J. Phys. Chem. 1995, 99, 13461-13466
13461
Laser Flash Photolysis Studies of Metal Carbonyls in Supercritical COZand Ethane Qin Ji, Edward M. Eyring,* and Rudi van Eldik? Department of Chemistry, University of Utah, Salt Lake City, Utah 84112
Keith P. Johnston Department of Chemical Engineering, University of Texas at Austin, Austin, Texas 78712
Steven R. Goates and Milton L. Lee Department of Chemistry, Brigham Young University, Provo, Utah 84602 Received: March 17, 1995; In Final Form: June 2, 1995@
The ring-closure reaction of M(C0)5L-L (M = W, Mo) where L-L denotes a bidentate ligand was chosen for its comparative independence of solvent properties to demonstrate the repulsive (or intrinsic) part of the activation volume. The ring-closure reaction rate constant was determined in supercritical CO;? and in supercritical ethane over the range between 1000 and 3500 psi at several temperatures (35, 42, 48, and 60 "C). The activation volume was observed to be as high as +7000 cm3/mol just above the critical point in each of these solvents. The ring-closure activation volume was also determined in liquid C02 and in several other liquid solvents for comparison. These studies demonstrate a huge repulsive contribution to the activation volume in these two supercritical fluids.
Introduction Supercritical fluid (SF) solvents, often viewed as "dense gases", are interesting reaction media because they permit us to vary continuously physical properties (such as density, viscosity, dielectric constant, diffusion coefficient, etc.) of the solvent medium with relatively small changes in pressure and temperature and no change in the chemistry. Activation volumes of chemical reactions have been studied in the liquid state for some time.' However, relatively little is known about activation volumes in supercritical fluids. There is an obvious difference. While activation volumes in liquids are typically between -50 and 50 ~ m ~ / m o l ?they - ~ can be thousands of cm3/ mol negative or positive in supercritical fluids, as has been demonstrated for the thermal decomposition of a-chlorobenzyl methyl ether7 and for other reactions that have been reviewed re~ently.~.~ In liquid solvents, the activation volume is typically described as the sum of two terms: an intrinsic contribution arising from changes in bond lengths and angles and a solvation term arising from electrostriction and other solvent effects.I0.' This philosophy has been applied to the supercritical state as well. ' * , I 3 The intrinsic contribution has been assumed to be within the order of f 5 0 cm3/mol, and the larger part of the activation volume, on the scale of thousands of cm3/mol, has been attributed to the solvation term. An alternative analysis of A F was offered by Johnston and Haynes,' based on the ideas of van der Waals. In this van der Waals model A F is separated into repulsive, AVeP, and attractive, AP", contributions. The attractive part is caused by the attractive solvent effects, and the repulsive part considers differences in excluded volume for the reactants and transition state caused by the breaking and making of bonds. On the basis of this theory, it was predicted that AVep can be thousands of cm3/mol. Therefore, even if there is no change in the attractive forces with the solvent in going from the reactant to transition state (AVI = 0), large
' Institute for Inorganic Chemistry, University of Erlangen-Numberg, Egerlandstr. 1, 91058 Erlangen, Germany. Abstract published in Advance ACS Abstracts, August 1, 1995. @
0022-3654/95/2099- 13461$09.00/0
values of A F can result from AVeP. Other possibilities are that both AVep and A P can be large and of the same sign or can be of opposite signs, resulting in some cancellation. Thus, this van der Waals model is quite different from the conventional model where AV(intrinsic) is negligible in regions where AV(so1vation) is large. The van der Waals model has been used to fit a number of experimental studies of reactions taking place in supercritical fluids.I4-l6 Because all of these reactions involved a substantial change in polarity or ionic charge in going from reactants to the activated complex, resulting in substantial values of AP", it was difficult to isolate the AVeP contribution. Integral equations have been used to determine solvent density effects on reactions in supercritical fluids.I7 Also, reaction volumes have been calculated in model systems containing Lennard-Jones solvents with a Percus-Yevick reference interaction site model.ls For the diatomic dissociation reaction Br2 2Br, the activation volume reached +lo0 cm3/mol when it was assumed that the attractive forces between solvent and reactant mimicked those between the solvent and separated bromine atoms, Le., Avd" = 0 cm3/mol. Although these theoretical results provide evidence for somewhat elevated values of AVeP, they do not demonstrate values of the order of thousands of cm3/mol. It is natural to ask how the formation of a single bond in a chemical reaction can produce such a large volume change. This question applies to both AVep and A P and can be addressed with transition state theory. As we show, large values for AVep do not arise merely from isolated reactant and transition state species, but also include solvent molecules. The objective of the present study is to test the hypothesis of the above van der Waals model that repulsive forces can produce large activation volumes in supercritical fluids. If so, this would mean that the conventional models for the liquid state which assume the intrinsic AV is small may not be applicable to highly compressible supercritical fluids. To achieve our objective, we must minimize any changes in attractive forces between the solvent and reactants relative to the transition state. Ethane was chosen as a solvent, since it has no dipole moment and an +
0 1995 American Chemical Society
13462 J. Phys. Chem., Vol. 99, No. 36, 1995
Ji et al.
