dramatically with pressure/density variation within the critical region.7,9 The pressure effect may be related also to solvation,16-18 variation of the dielectric constant,17 and others. In the general case, the effect of the pressure on the reaction rate constant is a result of specific interaction of the solvent and reacting chemical components. The aim of the present work was, first, to study experimentally the decomposition and oxidation of the aliphatic nitro compounds in SCW and to elucidate the main kinetic regularities of the reactions, namely, to determine how the reaction rate depends on the pressure and the nature of RNO2 nitro compounds differing in the number of C atoms in R radicals. The second aim is to suggest an explanation of the pressure effect on the apparent rate constants at the decomposition of the named nitro compounds in SCW in the framework of the transition-state (TS) thermodynamic model.19 2. Experimental Methods Experiments on RNO2 conversion in SCW were performed in a tubular flow reactor. Figure 1 shows the reactor setup. The initial mixture (flows 1 and 2) was fed into the reactor (6) by two high-pressure piston
10.1021/ie0496986 CCC: $27.50 © 2004 American Chemical Society Published on Web 11/16/2004
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The reagent conversion depending on the residence time was determined by the equation
dX/dτ ) kC0n(1 - X)n; τ ) 0, X ) 0
Figure 1. Schematic of the continuous-flow reactor system.
pumps (3). Flow 1 consisted of pure water or contained hydrogen peroxide in the oxidation experiments. The water was heated under pressure in heat exchanger 4 and fed to mixer 5. Flow 2, consisting of a mixture of water and a nitro compound, was fed by pump 3 into mixer 5. The flow’s ratio was kept constant and equal to 4, which retained a constant initial concentration of reagents at varying flow rates. The mixture for flow 2 was prepared by adding 1 mL of reagent to 100 mL of water under intensive stirring. Reactor 6 was a spiral stainless steel capillary (i.d. 1.0, o.d. 1.6 mm, and length 7 m) placed in electric furnace 7. The total volume of the reactor and mixer was equal to 5.66 cm3. This allowed the residence time to be varied from 0.5 to 8 min. The outlet mixture was cooled in heat exchanger 8. The pressure in the reactor was controlled by backpressure regulator 9. The samples of gaseous and liquid phases were taken in separator 10. The inlet and outlet reagent concentrations in the liquid-phase samples were measured with a good accuracy of about 5% using a Hewlett-Packard 6890 chromatograph equipped with a 30 m capillary column. Gaseous samples were analyzed using a gas chromatograph equipped with a Unibeads C packed column. 3. Results and Discussion Decomposition of NM (a), NE (b), and NP (c) in SCW. Primary experimental data represented a change in the reagent content (expressed as molar fractions) in the reaction products depending on the residence time. Here, molar fraction means the ratio of the outlet concentration of a reagent to its inlet concentration. Decomposition conditions were as follows: T ) 663.5664 K, P ) 27.2 MPa, reagent inlet concentration ) 0.037 mol/L; residence time varied within 50-500 s that provided the variation of the reagent conversion within 0.2-0.8. Analysis of the phase state of a reactionary mixture under selected pressures and temperatures by means of thermodynamic modeling showed that the selected mixture exists in the supercritical single-phase state.
