Kinetics of Methylene Chloride Hydrolysis and the Salt Effect under

Jan 30, 2001 - Torry et al.8 showed an interesting salt effect, which increased the ..... Benson, S. W. The Foundations of Chemical Kinetics; McGraw-H...
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Ind. Eng. Chem. Res. 2001, 40, 1026-1031

KINETICS, CATALYSIS, AND REACTION ENGINEERING Kinetics of Methylene Chloride Hydrolysis and the Salt Effect under Hydrothermal Conditions Yoshito Oshima, Budianto Bijanto, and Seiichiro Koda* Department of Chemical System Engineering, School of Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan

The reaction progress of methylene chloride under hydrothermal conditions was pursued using a corrosion-resistant flow reactor made from titanium tubing, paying attention to minimize the contribution of the preheating zone for the reaction. The relation between the CH2Cl2 conversion and residence time showed that the hydrolysis is first order in CH2Cl2. The rate constant increased monotonically as the temperature was raised but dropped to a large extent above the critical temperature. A relatively small increase of the rate constant was observed in the presence of NaCl under 360 °C. The kinetic behavior could be explained based on a SN2 mechanism under subcritical conditions, and the sudden drop of the rate constant at the critical point was attributed to the abrupt decrease of the dielectric constant of water. The salt effect was also analyzed along the same context. The reaction rate and the detailed reaction progress, however, under supercritical conditions are not yet fully understood. Introduction Supercritical water oxidation (SCWO) is a promising technology for the destruction of hazardous chemical compounds. High destruction efficiencies of this process have been demonstrated for a wide variety of organic materials, and most of the organic compounds are oxidized to CO2 and H2O within a reasonable residence time. Many chlorinated compounds are widely used as a solvent in the manufacturing industry, and it is important to develop effective means for the cleanup of water resources contaminated with these compounds. SCWO is expected to be applicable for the destruction for these chlorinated compounds. However, a detailed reaction mechanism of SCWO of chlorinated compounds is not yet clear, where the hydrolysis reaction is supposed to proceed together with the oxidation reaction. Investigation of the kinetics and mechanism of hydrolysis reactions of chlorinated compounds is important not only for practical applications but also for understanding the solvent effect of water in sub- and supercritical water. Methylene chloride (CH2Cl2) is chosen in this paper as a representative model of chlorinated compounds because it has been a widely used solvent in the manufacture of fine chemicals and is a common environmental contaminant. In previous researches, Tester et al.1-4 investigated the kinetics of CH2Cl2 hydrolysis in sub- and supercritical water. In the decomposition of CH2Cl2 in supercritical water,1 it was observed that most of the reactant was decomposed in the preheating zone where the temperature was still subcritical. Thus, they were forced to estimate the rate constants under supercritical conditions, subtracting the exclusively * Corresponding author. Tel.: +81-3-5841-7327. Fax: +813-5841-7255. E-mail: [email protected].

Figure 1. Schematic drawing of the apparatus.

large contribution of the preheating zone from the total reaction progress. In their recent paper,4 they used a batch reactor system in which a pulse of a regulated amount of CH2Cl2 was introduced into the reaction cell without being preheated, to avoid the decomposition in the preheating zone. They analyzed the experimental results with a Kirkwood model and concluded that a local maximum in the rate constant near the critical point of water is consistent with the change of solvent’s dielectric constant. In the present study, we designed a corrosionresistant flow reactor with a rapid-heating system and aimed to obtain precise kinetic information on CH2Cl2 hydrolysis in sub- and supercritical water. Experiments with addition of salt were also performed under sub-

10.1021/ie0005598 CCC: $20.00 © 2001 American Chemical Society Published on Web 01/30/2001

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1027 Table 1. First-Order Rate Constants of Dichloromethane Disappearance temp/°C 250 275 300 340 360 400 450 360 360 360 360 360

[CH2Cl2]0/(mmol dm-3) 0.6-5.1 0.7-4.9 1.1-5.6 1.0-4.9 0.9-4.4 0.3-1.1 0.2-0.8 3.4 3.4 3.3 3.3 3.3

