J . Phys. Chem. 1989, 93, 3378-3379
3378
niobium and iron clusters with hydrogen and deuterium.28 The present cluster result is consistent with a similar picture. Apparently a vacant s orbital (or s-d hybrid) or a vacancy in an MO derived from s orbitals is a quite general requirement for metal activation of alkane bonds. Implicit in this argument is the assumption that the clusters have low-spin electronic configurations. High-spin species would have a number of singly occupied orbitals. The orbitals derived from metal s and d orbitals could be occupied with fewer electrons in this case. The fact that the iridium and rhenium clusters are
reactive suggests that they have low-spin electronic configurations. Presumably both the symmetry and energy of the LUMO are important in determining the reactivity. The rate constant for the n = 4 cluster (Table I) indicates a somewhat enhanced reactivity for this cluster. It may be that this cluster which can assume full tetrahedral symmetry has a LUMO at an energy that is particularly appropriate to act as an acceptor. The inertness of the anionic clusters may be similarly rationalized. Such a cluster may have a vacancy in an orbital derived from atomic s orbitals, but the energy of that orbital in an anion will be near the continuum. Such an orbital would not be a good acceptor orbital. Hence the anions fail to react. The failure of the anions to react thus emphasizes the importance of the ability of the metal to accept charge density from a C-H bond in order to activate the bond.
(28) (a) Zakin, M. R.; Brickman, R. 0.;Cox, D. M.; Kaldor, A. J . Chem. Phys. 1988, 88, 3555. (b) Zakin, M. R.; Brickman, R. 0.;Cox, D. M.; Kaldor, A . J. Chem. Phys. 1988, 88, 6605.
Phase Separation and Critical Point of an Aqueous Electrolyte Solution Heike Glasbrenner and Hermann Weingartner* Institut fur Physikalische Chemie und Elektrochemie der Uniuersitat Karlsruhe, Kaiserstrasse. 12,
0-7500Karlsruhe, FRG (Received: January 18, 1989)
Aqueous solutions of tetra-n-butylammonium thiocyanate exhibit liquid-liquid phase separation at room temperature. The coexistence curve has an upper critical point at 423 K and a mole fraction of the salt of 0.052. There are indications for the existence of a lower critical point in the supercooled liquid at about 150 K. Corresponding-statesarguments and theories based on the restricted primitive model are not able to predict this phase separation. The shape of the coexistence curve in the neighborhood of the critical point can be described with a critical exponent p = 0.5 down to a reduced temperature difference ATIT = 5 X
Introduction It is well-known that corresponding-states ideas may qualitatively account for the equilibrium properties of ionic fluids and that the introduction of reduced thermodynamic variables may constitute a convenient basis for comparing the properties of real and model systems.l,2 Within the restricted primitive model (RPM) convenient variables are the reduced inverse temperature /3* = z2eZ/tkTaand the reduced concentration c* = ca3, where a is the hard-core diameter of the ions with charge fze and c is the total ion concentration.' A pure ionic fluid has a dielectric constant t = 1, while for electrolyte solutions an appropriate value for e has to be inserted. One of the main features of the P , c * diagram is a coexistence curve for two phases with an upper critical point. Different estimates within the RPM locate this critical point in the range from p*c = 11.5 to 13.5;3Pitzer quotes a value of 14.7.'.4 For pure ionic fluids this curve corresponds to the liquid-vapor transition, while for solutions it is related to a liquid-liquid phase separation. If z and a remain the same, the effective temperature is the temperature-dielectric constant product tT. With a = 3 8, and z = 1 the critical point requires E T= 3700 K in good agreement with the estimated critical temperature for pure NaCl ( t = l).I With the large value t = 80 for water near room temperature, aqueous 1 :1 electrolytes are at very high reduced temperatures and well above the critical region. Phase separation may however occur in some nonaqueous solutions with e < 10. In fact, there are some nonaqueous electrolyte systems which do unmix at room temperature^,^.^ but to our knowledge the critical point has only been located in a single case, Le., tetra-n-butylammonium picrate-1-chl~roheptane.~ Within studies of transport coefficients in aqueous solutions of low-melting tetraalkylammonium salts we have now found the first example for a comparatively simple aqueous electrolyte so-
* To whom correspondence should be addressed. 0022-3654/89/2093-3378$01 .50/0
lution which shows unmixing at room temperature. The salt is tetra-n-butylammonium thiocyanate (Bu,NSCN) which melts at 126.8 OC. There are no data for this molten salt, but results for the homologous pentyl salt6 indicate typical ionic properties.
Experimental Section Tetra-n-butylammonium thiocyanate was obtained from Fluka, Basel (Switzerland). It was purified by repeated recrystallization from ethyl acetate and dried at 100 OC under vacuum. The melting point was 126.5 "C. The desired amounts of the salt and of water were weighed into glass tubes. After degassing by freeze-pumpthaw cycles the samples were sealed under vacuum. For determining the coexistence curve the samples were heated in an oil bath controlled to f O . l "C. Stirring of the solutions was accomplished by Teflon-coated magnetic stirrers inside the samples. Measurements were made by direct observation of the formation and disappearance of the meniscus when crossing the coexistence curve from both higher and lower temperature.