insignificant Lewis acidity and basicity. Thus, it cannot form specific interactions with the metal center or the basic nitrogens on the ligand. A well-known ring-closure reaction, with detailed mechanistic information available, was chosen for its small solvent dependence. In general, flash photolysis of dissolved M(CO)6 (M = W) with ultraviolet light results in the loss of CO and the rapid formation of M(CO)s(solvent). In the presence of a strong nucleophile L (in this study, L = 1,lO-phenanthroline), the coordinated solvent molecule will be displaced to produce M(C0)5L as shown in reaction 1. When L is a bidentate ligand, M(C0)sL will undergo a subsequent thermal ring-closure reaction to produce the ring-closed M(C0)dL species as shown in reaction 2. M(CO), M(CO),
(7)
Differentiation of eq 6 yields
(a In klaP), = -AV'/RT
+ k d l - a - b - ...)
+ L-
k2
k,
M(CO),L
M(CO),L
+ solv
+ CO
The partial molar volume may be expressed in terms of a triple product relationship
(1) (2)
The ring-closure reaction for W(CO)5L is a particularly suitable reaction for our investigation of the van der Waals model because no ionic charges are involved, and there is very little change in polarity during activation. Earlier work2-6,19-23has shown that ring-closure reactions 2 strongly depend on the nature of the metal center M and the nucleophile L and depend much less on the solvent. In addition to supercritical ethane data, experimental results are also presented below for supercritical fluid C02 to determine whether its Lewis acidity and quadrupole moment can lead to attractive interactions which may cause A P t t to become important. New experimental data are reported for the ringclosure reaction of W(CO)5L (L = 1,lO-phenanthroline)in liquid toluene, fluorobenzene, heptane, and chlorobenzene. A similar ring-closure reaction of Mo(C0)sL (L = 1,lo-phenanthroline) was also investigated in liquid CO2 to facilitate a comparison between liquid state and supercritical fluid state volumes of activation.