(1)
where X is the degree of RNO2 conversion, C0 is the inlet concentration of RNO2 (mol/L), n is the apparent reaction order, τ ≡ VR/Q is the residence time (s), VR is the reactor’s volume, and Q is the flow rate (cm3/s). A comparison of the calculated and experimental dependencies showed that kinetic equations of the first order with respect to RNO2 (i.e., n ) 1) described the reagent conversion as a function of the residence time most adequately in all cases. Figure 2 illustrates the dependencies of ln(1 - X) on τ for NM, NE, and NP. The slopes of these lines give the apparent constants of the first-order reactions, which equal 0.0102, 0.0053, and 0.0044 L/s for NM, NE, and NP, respectively, at T ) 663.5-664 K and P ) 27.2 MPa. Analysis of the above data proves that as the number of C atoms in RNO2 increases, the rate of RNO2 decomposition in SCW decreases. In the present experiments, the gaseous products were not sampled for the analysis depending on the residence time; the samples were taken at the residence time when the reagent conversion was high. The analysis showed that the gaseous products of RNO2 decomposition at their conversion degree exceeding 50-70% contained ca. 2% H2 (11-20% at NM decomposition), 20-35% N2, 15-38% CO, 11-22% NO (only at the NM and NP decomposition), 1-2.5% CH4, 3-12% CO2, and N2O traces. From the analysis of these results from the decomposition of RNO2 in SCW, one can assume that at a particular time thermal decomposition of RNO2 on the reactor walls occurs, which explains the hydrogen content in the reaction products. (a) Effect of SCW Pressure/Density. Experiments on NM, NE, and NP decomposition in SCW in the flow reactor showed unambiguously that for all three compounds increasing the pressure caused an increase in the reagent conversion. Experiments on the pressure effect were performed at T ) 664 K and constant residence time. The data obtained on the pressure dependence of the reagent conversion were used to calculate the rate constant in the assumption of the first-order reaction rate. Figure 3 presents the dependencies of the reaction rate constants on the pressure for the three studied compounds. It is seen that the reaction rate constant increases exponentially with increasing pressure: k ) A exp(BP/RT), where A and B are characteristic constants for each reagent. (b) Oxidation Reactions. The studied nitro compounds were oxidized in situ by oxygen evolved by hydrogen peroxide dissolved in water in flow 1 (see Figure 1). Figure 4 presents the change of the molar
Figure 2. Plot of ln(1 - X) against the residence time: (a) NM; (b) NE; (c) NP.
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Figure 4. Dependence of the molar fraction at the oxidation of aliphatic nitro compounds in SCW on the residence time: (a) NM (triangles); (b) NE (diamonds); (c) NP (circles). Table 1. Reactivity of Aliphatic Nitro Compounds reagent
initial concn, mol/L
degree of conversion
CH3NO2 C2H5NO2 1-C3H7NO2
0.037 0.029 0.0224
0.35 0.71 0.79
conversion on the residence time were processed on the assumption of first-order reaction with regard to RNO2 and zero-order reaction with regard to O2. The latter assumption seems to be quite correct because most of work devoted to the oxidation of organic compounds in supercritical fluids (for example, ref 4) report experimentally determined reaction orders with regard to oxygen to be well below unity. The dependence of -ln(1 - X) on τ for the oxidation of NP at P ) 27.3 MPa and T ) 663.5 K proves well the suggestion on the firstorder reaction regarding the initial reagent and the zeroorder reaction regarding oxygen. The first-order constant in this case is equal to 0.0052 L/s. Data of Table 1 show that the oxidation rate of aliphatic nitro compounds in SCW increase close to linear with an increase in the number of C atoms in RNO2. In principle, this observation confirms the suggestion that as the number of CH groups in aliphatic nitro compounds increases, the energy of the R-NO2 bond decreases and, consequently, the reactivity increases.20 However, it remains unclear why the same compounds decomposing in SCW without oxygen demonstrate the “reverse” reactive behavior. 4. Pressure Effect Modeling
Figure 3. Pressure dependence of the apparent rate constants for the decomposition of aliphatic nitro compounds in SCW: (a) NM; (b) NE; (c) NP.
fractions of NM, NE, and NP upon their oxidation in SCW depending on the residence time. Additional experiments were performed to compare the reactivities of NM, NE, and NP oxidized under the same conditions (P ) 24.2 MPa, T ) 683 K, inlet concentration of O2 ) 0.084 mol/L, and τ ) 89 s), and the results are shown in Table 1. The oxygen content in the reaction products changed with the residence time and were not determined, and therefore, the experimental dependencies of the reagent
The above experimental results show that the decomposition rate of NM, NE, and NP in SCW depends strongly on the pressure. Therefore, it seems important to understand the mechanism of such a phenomenon with the use of thermodynamic models. The TS model is one of them.19 According to the TS theory, the chemical reaction proceeds through the TS, which appears at the top of the energy barrier between the initial and final reaction states. In the framework of this theory, the main stage of RNO2 decomposition is the formation of TS, which exists in equilibrium with the initial RNO2: SCW,equilibrium