FCH2Cl2/Fwatera 1 4- /9 1/ -1/ 4 9 1/ -1/ 4 9 1/ -1/ 4 9 1/ -1/ 4 9 1/ -1/ 4 9 1/ -1/ 4 9 1/ 4 1/ 4 1/ 4 1/ 4 1/ 4 1/

rate constant k/s-1 b 10-2

2.62 ( 1.27 × 2.51 ( 1.48 × 10-2 7.16 ( 2.06 × 10-2 1.49 ( 0.23 × 10-1 2.08 ( 0.22 × 10-1 2.53 ( 0.43 × 10-2 2.07 ( 0.91 × 10-2 2.14 ( 0.29 × 10-1 1.99 ( 0.18 × 10-1 1.94 ( 0.06 × 10-1 2.37 ( 0.31 × 10-1 2.70 ( 0.42 × 10-1

conditionsc standard standard standard standard standard standard standard oxidation, [O2] ) 4.7 mmol dm-3 oxidation, [O2] ) 23.7 mmol dm-3 12 mmol dm-3 of NaCl added 58 mmol dm-3 of NaCl added 117 mmol dm-3 of NaCl added

aF b CH2Cl2 and Fwater designate the volumetric flow rate of a CH2Cl2 solution and water, respectively. ( value corresponds to 95% confidence interval. c Standard condition: pressure ) 24.1 MPa, without O2, without NaCl.

critical conditions for a better understanding of the reaction mechanism. Experimental Section The experiments were performed using a corrosionresistant flow reactor made from titanium tubing. The fact that the corrosion was negligibly small was supported by measuring the titanium ion to be less than 0.01 ppm always in the effluent, using ICP analysis. Figure 1 is a schematic drawing of the apparatus used in this study. The aqueous solution of CH2Cl2 and water were separately pumped using high-pressure HPLC pumps (Tosoh CCPP-D). The reactor (3.2 mm o.d., 1.6 mm i.d., and 0.5 or 3 m length) and the preheating tube of water (SUS-316 tubing of either 1.6 mm o.d. × 14 m length or 3.2 mm o.d. × 8 m length) were immersed in a fluidized sand bath. To keep the contribution of the preheating stage where the hydrolysis reaction of CH2Cl2 may proceed to some extent as small as possible, the solution of CH2Cl2 was directly introduced into the reactor without preheating. The flow rate of preheated water was always at least 4 times larger than that of the solution of CH2Cl2 so as to heat up the solution of CH2Cl2 very quickly to the reaction temperature after mixing two streams. For example, the temperature of the solution was estimated based on the heat balance to be ca. 382 °C when the CH2Cl2 solution at ambient temperature and the preheated water at 400 °C were mixed with the volumetric ratio of 1:4 in the preheating zone. The fluid emitted from the reactor was promptly cooled by external cooling-water flow, depressurized using a back-pressure regulating valve (GO Inc., BP66), and separated to gaseous and liquid parts in a gasliquid separator. The quantitative analysis of the liquid sample was performed using a HPLC (Shimadzu LCVP) equipped with a Jasco Finepak SIL C18S column. The mobile phase was acetonitrile and water (3:7 by volume), and the UV absorbance was monitored at 193 nm. Chloride ion (Cl-) was monitored using ion chromatography (Jasco Gulliver series) equipped with a Shodex ICI-524A column. Some of the samples were also analyzed with ICP-MS (Hewlett-Packard 4500) to detect the dissolved metals resulting from the corrosion of reactor material. The hydrolysis experiments were conducted over the temperature range of 250-450 °C, and the typical pressure was 24.1 MPa. The concentration of the CH2Cl2 feed solution was typically 0.03 mol/ dm3. The concentration of CH2Cl2 at the inlet stage of the reactor was thus usually 0.2-5.6 mmol dm-3 (as shown in the table and figure captions in the Results section), according to the different mixing ratio of the

Figure 2. First-order plot of CH2Cl2 hydrolysis under subcritical conditions. (Reaction temperature (°C): 250 (4), 300 (3), 340 (0), and 360 (O). The filled circles with dotted line correspond to the result in the presence of oxygen at 4.7 mmol dm-3.)

