R. P. Gordon
Upsala College East Orange, New Jersey 07019
A Supercritical Phase Separation The gas-gas equilibrium
M o s t teachers of chemistry and of physics are inclined to assert that all gases are miscible in all proportions. Many textbooks of general and physical chemistry state or imply that no separation of gaseous phases has ever been observed. Yet, systems are known in which behavior best described as gas-gas phase equilihrium has been observed. The knowledge of the existence of this kind of hehavior should no longer - be ignored. I t is interesting to note that J. D. van der Waals predicted this phenomenon in 1894 ( I ) . The essential requirement is a binary system having one component much more volatile than the other. If the liquid phase of such a system shows strong positive deviations from Raoult's Law, then there may he phase separation which persists far ahove the critical point of the lessvolatile component. The basis of van der Waals' reasoning was a topological analysis of possible folds in the A-T-X surface for binary systems (where A is the Helmholtz potential and X is a mole fraction). H. Kamedingh Onnes and W. H. Keeson made a similar prediction in 1907, and noted that the phase separation should he described as the immiscibility of two gas phases (2). However, it was not until 1940 that the first observation of this kind was made, by Krichevskii, on the Nz-NH3 system (3). The reality of the phenomenon has been amply confirmed. At present, a fairly large numher of binary (and a few ternary) systems exhibiting gas-gas immiscibility are known and have been cataloged (4). Of particular note are the systems NHrCH4, SO2-N2,and n-hutaneH,O. A few of these systems have been found to exhibit the harotropic phenomenon, a gravitational inversion of phase position on suitably changing the pressure or temperature. The argon-NHs system (5) and the C02-H,O system (6) are examples which show this behavior. We will try to show in a simple and pictorial manner how the ahove phase separation hehavior may arise. Consider the series of illustrations shown as Figure 1. A typical P-X diagram (at constant temperature) for an ideal binary solution is shown as Figure 1A. The vapor pressures of the two pure components A and B are Pao and P$. Ahove the upper line (the bubble-point line), the system is entirely liquid. Below the lower curved line (the dew-point line), the system is entirely gaseous. Within the shaded region, liquid and vapor phases exist in equilihrium. Figure 1B is similar to the ahove. I t shows that small positive deviations from ideality of the solution cause curvature of the bubble-point line. Large positive deviations may produce a new feature on the P-X diagram. Figure 1C shows that hoth bubble-point and
dew-point lines have an osculating maximum a t the concentration of a constant-boiling mixture, or azeotrope. There are two distinct and separated regions of liquid-vapor equilihrium. However, the two liquids of which the solution is composed are everyvhere miscible, giving a homogeneous liquid phase over the whole range of composition. Positive deviation indicates that A-A and B-B interaction forces are larger than the A-B interaction. Thus, in many cases, a given pair of liquids may he miscible only over limited ranges of concentration, and immiscible between these ranges. The resulting P-X diagram may be as shown on Figure ID. Next consider a similar system a t a temperature above the critical temperature of the more volatile component A. Thus, there is no PAO and the curve does not reach the X B = 0 axis. The resulting curve may have the shape shown in Figure 1E. We may consider that the left branch of the curve gives the solubility of the liquid (B) in the supercritical gas (A). Note that this curve has hoth a minimum and a maximum. The right branch of the curve may be said to show the solubility of the gas (A) in the liquid (B). This curve shows only a single maximum of solubility (that is, a minimum for X e ) . The ahove P-X diagrams are merely constant-temperature slices of a P-T-X phase solid. The series of illustrations shown as Figure 2 presents a numher of such phase solids. The solid-phase regions of the various systems are not pictured, hon-ever. Figure 2A is drawn for a typical simple binary system which does not deviate greatly from ideal behavior. Rote the "critical line" which joins the critical points of the pure components. The system, above and to the right of the critical line, commonly is termed a "fluid" or a "gas" (or a gas mixture). Let us assume that the components A and B differ greatly in volatility, with A the more volatile. Then, it may be very difficult to observe the entire P-T-X region between the two pure-component critical points. We may he able to study conveniently only a portion of this region, which may appear as pictured in Figure 2B. Now, let us consider the P-T-X diagram for a system of the sort shown in Figure 1E. This now appears as Figure 2C. As the temperature increases, the "waist" of the two-phase region becomes increasingly narrow. Ultimately, it pinches off entirely, and the region becomes bifurcated into two regions which are reminiscent of a lobster claw. One prong continues until it terminates a t the critical point of the less volatile component B. The larger prong continues into regions of temperature and pressure far beyond the critical point of B; regions 15.hich generally are considered to represent gaseous states. Ahove the point of bifurcation, Volume 49, Number 4, April 1972
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we may choose to label the upper two-phase prong G G, to distinguish i t from the lower L V region. This choice is arbitrary, of course. The figure shows that the two regions are separated by no real discontinuity. A P-X section of the above figure is shown as Figure 2D. The section is taken somewhere between the temperature of bifurcation and the critical temperature of pure B. At higher temperatures, the L V region disappears, but the G G region persists, moving to higher pressures. O b ~ e that ~ e the continuous region between the two shaded regions could be described equally well as corresponding to a liquid or to a vapor. Next, we consider the P-T sections of the P-T-X phase solids. For a simple system, as described by
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Figvre 2. (A) Liquid-vapor phare behavior of simple binary system. IBI Liquid-vapor phare behavior of simple binary r y s t e m 4 o r obove critical temperotvre of component A. ICI Possible liquid-vapor phase behavior of ryrtem of type shown on Figure 1lE). ID1 P-X Section of Figvre 2(CI below the critic01 pointof pure 8.