I
Discussion The liquid-liquid coexistence curve is plotted in Figure 1 against the mole fraction x1of the salt. The upper critical point is located at T, = 423 f 1 K and x, = 0.052 f 0.002. At 25 OC the and coexisting phases have the mole fractions xl' = 2.5 X xl" = 0.24 which corresponds to molar concentrations of 0.13 and 2.78 mol dm-3, so that the two-phase region is extremely asym( I ) Pitzer, K. S. J . Phys. Chem. 1984, 88, 2689. (2) Friedman, H. L.; Larsen, B. J . Chem. Phys. 1979, 70, 92. (3) Stell, G.; Wu, K. C.; Larsen, B. Phys. Reu. Lett. 1976, 37, 1369. (4) Pitzer, K. S.; Schreiber, D. R. Mol. Phys. 1987, 60, 1067. (5) Pitzer, K. S.; de Lima, M. C. P.; Schreiber, D. R. J . Phys. Chem. 1985, 89. 1854. (6) Kenausis, L. C.; Evers, E. C.; Kraus, C. A. Proc. Natl. Acad. Sci. U.S.A.1962, 48, 121.
0 1989 American Chemical Society
The Journal of Physical Chemistry, Vol. 93, No. 9, 1989 3379
Letters
log CX;-X'J
I I'CI
150:0 1
11 O 0
O
O
00
0 0
50 0
0
0
5
10
15
o o
20
25
I 30
lozx,
Figure 1. Liquid-liquid coexistence curve for aqueous tetra-n-butylammonium thiocyanate. x , is the mole fraction of the salt.
Figure 2. Logarithmic plot for determining the critical exponent 8. The solid line shows 8 = I / * . Excluding the two points at the lowest reduced temperatures, for which the uncertainty is too large, the fit yields 6 =
metric and confined to the solvent-rich regime. It would also appear that there is a lower critical point near 250 K,but in this region the solutions were highly viscous and tended to supercool, so that equilibrium was very sluggish, and neither the crystallization curve nor the liquid-liquid coexistence curve was sufficiently reproducible. It is clear from the estimates given above that the RPM cannot account for a phase separation in aqueous solutions near room temperature. We also note that, because the product tT decreases with increasing temperature, the upper critical point in the RPM would correspond to the lower critical point in the real system. Of course, the assumption in the RPM of a continuous dielectric retaining its solvent properties regardless of the salt concentration cannot be valid in the more concentrated solutions. One may also speculate that the Coulombic part of the potential is overshadowed by other contributions, and that the size difference of cations and anions and the nonspherical shape of SCN- may be of relevance. Furthermore, it may be noted that the hydrophobic interaction between the Bu4N+ cations manifests itself in a considerable non-Coulombic contribution to the cation-cation p ~ t e n t i a l . ~ In all systems with liquid-liquid phase separation reported so ion pairs and higher ion associates seemed to be present, but it is known that the Bjerrum association model alone cannot predict phase separation.2 Preliminary conductance measurements in dilute Bu4N SCN solutions at 25 OC have yielded an ion-pair association constant near 10 dm3 mol-'. However, it is known that the determination of association constants of this order of magnitude is subject to large uncertainties. Moreover, in the case of SCN- there appears to be no well-established limiting conductance obtained with modern conductance equations, so that a quantitative analysis of these data awaits the redetermination of the limiting conductance of SCN-, presently in progress in this laboratory. We also note that we have no indication for the presence of higher ion associates. Conductance measurements
0.049 f 0.07.
(7) Ramanathan, P. S.; Krishnan, C. V.; Friedman, H. L. J . Solution Chem. 1972, I , 237. (8) de Lima, M. C. P.; Schreiber, D. R.; Pitzer, K. S. J . Phys. Chem. 1987, 91, 4087 and references cited therein.
in both miscibility regions gave no evidence for a minimum in the molar conductance typical for the formation of higher ion associates. Finally, we recall that the shape of the coexistence curve near T, is usually discussed in terms of the critical exponent (3 in the expression (XI1
- X l t 1 ) = B [ ( T - Tc)/Tc]8
where B is a constant specific to the particular system. While it was not the focal point of interest in this study to determine (3, we note that the logarithmic plot in Figure 2 yields (3 = 0.49 f 0.07, which is consistent with the "long-range" exponent (3 = down to a reduced temperature of 5 X confirming the results of the little work done so far for fused salts? nonaqueous electrolyte s o l ~ t i o n sand , ~ dilute NaCl in water near the critical point of water.1° On the other hand, observed values for nonelectrolytes are in the range 0.3-0.35,which is predicted in fluctuation theories, if the range of fluctuations exceeds the range of interparticle forces. Due to the r-' dependence of the Coulomb potential as compared with the r4 dependence for nonelectrolytes, the fluctuation effects appear to be negligible for electrolytes in the temperature range covered by our measurements. In fact, it is an open question whether there will be a crossover from 0.5 to 0.311at temperatures closer to T,. In this context it is also worthwhile to note that a r4 dependence of the potential, as obtained for the interaction of ions with a rotating dipole, is sufficiently long range to yield (3 = 1/2.12 We are currently performing further measurement for characterizing the structure of the solutions in the neighborhood of the critical point in this and other electrolyte solutions exhibiting liquid-liquid phase separation. (9) Buback, M.; Franck, E. U. Eer. Bunsen-Ges. Phys. Chem. 1972, 76, 350. (10) Pitzer, K. S.; Bischoff, J. L.; Rosenbauer, R. J. Chem. Phys. Lett. 1987, 134, 60. (11) Chieux, P.; Sienko, M. J. J . Chem. Phys. 1970, 53, 566. (12) Fisher, M. E.; Ma, S.-k.;Nickel, B. G. Phys. Rev. Lert. 1972, 29,917.