RNO2 798 [Rσ+NO2σ-]
(2)
Then TS irreversibly decomposes to the reaction products: slowly
[Rσ+NO2σ-] 98 products
(3)
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To a first approximation, a polarized molecule of RNO2 with loose bonds may be considered as the TS in reaction (2). The NO2 group in the RNO2 molecule facilitates delocalization of the negative charge on the carbanion in the hydrocarbon radical toward more electronegative atoms, like oxygen. Subsequent decomposition of the TS to carbcation R+ and nitroanion NO2results in the formation of the diverse reaction products detected in the present experiment. The rate of RNO2 decomposition by eqs 2 and 3 in a plug-flow reactor is described by the equation
dyRNO2/dτ ) -k#y#
(4)
where yRNO2 is the reagent mole fraction, k# denotes the rate constant of limiting stage (3), and y# is the mole fraction of the TS. Equilibrium of reaction (2) is described by the equation
-RT ln K# + RT ln(fTS/fRNO2) ) 0
(5)
where K# is the equilibrium constant and fi ) PyiΦi is the fugacity of the ith reagent (i ) TS and RNO2). Fugacity coefficients Φi ) Φi(y,T,P) are the functions of temperature, pressure, other critical and standard characteristics of the individual reagent, and the molar composition of the mixture. They are calculated using the real-gas equation of state.21 Assuming TS to be an ordinary molecule, the equilibrium constant of reaction (2) may be expressed in terms of variation of the standard Gibbs free energy (∆G#):
-∆G# ) RT ln K#
(6)
Index # is related to the variation of free energy during the process of activation when both the initial reagent and TS are assumed to be in the standard state. The state of ideal gas at the process temperature and zeroapproaching pressure is accepted as the standard state. Taking into consideration eq 5, y# can be calculated through the experimentally determined molar fraction of yRNO2 by the equation
y# ) K#
ΦRNO2 y ΦTS RNO2
(7)
Substituting eq 7 into eq 4, we obtain
dyRNO2 dτ
) -k#K#
ΦRNO2 y ) -kobsyRNO2 ΦTS RNO2
(8)
where
ΦRNO2 kobs ) k#K# ΦTS
(9)
The partial derivative of the fugacity coefficient with respect to pressure at constant temperature and mixture composition is equal to the partial molar volume (V h i) of a component:
(
)
∂ ln Φi ∂P
T
)
V hi RT
(10)
Table 2. Parameters of Equation 12 reagent NM NE NP
∆V h , cm3/mol
k0 × 104, 1/s
-702.6 ( 31.1 -763.3 ( 19.3 -730.8 ( 23.9
2.792 ( 0.305 1.765 ( 0.196 1.407 ( 0.123
Finding the logarithm of eq 9 with its following differentiation and inserting eq 10 give
(
)
∂ ln ΦRNO2 ∂lnΦTS ∂ ln kobs -∆V h# ) (11) ) ∂P ∂P ∂P RT h TS - V h RNO2; i.e., the difference between the ∆V h# ) V partial molar volumes (PMVs) of the TS and reagent is the activation volume of the reaction. A modified method for the calculation of the PMV of the substance in a solvent using the cubic equation of state is presented in the Appendix. In the critical region, the ∆V h # value may be either negative or positive. For example, for the reaction of 2-propanol dehydration in SCW, we obtained the value of ∆V h # equal to -6200 cm3/mol.22 As a rule, such extreme values of ∆V h # prove the fact that even insignificant pressure variation in the critical region causes profound alteration of the fluid density. According to eq 11, at pressure-independent ∆V h# < 0, the apparent reaction rate constant increases exponentially with an increase in the pressure. Exactly this effect is observed at the decomposition of NM, NE, and NP in SCW (see Figure 3). Note that ∆V h #NM, ∆V h #NE, and # ∆V h NP are negative values and independent of the pressure in the interval of 22.7-32.0 MPa at a temperature of 664 K. Integration of eq 11 reduces to
h #P/RT) kobs ) k0 exp(-∆V
(12)
where ln k0 ≡ (ln kobs)Pf0 ) ln(k#K#) because fugacity coefficients ΦRNO2 and ΦTS in eq 11 tend to 1 at P f 0. Unknown parameters k0 and ∆V h # in eq 11 were calculated by the least-squares method and are presented in Table 2. The data of Table 2 show that the studied nitro compounds had similar values of activation volume ∆V h# within the confidence interval. At the same time, the decomposition rate of the nitro compounds, characterized by k0, decreased almost linearly with an increase in the number of C atoms (nC) in the molecule. The experimental data showed that the activation volumes in the studied reactions were independent of the pressure. However, according to eq 10, the PMVs of the reagents and TS must be pressure-dependent. So, to verify the validity of using the TS theory for modeling of the studied reactions, it is necessary to demonstrate that, although PMVs of the reagents vary with pressure, their difference remains constant. Lines 1-3 in Figure 5 show the pressure dependencies of the PMVs of the studied aliphatic compounds in SCW calculated by the method proposed in the Appendix when the binary coefficients kij and cij in the equation of state equal zero. As shown in Figure 5, the pressure dependencies of PMVs of the studied compounds in SCW are similar in shape but differ in value, mainly in the critical region. Under supercritical conditions, the interactions between the reagent and solvent molecules are essentially different, and the values of kij and cij that characterize these interactions are needed in order to improve the calculation accuracy.