Theory For the elementary chemical reaction
+ + ... = M'
U A bB
(8)
where k, is the isothermal compressibility, and it is assumed that the transmission coefficient does not change with pressure. The activation volume comes from differentiation of AGO$ and KY* and is given as
hv
fast
M(CO),L
K: = exp(-AC"/RT)
(9)
-. M(CO), + C O
+ solv -M(CO),(solv)
M(CO),(solv)
Ka* may be expressed in terms of the standard state free energy
where v is the specific volume and kT is the isothermal compressibility. For a dilute solution, v and kT are essentially properties of the pure solvent. Consider dilute naphthalene in C02 near its critical p ~ i n t . * The ~ - ~addition ~ of a small amount of naphthalene diminishes P at constant T and V since the solute-solvent attractive forces exceed the solvent-solvent forces. To return to the initial pressure, a large volume contraction is required since kT is large. Near the critical point where the compressibility is large, can reach thousands of cm3/mol negative, e.g., for naphthalene in C02,24925 The large values of V, are due to kT, since the magnitude of aP/an, does not change to a significant degree with density in the region near the solvent critical point.24 Thus, eq 10 separates into two terms: a pure solvent contribution and a factor aPian, which describes the repulsive and attractive solute-solvent interactions. This Krichevski parameter, aPl anl,plays a central role in determining the sign of partial molar volumes and has been used to define attractive (aPlan, < 0) and repulsive (apian, > 0) supercritical fluid systems.26 We now summarize an earlier explanation' of why either repulsive or attractive forces can have a large effect on A V . According to the van der Waals theory of fluids, the pressure may be separated into repulsive and attractive contributions. Applying this separation to aP/an, and substitution of eq 10 into eq 9 yields
v,
+
AV= ~ V k p { ( a P / a d - u apian, - b apianb)repUIS1ve
(3)
the transition state theory rate constant k (based on concentration units such as molarity) is given by
where K is the transmission coefficient, kB is Boltzmann's constant, h is Planck's constant, and Kct is the concentrationbased equilibrium constant for the reaction between the reactants and transition state. Kci can be expressed in terms of an activity based equilibrium constant Kaf as
where yi is the activity coefficient and 8 is the density. The activity coefficients describe changes in free energy with composition and pressure. Substitution into eq 4 yields
(ap/ant - u apian, - b aplanb)attraCtlve} (11) According to this result, a difference in either the repulsive or attractive parts of aPlan,, or both, can lead to a large A V , since each factor is magnified by kT. On the basis of this argument, it is not necessary for the repulsive part to be small, as is the case for the intrinsic contribution to A V in liquid solvents.
Experimental Section Molybdenum hexacarbonyl (Aldrich, 98%) and tungsten hexacarbonyl (Aldrich, 98%) were vacuum-sublimed before use. The 1,lO-phenanthroline(Aldrich, >99%) was used as obtained. SFC grade carbon dioxide was purchased from Scott Specialty Gases (Longmont, CO). Research grade ethane ('99.95%) was purchased from AGA Gas, Inc. (Maumee, OH). A schematic diagram of the pulsed laser flash photolysis apparatus is shown in Figure 1. A Quanta Ray DCR-2 Nd: YAG laser sends a 6 ns duration laser pulse (about 100 mJl pulse) of wavelength A = 355 nm through the sapphire window
J. Phys. Chem., Vol. 99, No. 36, 1995 13463
Metal Carbonyls in Supercritical C02 and Ethane
i
: Light From Xefmn Lamp
Monochromator
355 nm Laser Pulse
I
:
j
To Computer
t
High Pressure Cell
v
v
A
Figure 1. Block diagram of laser flash photolysis apparatus for making spectroscopic kinetic measurement in supercritical fluid solvents.
Results and Discussion
*
T ("C)
solvent supercritical fluid ethane 35 (Tc = 32.2 "C, 40 P, = 706.5 psi) 48
*
AV (cm3/mol)" AV (Lhol)" (between 2000 (near critical point) and 3500 psi)
~~
supercritical fluid COz (Tc= 31 "C,