feed solution and the preheated water flow as well as the reaction temperature and pressure. When the effect of O2 was investigated, an appropriate amount of H2O2 was mixed in the main water flow. The H2O2 added was completely decomposed to H2O + O2 in the preheating tube, as discussed in the previous report.5 When H2O2 was not added, the concentration of O2 in the solution was estimated to be less than 0.01 of that of CH2Cl2, based on Henry’s constant of O2 in water at ambient temperature before the high-pressure pump. Results Kinetic Behavior. The time profiles of CH2Cl2 conversion in subcritical (250-360 °C) conditions were investigated. The larger conversion of CH2Cl2 was achieved at higher reaction temperature. Using the experimental data, ln(1 - X), where X designates the CH2Cl2 conversion, was plotted against the residence time, whose results are shown in Figure 2. The good linear relationship between ln(1 - X) and the residence time implies that the hydrolysis is a first-order reaction with respect to the CH2Cl2 concentration. The obtained first-order rate constants are tabulated in Table 1. ( means the interval of 95% confidence in the leastsquares fitting. We pursed the reaction in the presence of O2 at 360 °C and recognized that the conversion of CH2Cl2 was not affected by the presence of O2, the amounts of which were 1.35 and 6.75 times as large as the stoichiometric necessity according to CH2Cl2 + O2 f CO2 + 2HCl. Some typical plots are shown in Figure 2, together with the results without any O2 added. The rate constants are also tabulated in Table 1. The O2 oxidation does not contribute to the initial consumption of CH2Cl2.

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Figure 3. Arrhenius plot of the rate constant obtained in the present study (b), together with the experimental results in the previous report4 (0) and the theoretical curve modeled by Marrone et al.1 The dotted line corresponds to the corrected rate constants by taking the effect of the water density on the theoretical rate constant into consideration.

The Arrhenius plot of the rate constant is shown in Figure 3, together with the experimental results in the previous report4 and the theoretical curve modeled by Marrone et al.1 The first-order rate constants of CH2Cl2 disappearance at temperatures over the critical temperature of water are also shown in Figure 3. It should be noted that, in the supercritical region, the first-order plots stay almost on a straight line, but the y intercept is not zero. Assuming that the reaction proceeds to some extent in the preheating as well as the cooling stages and that the above-mentioned contributions are not strongly dependent on the adopted residence time, the slope of the plot is considered to correspond to the first-order reaction progress at the given supercritical temperature. As shown in Figure 3, the rate constant in the range above the critical temperature drops to a large extent and has little dependence on the reaction temperature. The profile of the obtained rate constants in Figure 3 shows a trend very similar to the result in the previous experiments by Salvatierra et al.4 The characteristic temperature behavior of the CH2Cl2 hydrolysis rate is now supported by both the present experiments and the previous experiments,4 which have been carried out using a quite different experimental setup. Effect of NaCl Addition to the Reaction Rate. To gain more information about the reaction mechanism, several hydrolysis experiments were conducted in the presence of added NaCl. Because the solubility of salts in supercritical conditions is very low, we just performed the experiments in subcritical water, which affords sufficient solubility of salts. The dependence of the firstorder rate constant on the NaCl concentration is shown in Figure 4. The straight line in Figure 4 corresponds to the result of the regression analysis, assuming the reaction rate obeys the equation

ln(1 - X) ) -kt ) -k0(1 + a[NaCl])t

(1)

where k0 is the rate constant in the absence of NaCl. The calculated value of the slope, a, is 0.52 ( 0.12. It is thus suggested that the addition of NaCl caused an increase of the reaction rate, by ca. 25% in the presence of 0.1 mol dm-3 NaCl. Discussion Temperature Dependence of the Rate Constant and Reaction Mechanism. The nature of the CH2Cl2

Figure 4. Effect of the NaCl addition on the hydrolysis rate constant at 360 °C. The concentration of CH2Cl2 at the inlet of the reactor is 3.3 mmol dm-3.

hydrolysis is well described by Marrone et al.1 According to them, the reaction consists of the sequential reactions

CH2Cl2 + H2O f CH2ClOH + HCl and

CH2ClOH f CH2O + HCl The first step is rate-determining. The first step proceeds along with a bimolecular type SN2. The attacking nucleophilic reagent is H2O rather than OH-, considering the quite different concentrations between H2O and OH- under the present neutral and/or acidic conditions. Marrone et al.1 searched for the transition structure of the above reaction by ab initio calculation, and the combination with a Kirkwood theory was adopted for incorporating the solvent dielectric constant effect on the stability of the reactants and transition state. The activation energy was taken from the experimental results at a lower temperature region where the effect of the dielectric constant as well as the water density on the reaction rate is negligibly small. The predicted rate constant by Marrone et al.1 (later drawn also by Salvatierra et al.3) as a function of the reaction temperature is already reproduced from their work4 in Figure 3, together with the present experimental results and also those by Salvatierra et al.4 We consider it to be more adequate to correct the first-order rate constant against the water density change along with the temperature change. This is because the observed rate constant k is, exactly speaking, k2[H2O], where k2 is the bimolecular rate constant, provided that the reaction mechanism is bimolecular and the nucleophile is water. The corrected theoretical rate constants against the water density change are also plotted in Figure 3 by the dotted line. The correction is small in the subcritical region even near the critical temperature, while the correction is substantial in the supercritical region. The experimental results of the present work and those by Salvatiera et al.4 are in good agreement, in particular, in the subcritical region. It is worth noticing that the maximum of the rate constant is found just below the critical temperature in the present experiments. The large drop of the rate constant is observed near the critical temperature in both of the two experiments. These results are in good accordance with the prediction (regardless of the correction of the density effect).