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Figure 5. Pressure dependencies of the PMV at zero coefficients of binary interactions: curve 1, NM-SCW; curve 2, NE-SCW; curve 3, NP-SCW. Curve 4: pressure dependence of the PMV of NM-SCW at kij ) -0.1 and cij ) 0.1. T ) 665 K.
On the basis of the earlier proposed calculation method22 and “scanty” experimental data reported in the literature on NM equilibrium in SCW at atmospheric pressure,23 we calculated the following numerical values: kij ) -0.1 and cij ) 0.1. Line 4 in Figure 5 shows the pressure dependence of NM PMV in SCW calculated using these kij and cij values. The PMV behavior and values are strongly dependent on the kij and cij numerical values. However, numerical values of these coefficients for water-containing binary compositions are known to vary strongly with varying temperature and pressure, especially in the critical region. Taking into account the results of earlier studies and the found dependencies of kij and cij on temperature and pressure, we estimated numerical values of these coefficients for the NM-water pair to vary within kij ) -(0.3-0.5) and cij ) 0.3-0.5. To calculate the TS PMV, it is necessary to select the TS model and determine its physical parameters. It is reasonable to suggest to a first approximation that critical parameters of the TS considered as the polarized RNO2 molecule with loose bonds remain equal to critical parameters of the initial molecule,19 whereas the coefficients of binary interaction kij and cij change. Besides, these coefficients are assumed to be a function of the pressure. In this regard, the calculation of the TS PMV reduces to minimization of the sum of squared deviations between the calculated and so-called experimental values V h exp h +V h RNO2: TS ) ∆V
Q)
∑k
(
)
V h calc h exp TS - V TS V h exp TS
2
f min
(13)
where V h calc TS is the TS PMV calculated by the proposed model (see the Appendix A). In eq 13, the determination of kij and cij was solved in two ways when kij and cij are pressure-independent, and the function of pressure is
kij ) A0 + A1/P + A2P and cij ) B0 + B1/P + B2P (14) where A0, A1, A2, B0, B1, and B2 are the required unknown model parameters. As a result of the minimi-
Figure 6. Pressure dependence of the PMV: curve 1, NM-SCW at kij ) -0.3 and cij ) 0.3; curve 2, TS calculation at kij ) -0.5346 and cij ) 0.5240; curve 3, TS calculation at variable kij and cij; curve 4, TS “experiment”. T ) 665 K.
zation procedure, we obtained the linear dependence of kij and cij on pressure with coefficients
A0 ) -8.020 ( 0.158
A1 ) 0
B0 ) -7.904 ( 0.243
B1 ) 0 B2 ) 0.033 ( 0.001 (15)
A2 ) 0.030 ( 0.001
Figure 6 illustrates the results of the TS PMV and NM PMV in water (V h RNO2) calculations. Curve 1 represents the pressure dependence of V h RNO2 calculated at k12 ) -0.3 and c12 ) 0.3. Curve 4 represents the “experimental” pressure dependence of the TS PMV calculated by h + V h RNO2, where ∆V the equation V h exp h ) -700 TS ) ∆V 3 cm /mol obtained in the experiment (see Table 2). Curve 2 is the calculated pressure dependence of the TS PMV obtained using constant values kij ) -0.53 and cij ) 0.52 resulting from the solution of eq 13. Curve 3 represents the pressure dependence of the TS PMV calculated with variable kij and cij determined by eq 14 with coefficients (15). Figure 6 shows that the pressure dependence of the TS PMV calculated using variable kij and cij agrees well with the “experimental” dependence. 5. Conclusion Principal regularities on the decomposition and oxidation of aliphatic nitro compounds (NM, NE, and NP) in SCW were studied using a flow reactor. Reaction rate constants were calculated on the assumption of firstorder reaction. It was shown that the rate of NM, NE, and NP decomposition strongly depended on the pressure and varied over a wide range. Analysis of the results obtained showed that the oxidation rate of aliphatic nitro compounds in SCW linearly increased with an increase in the number of C atoms in the compound, while the decomposition rate of aliphatic nitro compounds in SCW linearly decreased with an increase in the number of C atoms. The effect of the pressure on the rate constants on the decomposition of NM, NE, and NP in SCW was explained on the basis of a thermodynamic model in the framework of the TS theory. Application of the TS theory proved the experimental fact that the reaction activation volume was
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independent of pressure. The nature of the initial nitro compounds and TS differ only in the character of the solvent-reagent interactions. The studied nitro compounds showed similar values of TS activation volumes, which suggested that they have the same TS nature in all three cases.