P, = 1071 psi) In this work, flash photolysis of the mixture of W(CO)6 and 1,lO-phenanthroline (phen) in supercritical fluids (ethane and CO2) results in a rapid formation of intermediate W(CO)5. The intermediate M(CO)5 (M = Mo, Cr, W) formed upon photolysis has been widely investigated, and the photolysis measurem e n t ~ ~ * showed -~' that the ground state of M(C0)s is very unstable and extremely reactive, reacting with solvent at rates near the diffusion-controlled limit to form a solvent-coordinated M(CO)5(solv) species. In the presence of the strongly nucleophilic ligand 1,lO-phenanthroline, the coordinated solvent molecule of this intermediate was quickly replaced by the ligand, resulting in a rapid increase in absorbance at 390 nm, the absorbance maximum for the ring-opened W(CO)s(phen) species. This is followed by a rapid increase in absorbance at 500 nm, the absorbance maximum for the ring-closed W(COk(phen) species. The measurements at 390 and 500 nm suggest that reaction 1 is much faster than reaction 2 and is not the ratelimiting step. The measurement at 500 nm shows that kobs is independent of ligand concentration [phen], and the kobs value is of the same order of magnitude as first-order rate constants repotted for this reaction in liquid fl~orobenzene,2~ which further demonstrates that reaction 2 is the rate-limiting step. The logarithm of the rate constants for the ring-closure reaction of W(CO)5L (L = 1,lO-phenanthroline)in supercritical fluid ethane at different temperatures is plotted versus the pressure in Figure 2. From Figure 2 it is clear that the largest reaction rate deceleration with increasing pressure in the supercritical fluid occurs near the critical point,. and the deceleration diminishes with increasing pressure and temperature. From Table 1, we see that the volume of activation is 6.7 x lo3 cm3/mol in supercritical ethane at a pressure and temperature slightly above the critical point, and much smaller values apply at higher temperature and pressure. In supercritical ethane, the large positive Ahvi simply indicates that the gain in
A
5
From Pump System
of a homemade high-pressure cell at 90' to the path of the Wansient absorption probe beam. The detection system consisted of an Oriel 75 W xenon lamp, a D u r " monochromator, and a Hamamatsu 1P28 photomultiplier tube (PMT). The voltage signal from the PMT is sent to a leCroy 9400 oscilloscope interfaced (GPIB) to a 386-based computer (ARCHE DX-40). Data are analyzed by KINFIT software from OLIS (Bogart, GA). The temperature is controlled to within f 0 . 1 "C by a temperature probe (Omega CF-000-RTD-4-60-2). The pressure is adjusted with a 200 cm3 syringe pump and is measured to within & l o psi by a pressure transducer (SETRA 280E) with a DATUM pressure meter (DATUM 2000). The experimental methods in this study, including the design of the high-pressure cell and the pumping system, are described in detail elsewhere.27
A
v
60 35 42 48 60
$6.7 (770-800)b +6.2 (825-850) +3.9 (910-940) +3.0(1000-1050) +7.2 (1 145- 1160) +3.6 (1270-1300) +1.4 (1320-1375) +0.47 (1300-1360
+181 +36 +33 +11
"The relative deviation for A F values is approximately 10%. Values in parentheses are pressures in psi. molecular volume due to movement of a CO ligand away from the metal center exceeds the loss in volume arising from ring closure. To determine how the solvent polarity and polarizability influence the reaction, experiments were performed in several liquid solvents (toluene, fluorobenzene, heptane, and chlorobenzene) at 25 "C. As seen previously, the changes are quite small, as shown in Table 3. For example, the rate constant increases only a slight amount as the solvents changed from 90 vol % heptane-10 vol % toluene to pure toluene. A modest increase is observed for chlorobenzene and fluorobenzene. The rate constant increases with the dielectric constant of the solvent, but only a modest amount. The ring-closure reaction of W(CO)5L was also investigated in liquid ethane. In liquid ethane, Ahvi was expected to have a very small positive value. However, the experimental A F value found in liquid ethane is too small to tell whether it is negative or positive due to the margin of error. The same reactions were also investigated in SF C02 instead of ethane. The logarithm of the reaction rates of different temperatures is plotted versus pressure in Figure 3, and the results (Table 1) are very similar to those in SF ethane. The volumes of activation for the higher pressure range (between 2000 and 3500 psi) are too close to zero to determine whether they are negative or positive due to the f 1 0 % margin of error. Therefore, the Ahvi values for a higher pressure range are not presented in Table 1. Similar experiments were carried out with Mo(CO)6 and 1,lO-phenanthroline in liquid C02. The results (Figure 4 and Table 2 ) indicate that volumes of activation behave like those
Ji et al.