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In the supercritical region, the experimental rate constant drops to a large extent in accordance with the prediction. However, the degree is smaller compared to the prediction, when the correction of the density change is performed. This problem will be discussed later. Similar, very interesting behavior of the hydrolysis rate constants near the critical point is also found for different hydrolysis reactions. For example, Krammer and Vogel6 reported that the ethyl acetate hydrolysis has a maximum rate near 350 °C, and they attributed this behavior to the change of the dominant reaction mechanism due to the large difference in the dielectric constant between the sub- and supercritical water. The characteristic temperature effect such as that found in the CH2Cl2 hydrolysis thus seems to be rather ubiquitous in hydrolysis reactions. Effect of NaCl Addition and the Reaction Mechanism. Understanding of the salt effects is important from two different viewpoints. First, the hydrolysis as well as oxidation in hydrothermal water is often carried out in the coexistence of various salts in practical applications for destruction of exhaust materials. Thus, the present finding that the existence of NaCl does not retard the hydrolysis reactions but rather accelerates them is indeed desirable. Second, the study of the salt effect is expected to help in understanding the reaction mechanism, though the analyses so far are still in an infant stage. Among them, Huppert et al.7 studied the salt effect on the hydrolysis reaction of o-methoxyphenol in supercritical water and suggested a polar transition state for qualitatively explaining the increase of the rate constant with the increase of the salt concentration. Torry et al.8 showed an interesting salt effect, which increased the reaction rate at a small salt concentration and then decreased it, on the hydrolysis of dibenzyl ether and benzylphenylamine. Very recently, Penninger et al.9 studied the hydrolysis of diphenyl ether at superctitical temperatures and analyzed the corresponding salt effect employing a SN1 proton-catalyzed mechanism. On the other hand, the structure of NaCl solutions has been studied from ambient to supercritical conditions using a molecular dynamics simulation method as well as experimental methods.10 It is established that Na+ and Cl- ions are mostly or partly dissociated and effectively hydrated in water at the high dilution. However, the physicochemical nature of the hydration shells surrounding the ionic species are not enough known to allow for us to analyze the reaction progress in the neighborhood of the ionic species. Thus, at present, the effect of neutral salt will be analyzed using a continuum dielectric theory11 as shown below. The rate constant k for the reactions

AzA + BzB f ABzA+zB

zAzBe2λ 1/2 k I ) k0 4π0rkBT

(3)

where

λ)

(

2e2 0rkBT

)

log

k ) 4.9zAzBI1/2 k0

1/2

(4)

(5)

gives about a 10 times larger salt effect than what was found experimentally. The idea is thus supported that the reaction responsible for the hydrolysis is not proceeding between ionic species, which is not in disagreement with the SN2 reaction mechanism. At the same time, it is important to notice that the increase of the rate constant in the presence of NaCl is contrary to the common ion effect usually observed in SN1-type reactions. The small positive salt effect observed may be explained considering that an increase in the ionic strength stabilizes a polar transition state in the SN2 reaction. Marrone et al.1 predicted the rate constant using the Kirkwood theory described by the following equation:

ln

(

)

NA(1 - r) µ*2 µA2 µB2 k ) 4π0RT(2r + 1) r*3 rA3 rB3 k0

(6)

Here, NA is Avogadro’s constant, µ, the dipole moment, and ri, the equivalent spherical radius of the species. The subscripts *, A, and B describe the transition state and the individual reactants, respectively. Ab initio calculation was adopted for obtaining the dipole moment and the equivalent spherical radius of the transition state. The obtained results were successfully applied for explaining the temperature effect of the rate constant as already discussed. We will adopt the same idea for explaining the salt effect. In the presence of neutral salt, water molecules are considered to gather around the ionic species of the dissolved salt and the local density of the surrounding water is expected to increase. The increase of the density results in an increase of the dielectric constant, which then causes an increase of the hydrolysis reaction rate according to the Kirkwood theory, provided that the SN2 reaction indeed proceeds in the neighborhood of the ionic species as well. The increase of the density and the dielectric constant surrounding the ionic species can be estimated according to the procedure of Quint and Wood.12 They derived the following equation relating the distance r from the center of the ionic species, the density F, and the dielectric constant r based on the continuum dielectric model:

(2)

between ionic species of charges zA and zB in the medium of the dielectric constant r is described as

ln

Here, k0 is the rate constant in the gas phase, e, the unit charge, r, the (relative) dielectric constant, kB, the Boltzmann constant, and I, the ionic strength. Adopting the dielectric constant at 360 °C and 24.1 MPa, which is ca. 13, we obtain the following equation: This equation

e2

r4 ) (4π0r)2

∫F

(7)

2

F 0

0βF2

( ) ∂r ∂F

dF

T

Here, 0 is the permittivity of the vacuum, F0 is the density of the medium at infinity, and β is the isothermal compressibility. At the same time, the dielectric constant is related to density according to the equation derived by Uematsu and Franck.13 The value of β can be derived from the steam table.14 The obtained density and dielectric constant distributions at r from the center

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Summary and Conclusions

Figure 5. Density and dielectric constant distribution as a function of distance from the center of the ionic species at 360 °C and 24.1 MPa.

of the ionic species in the subcritical water at 360 °C and 24.1 MPa are shown in Figure 5. The relative reaction rate k2[H2O] at the distance r against the rate at the bulk r ()13) can be estimated by adopting eq 6, considering the water density effect altogether. The obtained relative values at r are integrated in the sphere surrounding the ionic species from r ) 0.2 to 1.0 nm. The reaction rate is then summed up for all of the existing Na+ and Cl- altogether, assuming the ions are completely isolated from each other. The region outside the 1 nm sphere is treated as the bulk. Thus, we estimated the increment of the reaction rate against the concentration of the dissolved NaCl. The individual values of the dipole moment and the equivalent spherical radius were taken from Tables 3 and 4 of Marrone et al.1 Because the transition state structure is dependent on the dielectric constant of the medium, we adopted the average values within the range listed in their table. The adopted equivalent spherical radii were 0.214, 0.298, and 0.326 nm for H2O, CH2Cl2, and the transition state, respectively. While the adopted dipole moments were 1.89, 1.79, and 9.08 D for H2O, CH2Cl2, and the transition state, respectively. The calculated increase of the reaction rate was 7.8% at the ionic strength of 0.1 mol dm-3, neglecting the effect of the decrease in the water density in the bulk region. When the largest dipole moment of the transition state at r ) 1.3 was employed, the increase of the rate constant calculated was 9.3%. Though the present prediction, i.e., less than 9.3%, is smaller than the experimental increase obtained in Figure 4, we consider that the experimental increase is mostly understood on the basis of the above context, noting the crudeness of the theory. Reactions under Supercritical Conditions. We could not obtain enough information for discussing the reaction in the supercritical temperature region. One important thing is, however, that the observed rate constant might consist of some other reactions other than the hydrolysis reactions. Even the rate constant by Salvatierra et al.4 seems to be larger than the prediction of the hydrolysis reaction, when corrected for the density effect. Some heterogeneous reaction may proceed to some extent in addition to a small contribution of radical reactions at higher temperatures than the critical temperature. More detailed information about the hydrolysis and oxidation reactions may be desirable in the supercritical water.

The reaction of CH2Cl2 in subcritical water is exclusively hydrolysis even in the presence of some amount of O2. The reaction rate which is proportional to the first order to the CH2Cl2 concentration demonstrates a very interesting temperature dependence, that is, its abrupt decrease near the critical temperature. These kinetic behaviors could be quantitatively described by the theory derived by Marrone et al.1 assuming a SN2 reaction mechanism in the subcritical region. The small salt effect observed experimentally also seems to be in agreement with the present mechanism. However, the reaction progress and mechanism in the supercritical region still remain to be solved. Acknowledgment This work is supported by Research for the Future Program of the Japan Society for the Promotion of Science (96P00401), which is greatly appreciated. Nomenclature a ) coefficient of the apparent first-order rate constant proportional to the NaCl concentration e ) unit charge [C] I ) ionic strength [mol dm-3] k ) first-order rate constant [s-1] k0 ) first-order rate constant in the gas phase [s-1] k0 ) first-order rate constant in the absence of NaCl [s-1] k2 ) second-order rate constant [dm3 mol-1 s-1] kB ) Boltzmann constant [J K-1] NA ) Avogadro’s number [mol-1] r ) distance from the center of the ionic species [nm] ri ) equivalent spherical radius of species i [nm] R ) gas constant [J K-1 mol-1] t ) residence time [s] T ) absolute temperature [K] X ) conversion zi ) charge of ionic species i [C] β ) isothermal compressibility [m2 N-1] r ) relative dielectric constant 0 ) permittivity of the vacuum [C2 m-1 J-1] µi ) dipole moment of species i [D] F ) density [kg m-3] F0 ) density of the medium at infinity [kg m-3]