Differentiation of eq A4 with respect to am and bm gives
∂P ∂P 1 )) ∂am Vm(Vm + bm) ∂bm am RT + (A7) 2 (Vm - bm) Vm(Vm + bm)2
Acknowledgment This work is supported in part by the 21st century COE program of Pulsed Power Science, Japan Society for the Promotion of Science and in part by ISTC, project #2383. Appendix Calculation of the PMVs. The PMV is the partial derivative of the mixture volume with respect to number of moles
V hj )
[ ] ∂(nVm) ∂nj
(A1)
T,P,ni,i*j
∂Vm ∂Vm ∂n ∂V ∂(nVm) ) ) Vm +n ) Vm + n ∂ni ∂ni ∂ni ∂ni ∂ni (A2)
[
]
∂P/∂ni ∂Vm ∂P ∂am 1 ∂P ∂bm ) )+ ∂ni ∂P/∂Vm ∂P/∂Vm ∂am ∂ni ∂bm ∂ni
(A3)
where am and bm are the coefficients of the RedlichKwong-Soave (RKS) equation of state:
P)
am RT Vm - bm Vm(Vm + bm)
(A4)
and the functions of temperature and molar composition of a mixture,21 which can be expressed as
am )
1
∑ij aijyiyj ) 2∑ij aijninj ) n
bm )
1
1 n
nTAn
2
∑ij bijyiyj ) 2∑ij bijninj ) n
1 n
nTBn (A5)
2
where n is the column vector with elements ni, A and B are the matrixes with elements aij and bij. Coefficients aij and bij are determined by the known mixing rules using individual component coefficients of the RKS equation:
aij ) (1 - kij)xaiaj
(
∂am 2 1 ∂n 1 ∂nT ) - 3nTAn + 2 An + 2nTA ∂ni ∂n ∂n n n n i i 2 1 ) - am + ( n n2
bij ) (1 - cij)(bi + bj)/2
(A6)
where ai, aj, bi, and bj are the coefficients of the ith and jth components21 and kij and cij are the empirical coefficients of binary interactions between the ith and jth components.
)
∑k aiknk + ∑k akink) ) 2 n2
where Vm is the molar volume of the mixture (L/mol), nj is the number of moles of the jth component, and n ) ∑jnj. Because the current literature demonstrates some ambiguity regarding the models for calculation of PMVs based on the equations of state, let us consider a correct procedure for model derivation in more detail. So,
V hi ≡
Next, the equation for the am derivatives is given:
(
∑k aiknk - amn)
(A8)
Similarly, one can obtain the equation for the bm derivatives:
∂bm ∂ni
)
2
( n2
∑k biknk - bmn)
(A9)
Inserting eqs A7-A9 into eq A1, we obtain the equation for the calculation of PMVs of both initial reagents and TS. Literature Cited (1) Aymonier, C.; Beslin, P.; Jolivalt, C.; Cansell, F. Hydrothermal oxidation of a nitrogen-containing compounds: the funuron. J. Supercrit. Fluids 2000, 17, 45-54. (2) Cocero, M. J.; Alonso, E.; Torio, R.; Vallelado, D.; FdzPolanco, F. Supercritical water oxidation in a pilot plant of nitrogenous compounds: 2-propanol mixtures in the temperature range 500-750 °C. Ind. Eng. Chem. Res. 2000, 39, 3007-3016. (3) Iyer, S. D.; Nicol, G. R.; Klein, M. T. Hydrothermal reactions of 1-nitrobutane in high-temperature water. J. Supercrit. Fluids 1996, 9, 26-32. (4) Helling, R. K.; Tester, J. W. Oxidation compounds and mixtures in SCW. Environ. Sci. Technol. 