13464 J. Phys. Chem., Vol. 99, No. 36, 1995
the basic free nitrogen on the ligand. Therefore, it is reasonable to assume that the strengths of the solute-solvent interactions do not change much upon activation. Equation 12 may be factored in a manner as was done previously in eq 9 to yield repulsive
A$ = vk+{(aPlanf - aP/anw~co)5L)
-1
1000
1500
., .,
2000
2500
3000
3500
Plerrun (pi)
Figure 3. Plot of In kobs versus pressure for the thermal ring-closure reaction of W(CO)s(phen) in supercritical C02 at several tempera35 "c; 40 "c; A, 48 "c; 7 , 60 "c. tures:
I 900
.,
1400
4900
2400
2900
3400
Pressure(p8i)
Figure 4. Plot of In kobs versus pressure for the thermal ring-closure reaction of Mo(CO)s(phen)in liquid C02 at several temperatures: 0 , 10 "c; 20 "c; A, 30 "c. TABLE 2: Activation Volumes for the Thermal Ring-Closure of Mo(CO)s(phen) in Liquid CO2 at Several Temperatures solvent T ("C) AV (cm3/mol) liquid C02 (P = 1000-3500 psi) 10 +16.2 f 0.2 20 +23 5 2 30 +36 z t 2 observed previously in other liquid solvents (Table 3). Compared to the activation volume in liquid C02, the much larger A V in supercritical C02 simply reflects the small positive values in liquid C02, which are then magnified by kT. In the ring-closure reaction of W(CO)5L, there is no change in the number of moles between the reactant and transition states, so that the term kdl - a - b ...) goes to 0 in eq 6. Consequently, the activation volume will be the same whether the rate constant is expressed in concentration or mole fraction units. For this reaction, the activation volume is
Upon activation, one CO ligand moves away from the metal center and the complex undergoes ring closure. We assume that the change in polarity upon the ligand exchange is small given that solvent polarity effects on the rate constant are small, as shown for the liquid solvents above. Ethane is a weak nucleophile and does not have a significant tendency to interact with the metal. Furthermore, it does not interact strongly with
+
It may be further assumed that the difference in the aPlan factors is essentially 0 for the attractive term. In supercritical ethane, the large positive A V simply reflects the small values in nonpolar liquids, which are then magnified by kT. The term in parentheses in eq 13, which describes solute-solvent forces, is positive both in liquids and in supercritical fluids. .This term indicates that the transition state occupies more volume than the reactant state. Furthermore, the transition state with surrounding solvent occupies considerably more volume than the reactant with surrounding solvent, so that A V is more than 1000 cm3/mol. The surrounding solvent includes several coordination shells. With the approach to the critical point, the correlation length of the solute-solvent interactions grows. This physical picture reflects the mathematical relationship in eq 11, which indicates that, in regions where k T of the solvent is large, the aP/an term is magnified to give a large A F . The steep change in A F with pressure just above the critical point is similar to the behavior of the isothermal compressibility, kT, of the pure solvent, as has been observed for a variety of reactions. This lends further support to the validity of eq 13. Because the rate constant does change modestly with solvent polarity, the attractive term in eq 13 contributes somewhat to the activation volume. However, the repulsive term must be dominant, as is evident from an analysis of the sign of the attractive term. As the dielectric constant increases, the rate constant increases in the liquid solvents. In a supercritical fluid, dielectric constant increases with pressure. Thus, the attractive contribution to the activation volume must be negative to increase the rate constant with pressure. However, the total activation volume is positive for the experiments. Therefore, the repulsive contribution to A V is dominant, and AV(repulsive) is a larger positive value than AV(tota1). At the critical point of pure ethane, the VI of CO at infinite dilution goes to positive infinity, since CO-ethane interactions are weaker than ethane-ethane interactions. In essence, CO drives the highly compressible mixture toward the vapor state. The Lennard-Jones potential constant (Elk) for ethane is 243 K and is only 100 K for CO. Thus, the movement of a CO ligand away from the metal center leads to a positive A V , despite the reduction in volume arising from the formation of the second bond between a ligand N and the metal. - We now address a potentially confusing point. Both @ and VW(CO)~L are large negative numbers near the solvent critical point.25 In each case the solute-ethane interactions exceed the ethane-ethane interactions and cause solvent contraction. Therefore, each of these solutes is in an attractive system; Le., the negative aP/an,(att) has a greater magnitude than the positive aP/ani(rep). The A F is the difference between the two values of Vi. The attractive parts tend to cancel, so that the difference in the repulsive contributions drives A V (see eq 11). Therefore, A V can be controlled by AVeP even for two solutes that form an attractive system in CO?;. One may question whether activation volumes provide useful information about mechanisms of reactions in supercritical fluid, since the values are so large. Mechanistic information may be
Metal Carbonyls in Supercritical C02 and Ethane
J. Phys. Chem., Vol. 99, No. 36, 1995 13465
TABLE 3: Solvent Effects on the Thermal Ring-Closure Reaction of Mo(C0)sL and W(C0)sL with 1,lO-Phenanthrolinein Several Liquid Solvents dielectric constant AV (cm3/mol) for AV (cm3/mol) for kobs (Us) for ring closure at 25 “C, 1 atm ring closure of Mo(C0)5L ring closure of W(CO)5L of W(CO)5L at 25 “C, 1 atm solvent heptane“ toluene chlorobenzene fluorobenzene a
1.902 2.379 5.621 5.42
-3.0 -1.6 -9.8 -2.9
90% heptane, 10% toluene by volume.
