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J . Phys. Chem. 1992, 96, 2409-2410 to a different sensitivity of both quantities to hydrophobic and hydrophilic contributions.2 At least part of these more phenomenological arguments also apply to the systems considered here. It is more difficult to relate the unusual pressure dependence of the miscibility gap to available thermodynamic data for the lower homologues. The pressuredependence of the critical solution temperatures (LCST’s and UCST’s) is given by1I9l3
where V, is the molar volume, t“, the molar excess volume, and subscript c means at the critical solution point. To a first approximation this implies a change of sign of v“, from minus to plus with rising pressure along the critical loci. If the usual regularities in the homologous series hold also for v“,,our results imply that either such a change in sign is also present for the lower homologues, or that there is at least a tendency toward such a change within the homologous series. Unfortunately, the available molar volume and compressibility datal” are too limited to test this prediction. Finally, we note that some results of detailed studies of various types of phase behavior of nonelectrolyte mixtures” are of direct relevance for the present work. Generalizing this results to electrolyte systems, and assuming regularities in the thermodynamic properties of the homologues series, the following general conclusions on the phase behavior of R4NX-water systems can be drawn. There are two regions of immiscibility at high and low pressure, respectively. For the higher homologues, as represented by iPe4NBr, both regions overlap, leading to the recently observed immiscibilities at atmospheric pressure7 and, at least for i-Pe4NBr, to the hyperbolic shape of the p,T,x surface reported here. Increase of the length of the alkyl chains leads to a broadening of both immiscibility zones,resulting in the increase of the gaps a t atmospheric pressure reported r e ~ e n t l y .Decrease ~ of the chain length results in complete miscibility of the lower homologues in the entire (p,T,x) range accessible by our experiments (480 K, 250 MPa). This may be interpreted as a separation of both immiscibility zones. The low-pressure immiscibility shifts to lower pressures and eventually is displaced completely to the region of negative pressures, while the high-pressure immiscibility shifts toward higher pressures, thus resulting in complete miscibility in an intermediate regime including atmospheric pressure. Due to the lack of a sufficient data base, it is difficult to give more definite predictions. The hypothetical immiscibility regions at negative pressure, predicted for the lower homologues, are well-known from none-
lectrolyte thermodynamics.11J3 In the case of Bu4NBr, some support for this interpretation comes from the observation16that under ambient conditions the addition of small amounts of typical “salting-out” salts like Na2S04or KCl to aqueous Bu4NBr results in liquid-liquid phase separation. In analogy to similar observations on salting-out out of hydrophobic nonelectrolytes in aqueous solutions (e.g., in the system 3-methylpyridine + H20 salt”) this may be interpreted as a displacement of the hypothetical immiscibility region from negative toward positive pressures upon addition of salting-out electrolytes. In conclusion, we can state that the observed phase behavior appears to be closely related to the known thermodynamic pecularities of the completely miscible lower homologues which are usually attributed to the presence of hydrophobic effects, thus suggesting that phase separation is mainly driven by hydrophobic forces. This reconfirms our earlier a n a l y ~ i sand ~ , ~the results of the calculations of Friedman and co-workers? in which unmixing has been attributed to the presence of cation-cation and cationanion pairs as manifestations of the hydrophobic effect in such systems. We may therefore speak of hydrophobic (or solvophobic) phase separation,'^^ in contrast to the Coulombic phase separation due to long-range Coulombic forces observed in certain electrolyte solutions in solvents of low dielectric c ~ n s t a n t . ~ ~ ~ ~ ~ ’ ~ The nature of the driving force for unmixing is of special interest for interpreting the unusual critical behavior of some ionic fluids. Recent experiments by Singh and PitzerIs and ourselves19 in electrolyte solutions exhibiting Coulombic unmixing have given evidence that the near-critical behavior of some ionic fluids is quite different from that of nonelectrolyte systems in that apparently classical critical behavior is observed rather than the king behavior found at liquid-gas and liquid-liquid critical points of nonelectrolytes. This contrasts, however, sharply with an Ising-like behavior observed by Japas and Levelt-Sengers* for the system tetra-n-pentylammonium bromide + water. A possible rationale is that the different driving forces lead to this discrepant behavior. In contrast to the nonaqueous electrolyte systems, hydrophobic forces appear to dominate the critical behavior in R4NX H 2 0 systems, Coulombic forces playing a minor role.
+
+
Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. (16) Weingartner, H. Unpublished results. (17) For a more detailed discussion of the differences of the molecular structures leading to Coulombic and hydrophobic unmixing see for example refs 7 and 9. (18) Singh, R. R.; Pitzer, K. S.J . Chem. Phys. 1990, 92, 6775. (19) Weingartner, H.; Wiegand, S.; Schrkr, W. J. Chem. Phys. 1992,96, 848.