Literature Cited (1) Marrone, P. A.; Arias, T. A.; Peters, W. A.; Tester, J. W. Solvation Effects on Kinetics of Methylene Chloride Reaction in Sub- and Supercritical Water: Theory, Experiment, and ab initio Calculations. J. Phys. Chem. A 1998, 102, 7013. (2) Marrone, P. A.; Gschwend, P. M.; Swallow, K. C.; Peters, W. A.; Tester, J. W. Product Distribution and Reaction Pathways for Methylene Chloride Hydrolysis and Oxidation under Hydrothermal Conditions. J. Supercrit. Fluids 1998, 12, 239. (3) Tester, J. W.; Marrone, P. A.; DiPippo, M. M.; Sako, K.; Reagan, M. T.; Arias, T.; Peters, W. A. Chemical Reactions and Phase Equilibria of Model Halocarbons and Salts in Sub- and Supercritical Water (200-300 bar, 100-600 °C). J. Supercrit. Fluids 1998, 13, 225. (4) Salvatierra, D.; Taylor, J. D.; Marrone, P. A.; Tester, J. W. Kinetic Study of Hydrolysis of Methylene Chloride from 100 to 500 °C. Ind. Eng. Chem. Res. 1999, 38, 4162. (5) Thammanayakatip, C.; Oshima Y.; Koda, S. Inhibition Effect in Supercritical Water Oxidation of Hydroquinone. Ind. Eng. Chem. Res. 1998, 37, 2061. (6) Krammer, P.; Vogel, H. Hydrolysis of Esters in Subcritical and Supercritical Water. J. Supercrit. Fluids 2000, 16, 189. (7) Huppert, G. L.; Wu, B. C.; Townsend, S. H.; Klein, M. T.; Paspek, S. C. Hydrolysis in Supercritical Water: Identification

Ind. Eng. Chem. Res., Vol. 40, No. 4, 2001 1031 and Implications of a Polar Transition State. Ind. Eng. Chem. Res. 1989, 28, 161. (8) Torry, L. A.; Kaminsky, R.; Klein, M. T.; Klotz, M. R. The Effect of Salts on Hydrolysis in Supercritical and Near-critical Water: Reactivity and Availability. J. Supercrit. Fluids 1992, 5, 163. (9) Penninger, J. M. L.; Kerste, R. J. A.; Baur, H. C. L. Hydrolysis of Diphenyl ether in Supercritical Water Effects of Dissolved NaCl. J. Supercrit. Fluids 2000, 17, 215. (10) Driesner, T.; Seward, T. M.; Tironi, I. G. Molecular Dynamics Simulation Study of Ionic Hydration and Ion Association in Dilute and 1 Molar Aqueous Sodium Chloride Solutions from Ambient to Supercritical Conditions. Geochim. Cosmochim. Acta 1998, 62, 3095. (11) Benson, S. W. The Foundations of Chemical Kinetics; McGraw-Hill Book Co.: New York, 1960; pp 521-528.

(12) Quint, J. R.; Wood, R. H. Thermodynamics of a Charged Hard-sphere Ion in a Compressible Dielectric Fluid. 2. Calculation of the Ion-solvent Pair Correlation Function, the Excess Solvation, the Water-like Fluid above the Critical Point. J. Phys. Chem. 1985, 89, 380. (13) Uematsu, M.; Franck, E. U. Static Dielectric Constant of Water and Steam. J. Phys. Chem. Ref. Data 1980, 9, 1291. (14) Haar, L.; Gallagher, J. S.; Kell, G. S. NBS/NRC Steam Tables; Hemisphere Pub. Co.: Washington, DC, 1984.

Received for review June 5, 2000 Revised manuscript received November 28, 2000 Accepted December 1, 2000 IE0005598