f 0.1’ f 0.1’ f 1.4’ f 0.223
-4.0 +3.6 -5.4 -8.2
’Cao, S . ; et al., manuscript in preparation.
f 0.2‘ f 0.1‘ f 0.2‘ f 0.223
73 & 1‘ 88 If 2‘ 219 f 8‘ 432 f 623
This work.
TABLE 4: Activation Volumes of Several Reactions in Supercritical Fluid Solvents reaction unimolec decomp of C6H5CHCl-O-CH3 I/& e- = I- on platinum 2-hydroxypyridine = 2-pyridone phenol oxidation hydrolysis of methoxynaphthalene 1-propanol dehydration
+
a
fluid
T:
P,b
AV (Wmol)
ref
C2Fd-k Hz0 CzhH6 Hz0 Hz0 Hz0
1.04 1.03 1.04 1.01 1.02 21
1.3 1.04 1.1 0.85 - 1.3 1.09 -1
-6 -1 -1.5 -1.4 -3.3 +1.2
7 14 15 31 38 39
’
T4 is the reduced temperature T/Tc. P, is the reduced pressure PIP,.
obtained if the activation volume is first normalized by the compressibility. For the reaction of interest here, the normalized value is given by
The magnitude of the normalized value is more typical of what is expected in liquid solvents. It can be analyzed to determine whether the excluded volume increases or decreases in the transition state, once a model is used to describe the attractive term.I4.l5 Thus, the activation volume approach may be used to investigate mechanisms in supercritical fluids as well as in liquid solvents. The behavior could be somewhat more complex in C02 since this solvent molecule can interact with the basic nitrogen on the ligand. However, the results in supercritical C02 are similar to those in supercritical ethane, suggesting that C02 Lewis acidbase interactions do not have a large effect on A F . Thus, these results lend further support to the controlling effect of AVeP on AV. The activation volume is a macroscopic quantity, and although it describes changes in solute-solvent interactions, it cannot be used to resolve the short-range and long-range contributions to these interactions. The local behavior of solvation in supercritical fluids has received a great deal of attention. Although the local behavior is not described by macroscopic partial molar properties, it can be characterized by other techniques. Spectroscopic measurement^^^ and computer simul a t i o n ~indicate ~ ~ that local densities of solvent molecules about solutes can be augmented above the bulk density to a greater degree at subcritical and near-critical densities than at higher more “liquidlike” densities. In both C0234and water,35solutesolvent clustering has been characterized in three density regions: gas-phase solute-solvent clustering, clustering in the near-critical region, and “liquidlike” solvation. Clustering usually increases as the density is decreased from well above gc to well below the critical density and is prevalent even down to er = @/ec= 0.1 This is a result of an increase in free volume and, to some extent, an increase in the local compressibility near the solute. However, clustering is a short-range local property that does not track the bulk thermodynamic solvent compressibility, which diverges at the critical point. The results of this study may be compared with a rapidly growing number of results in the literature. A variety of .33s34336
examples in supercritical fluids have demonstrated large activation volumes in highly compressible supercritical fluid solvents as shown in Table 4. Although kT is large in each of these studies, the reduced temperatures and pressures are somewhat different. For the unimolecular decomposition of a-chlorobenzyl methyl ether,’ the negative A V is due to the large increase in polarity as the transition state is formed. The transition state is solvated more strongly than the reactant. For the electrochemical reduction of 1 2 to I-, the negative A V results from electrostriction about the ion.I4 Here, the repulsive forces provide a positive contribution to AV, which was modeled with a Camahan-van der Waals equation of state. For the tautomerization of 2-hydroxypyridineto 2-pyridone, the more polar tautomer 2-pyridone is solvated to a greater extent than the less polar one.l5 Here each tautomer has a similar size. In the case of the hydrolysis of methoxynaphthalenein supercritical water?8 the charge decreases upon activation, so that the activation volume is positive. In all of these cases, the activation volume is consistent with the expected result from the changes in polarity upon activation. Therefore, it is difficult to decipher the effects of the repulsive forces, as was done in the present study.