“Hardness Profile” of a Reaction Path Dipankar Datta Department of Inorganic Chemistry, Indian Association for the Cultivation of Science, Calcutta 700 032, India (Received: November 22, 1991; In Final Form: January 21, 1992)
The variation of the hardness of a chemical species along a reaction path, which we call the “hardness profile”, is shown to go through a minima at the transition state. The hardness values are calculated by the MNDO method.
(1) Parr, R. G.; Pearson, R. G . J . Am. Chem. SOC.1983, 105, 7512.
0022-3654/92/2096-2409$03.00/0
(2) Pearson, R. G. Proc. Narl. Acad. Sci. U.S.A. 1986, 89, 1827.
0 1992 American Chemical Society
Letters
2410 The Journal of Physical Chemistry, Vol. 96, No. 6, 1992
1
-2.002 J
0 c
Y
W
c
0
a-400 0
i!
E
1
2
0
6.50
5 -251
80
30
r
ii
130
a Figure 1. Inversion of ammonia; variations of hardness TJ (in eV; full line) and the total energy E (in eV; broken line) with the reaction coordinate Q (in degrees; the angle made by an N-H bond with the C3 axis). 7-10 8 2
-5.10
0.50
2.50
1.50
0
V 4.50 501-1-0.50
1.50
a
2.50
Figure 2. Intramolecular proton transfer in malonaldehyde; variations
of hardness 9 (in eV; full line) and the total energy E (in eV; broken line) with the reaction coordinate Q (in angstroms; the distance between the proton and the hydroxyl 03.
higher the value of TJ,the harder is a chemical species and the less is its reactivity. Since along a reaction path the reactivity of the chemical species involved changes, a study of the change in the hardness of a species with the reaction coordinate, which we call the “hardness profile”, would be interesting. Herein we report the hardness profiles for two cases-inversion of ammonia (Figure l), where no bond is broken or formed, and the intramolecular proton transfer in malonaldehyde (Figure 2) where an existing bond is broken and a new one is formed. The 7~ values at various reaction coordinates are calculated via eq 1 at the MNDO level by using a standard MOPAC programs6 In both cases at the respective transition states 7~ attains a minima (Figures 1 and 2). Since a chemical species is most reactive at the transition state, its TJ value is minimum there, on the reaction profile, Le., at the transition state, a species becomes most soft. Such a variation of TJ along a reaction path is, probably, expected. Recently Parr and Chattaraj’ have shown that if a chemical species moves away from its equilibrium position, its hardness value decreases. Since in both examples chosen, at the transition states the two molecules are farthest from their equilibrium positions, the TJ value should be minimum at the respective transition states. However, one of the assumptions in the work
Figure 3. Variation in the chemical potential p (in eV) in (a, top) the inversion of NH, and (b, bottom) the intramolecular proton transfer in malonaldehyde. The respective reaction coordinates (Q) are same as in Figures 1 and 2.
of Parr and Chattaraj’ is that the chemical species in question maintains a constant chemical potential p which is defined’ as -p = (IP EA)/2. To check this aspect, we have also studied the variation in p along the paths of the two reactions mentioned above within the MNDO framework. In terms of the orbital energy, for a closed-shell species (using Koopmans’ theorem again)
+
P
=
(€HOMO
+ CLUMO)/~
(2)
As found from Figure 3a, in case of the inversion of NH3, p goes through a maxima at the transition state. In case of the other reaction, i.e., the intramolecular proton transfer in malonaldehyde, the variation in the numerical values of p is so small ( p varies from -4.980 to -4.863 eV only; moreover, here the maxima does not correspond to the transition state) that p can be taken as more or less constant throughout the reaction path (Figure 3b). From the analogy with classical thermodynamics, one probably expects a maxima in the value of “chemical potential” (eq 2) at the transition state. Not many diagnostic properties other than the total energy, the conventional one, can be attached to a transition state. However, very recently it has been shown* that the quantum chemical bond order of the bond being broken or formed in a chemical reaction goes through an inflection at the transition state. It should be noted that this bond order description is not helpful for a reaction where no bond is broken or formed as in case of the inversion of NH3 or the stereochemical changes in other fluxional molecules. Here we have shown TJ as a parameter that can be associated with the activated complex.
(3) Datta, D.; Sharma, G.T. Inorg. Chem. 1987, 26, 329. (4) Pearson, R. G. J . Org.Chem. 1989, 54, 1423. (5) Zhou, Z.; Parr, R. G . J . Am. Chem. SOC.1990,112, 5720 and refer-
Acknowledgment. Thanks are due to Prof. R. G. Parr for his kind interest in this work.
ences therein. ( 6 ) Dewar, M. J. S.; Thiel, W. J . Am. Chem. SOC.1977, 99, 4899. (7) Parr, R . G.; Chattaraj, P. K. J . Am. Chem. SOC.1991, 113, 1854.
(8) Maity, D. K.; Bhattacharyya, S. P. J . Am. Chem. Soc. 1990,112,3223.