1988, 22, 1319-1324. (5) Savage, P. E.; Gopalan, S.; Mizan, T. I.; Martino, Ch. J.; Brock, E. E. Reactions at supercritical conditions: Applications and fundamentals. AIChE J. 1995, 41, 1723-1778. (6) Savage, P. E. Organic chemical reactions in supercritical water. Chem. Rev. 1999, 99, 603-621. (7) Anikeev, V. I.; Yermakova, A. The effect of density of supercritical fluid on the constant rate of isopropyl alcohol dehydration. Russ. J. Phys. Chem. 2003, 77 (2), 265-268. (8) Baliga, B. T.; Whalley, E. Effect of pressure and temperature on the rate the acid-catalyzed hydration of ethylene. Can. J. Chem. 1965, 9, 2453-2456. (9) Narayan, R.; Antal, M. J. Influence of pressure on the acidcatalyzed rate constant for 1-propanol dehydration in supercritical water. J. Am. Chem. Soc. 1990, 112, 1927-1931. (10) Guo, Y.; Akgerman, A. Hydroformylation of propylene in supercritical carbon dioxide. Ind. Eng. Chem. Res. 1997, 36, 45814585. (11) Klein, M.; Mentha, Y. G.; Torry, L. A. Decoupling substituted and solvent effects during hydrolysis of substituted anisoles in supercritical water. Ind. Eng. Chem. Res. 1992, 31, 182-187. (12) Roberts, C. B.; Zhang, J.; Chateauneuf, J. E.; Brennecke, J. F. Laser flash photolysis and integral equation theory to investigate reactions of dilute solutes with oxygen in supercritical fluids. J. Am. Chem. Soc. 1995, 117, 6553-6560. (13) Ellington, J. B.; Park, K. M.; Brennecke, J. F. Effect of local composition enhancements on the esterification of phthalic anhydride with methanol in supercritical carbon dioxide. Ind. Eng. Chem. Res. 1994, 33, 956-974.
Ind. Eng. Chem. Res., Vol. 43, No. 26, 2004 8147 (14) Roek, D. P.; Chateauneuf, J. E.; Brennecke, J. F. A fluorescence lifetime and integral equation study of the quenching of naphthalene fluorescence by bromoethane in super- and subcritical ethane. Ind. Eng. Chem. Res. 2000, 39, 3090-3096. (15) Yu, J.; Eser, S. Kinetics of supercritical-phase thermal decomposition of C10-C14 normal alkanes and their mixtures. Ind. Eng. Chem. Res. 1997, 36, 585-591. (16) Chialvo, A. A.; Cummings, P. T.; Kalyuzhnyi, Yu. V. Solvation effect on kinetic rate constant of reactions in supercritical solvents. AIChE J. 1998, 44, 667-680. (17) Johnson, K. P.; Haynes, C. Extreme solvent effects on reaction rate constants at supercritical fluid conditions. AIChE J. 1987, 33, 2017-2026. (18) Kajimoto, O. Solvation in supercritical fluids: Its effects on the energy transfer and chemical reactions. Chem. Rev. 1999, 99, 355-389. (19) Glasstone, S.; Laidler, K.; Eyring, H. The theory of rate processes; Frick Chemical Laboratory, Princeton University: New York and London, 1941. (20) Khrapkovskii, G. M.; Shamov, A. G.; Shamov, G. A.; Shlyapochikov, V. A. Some peculiarities of the influence of mo-
lecular structure on the activation energy of radical gas-phase decomposition of aliphatic nitro compounds. Russ. Chem. Bull. 1996, 45 (10), 2309-2317. (21) Sandler, S. I. Chemical and Engineering Thermodynamics; John Wiley & Sons: New York, 1999. (22) Anikeev, V. I.; Yermakova, A. Coefficient of binary interaction for the RKS equation of state for a mixture of undercritical components. Theor. Fundam. Chem. Eng. (in Russian) 1998, 32 (5), 508-214. (23) Sazonov, V. P.; Marsh, K. N.; Hefter, G. T. IUPAC-NIST solubility data series. 71. Nitromethane with water or organics solvents: Binary systems. J. Phys. Chem. Ref. Data 2000, 29 (5), 1167-1332.
Received for review April 14, 2004 Revised manuscript received September 3, 2004 Accepted September 10, 2004 IE0496986