Figures 2A or 2B, the P-T section is as shown on Figure 3A. Again, the upper part of the curve is the bubblepoint line and the lower curve is the dew-point line. These lines join a t a point, C which is the critical point of the mixture. The P-T cross-section of Figure 2C differs drastically from the above, as shown by Figure 3B. The line separating the L V region from the G G region is drawn a t the temperature of the bifurcation point. However, the diagram shows clearly that this line corresponds to no physical separation. That is, the boundary between the regions is primarily one of nomenclature or semantics.
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Instead of cutting the T-P-X phase solid by a plane of constant X, we may project the critical locus onto an arbitrary P-T plane. For the system of Figure 2(C), this projection is as shown on Figure 4A. Note that the critical locus first moves left from the upper purecomponent critical point. I t reaches a minimum a t the temperature of the bifurcation point, and then moves
TEMPERATURE (A) Figure 3. (A) P-T cross-section of Figure 2lA) or 2(BI. of Figure 2IC).
(81 P-T cross-section
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ceed outward indefinitely far. This also implies that the G G loop shown on the P-X diagram of Figure 2D will never he closed at the top. The existence of gas-gas equilibria should not surprise us too greatly. The intermolecular forces responsible for positive deviations and for liquid-liquid phase separation must continue to operate in the vapor phase. This tendency toward gaseous phase separation is opposed by the mixing entropy term TAS and by the generally low density of gases. Because of the low density, the intermolecular distance is greater in gases than in the corresponding liquids. Thus, the effects of the intermolecular forces usually will be much smaller. We realize however, that, with sufficient pressure, gas densities can be made comparable to those of liquids, even at temperatures far above the critical. I t is perhaps surprising that gas phase separation has been observed at pressures as low as 35 atm in systems of Type B, such as He-%butane (10). Most of the pertinent experimental work has been published in Russian and in Dutch journals. This may explain why the phenomenonisnot widely known among English-speaking chemists. One notable exception is the J. Chem. Phys. article by Arons and Diepen (8). Using the van der Waals equation of state, these authors note that gas-gas phase separation of components 1 and 2 should be expected if
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TEMPERATURE ---C (A)
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Figure 4. IAI Projection of critical locus of syrtem of Figure 21CI onto a T-P plane. Thb syrtem is termed 7 y p e A." (81 T-P Prolection of critical l x u s of system of "Typo 8."
outward to much higher temperatures and pressures. This behavior is characteristic of a gas-gas system of "Type A," The N2-NHIsystem is of this type. Another sort of behavior, shown on Figure 4B, is termed "Type B." Here, the critical locus proceeds outward with positive slope and no temperature minimum. Systems having helium as one component are found to behave in this way. The second component may be xenon, COz,NH3, SOz,ethane, propane, methanol, cyclohexane or several other species. I n addition, the butane-water system has been found (7) to be of Type B. It has been suggested (8) that the critical locus may reach a temnerature maximum and then turn back to join a line fiom the critical point of the more-volatile component A. This is indicated by the dotted line (with question mark) of Figures 4A and B. However, no indication of such a reversal has been found for any system, even a t the highest temperatures and pressures. Rowlinson states (9) that there is no reason to expect such a reversal, and that the critical locus should pro252
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> 0.42 bz
and where al, bl and a,bz are the van der Waals constants of the component gases. - These conditions were found to hold for the helium-xenon system. Upon investigation, the predicted separation was observed. Some writers have objected to the gas-gas terminology. Zernike and Din (11) feel that the phases in question should be considered liquids, despite the fact that they exist far above the critical points of the pure liquid components. Bridgman (12) suggested that the phases should more appropriately be termed liquids, because their densities were comparable to those of ordinary liquids. This reasoning, however, is not really valid, particularly for the low-pressure (Type B) systems which now are known to behave as described above. It seems much more reasonable to recognize the supercritical phases as gases, and to describe their behavior as gas phase immiscibility. This terminology seems now to have gained general acceptance. This will necessitate some changes in future textbooks. Literature Cited (1) V A N DEB WAALE. J. D., Zillinsuoral.Kon. Acad. u. Wefenaeh. Amsterdam. 133 (1894). (2) ONNES. H. K., A N D KEEBOM.1%'. H . , P ~ c Xon. . Acod. Wltenxh. Amsterdam, 9,786 (1907). (3) K n ~ c ~ e v s u rI. r , R., A ~ t oPhysicochim. U.R.S.S.. 12. 480 (1940). (4) WEAGE,K. E.. " C h e m i d Reactions ot High Pressures," E. and F. N. Spon Ltd., London, 1967, p. 55. (5) Mron~La, A., DUMOULIN, E., A N D V A N Dna, J. J., Phvsica. 27, 886 (1961). (.6~ ) T ~ . A N D FRANCK.E. U..Z. Physik. Cham. (Frankfurt), 37, -.6 o n ~ m K.. 387 (1963). (7) T s t n ~ ~ D. s , S., A N D MABLENN~XOYA, V. YB.,Dokl. Noulc SSSR, 157, 426 (1964). (8) A ~ O N SJ. . DE s.. A N D DIEPEN. G. A. M.. J. Chrm. Phys.. 44,2322 (1986). , S.. "Liquids and Liquid Mixtures," (2nd ed.). Butter(9) R o w ~ r w s o r J. worth. London. 1969, p. 219. (10) J o w ~ a A. . E.. Thesis, Ohio State University. 1964. (11) DIN.F.,Nolum, London, 181,587 11958). (12) BnmoMAN, P. W., Rms.Mad.Phvr., 18.1 (1946).