Conclusion In this study, activation volume was used to interpret the extremely large pressure effect on the rate constant in a highly compressible near-critical supercritical state. The van der Waals model used in this work was found to be much more suitable than the conventional model used to describe liquid solvents. This study demonstrates that the repulsive (or intrinsic) part of the activation volume can be thousands of cm3/moleven when the attractive contribution to the activation volume is small.
Acknowledgment. This research was supported in part by the US.Department of Energy, Office of Basic Energy Sciences (E.M.E), by the Volkswagen Foundation (R.v.E.), and by the U.S. Army Research Office for University Research Initiative Grant DAAL 03-92-6-0174(K.P.J). References and Notes (1) van Eldik, R.; Asano, T.; Noble, W. J. Chem. Rev. 1989, 89, 549. (2) Zhang, S.; Dobson, G. R.; Bajaj, H. C.; Zang, V.; van Eldik, R. Inorg. Chem. 1990, 29, 3471. (3) Zhang, S.; Zang, V.; Bajaj, H. C.; Dobson, G. R.; van Eldik, R. J . Organomet. Chem. 1990,397, 219. (4) Wieland, S.; van Eldik, R. Organometallics 1991, 10, 3110.
13466 J. Phys. Chem., Vol. 99, No. 36, 1995 (5) Zang, V.; Zhang, S.; Dobson, C. B.; Dobson, G. R.; van Eldik, R. Organometallics 1992,11, 1154. (6) Zhane. S.: Baiai. H. C.: Zane. V.: Dobson, G. R.: van Eldik, R. J . Organometalics 199i,11,3901. (7) Johnston, K. P.: Haynes, C. Am. lnsr. Chem. Eng. J. 1987,33,2017. ( 8 ) Brennecke, J. F. AbS Symp. Ser. 1993,No. 514, 201. (9) Clifford, A. A. In Supercritical Fluids: Fundamentals For Apvlicarion: Kiran. E.. Leveltseneers. J. M. H.. Eds.: Kluwer Academic: 'Boston, i994; ~'449. (10) McCabe, J. R.; Eckert, C. A. lnd. Eng. Chem. Fundam. 1974,13, 168. ( 1 1) van Eldik, R. Inorganic High Pressure Chemistry; Elsevier Science Publishing: New York, 1986. (12) Shaw, R. W.; Brill, T. B.; Clifford, A. A,; Eckert, C. A.; Franck, E. U. Chem. Eng. News 1991,69, 26. (13) Wu, B. C.; Klein, M. T.; Sandler, S. I. Ind. Eng. Chem. Res. 1991, 30, 822. (14) Flarsheim, W. M.; Bard, A. J.; Johnston, K. P. J . Phys. Chem. 1989, 93, 4234. (15) Peck, D. G.; Mehta, A. J.; Johnston, K. P. J . Phys. Chem. 1989, 93, 4297. (16) Chateauneuf, J. E.; Roberts, C. B.; Brennecke, J. F. ACS Symp. Ser. 1992,No. 488, 106. (17) Kimura, Y.; Yoshimura, Y.; Nakahara, M. J . Chem. Phys. 1989, 90, 5679. (1 8 ) Ravi, R.; Souza, L. E. S. d.; Ben-Amotz, D. J . Phys. Chem. 1993, 97, 11835. (19)Schadt, M. J.; Lees, A. J. Inorg. Chem. 1986,25, 672. (20) van Eldik, R. Pure Appl. Chem. 1993,65, 2603. Y
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