HOW SHOULD WE DEFINE THE CRITICAL STATE?' 1. G. ROOF Shell Development Company, Houston, Texas
TEEgas-liquid critical state usually is mentioned briefly in the general chemistry course as an interesting physical phenomenon. I n the elementary physical chemistry course this phenomenon is again discussed and is usually expanded upon. Such interest in the critical state is certainly warranted on the basis of its practical importance in many present-day processes. While there is adequate justification for introducing the critical state in a first course of chemistry, one can well criticize the approach that appears to be customarily used. The definition commonly given t o and usually remembered by the student is one that applies only to pure substances. I n applied work one almost never deals with a pure substance--certainly not in chemical processing or in petroleum production and refining. The student should not be left with a concept of the critical state that is limited only t o pure substances when there is an alternative definition applicable to both pure substances and mixtures. The author's experience, both in teaching and in an industry in which chemists and engineers handle complex mixtures in the critical region, is that far too many persons when confronted with the phrase L'critical state" will recall 'Publication No. 98, Exploration & Production Research Division, Shell Development Co., Houston, Texas.
only the statement that the critical temperature is the highest temperature a t which gas and liquid phases can coexist. Perhaps more confusing is the less precise statement sometimes made that the critical temperature is that temperature above which gas and liquid phases cannot coexist (I). The purpose of this paper is to review a few points about the critical behavior of pure substances and of mixtures in order to emphasize the fundamental concept of the critical state that applies t o gas-liquid mixtures of any number of components: namely, the critical state is that state of temperature and pressure a t which the two phases become so nearly alike that they no longer can coexist. PURE SUBSTANCES
Let us consider the equilibrium between the liquid phase and the vapor phase of a pure material. The vapor pressure has a definite value a t a given temperature and is not dependent on the relative amounts of the two p h a s e ~ w h e t h e rthe substance is saturated vapor at its dew point, saturated liquid a t its bubble point, or any proportion of the two phases. The vapor pressure increases with temperature, as is illustrated by the lime axC in Figure 1, plotted from data (3) on pure butane a t elevated temperatures and pressures. The density of the butane, either as a liquid or as a vapor, is determined bv the Dressure and tem~erature(ex~ressed . . here in pounds per square inch absolute and degrees Fahrenheit, respectively). Included in Figure 1, are selected constant-density lines. It is apparent that in general when the two fluid phases coexist (at points along the line mC),the phases are of different density. However, the two approach the same value as the point C i s approached a t the upper end of the vapor-pressure curve. A plot of temperature vs. density of the two coexisting fluid phases is shown in Figure 2. According t o the Law of Cailletet and Mathias the average density of the two phases is constant and is equal to the critical density p,. Although this law is generally not true, the value of the average density is a linear or nearlinear function of the temperature, as shown by the dotted line in Figure 2. Some elementary texts do mention the increasing vapor density and the decreasing liquid density and their becoming equal a t the critical state. When this fact is mentioned, it is seldom emphasized, and it is not ~ o i n t e dout that as the critical state is a ~ ~ r o a c h ,e d . the two fluid phases also become increasingly alike in their other physical properties. If we were always to deal only with pure substances, we- could describe the gas-liquid critical ~state by either ~ ~ ~
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JOURNAL OF CHEMICAL EDUCATION
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of these two criteria: (1) The critical state is that state of temperature and pressure a t which the two coexisting fluid phases become so nearly alike that they no longer can coexist(S,4,5,6) ; or (2) the critical temperature [pressure] is the highest temperature [pressure] a t which the two fluid phases can coexist. In the next section we shall see that only the first of these two criteria is applicable to mixtures. The critical point of a pure substance represents a definite state of the system. There a substance has certain definite values for its physical properties; such as, critical density, critical refractive index, and critical Joule-Thompson coefficient. As we shaU see later, any particular mixture also has definite values for its physical properties a t its critical point. Various methods of determining the critical point have been described (7). One approach is to observe the disappearance of the meniscus between the liquid
I
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BUTANE
and the gas phases. If, instead of observing the meniscus by transmitted light, one notes the reflection from the interface, a slightly higher temperature may be attained before the diffuse surface is no longer discernible (8). Although the material a t the level a t which the interface has iust disan~earedis a t its critical state and possesses the critical values of its physical properties, one should recognize that not all of the material in a vertical cylinder is under the same environment. The pressure in the lower part of the cylinder is higher and, since dp/dp is large (actually infinite a t the critical point), the density is also higher. In general, the value of any physical property will depend on elevation in the cylinder. The critical state is not to he confused with that state a t which the properties of the material finally have become essentially uniform throughout the cylinder by a further (usually small) rise in temperature. Since the gravitational field does affect the distribution of the substance, there has been speculation (8) on the behavior of substances at the critical state in the absence of gravitational fields. If available, such information might resolve some questions about the theory of the critical state. The possibility of performing such experiments in space ships or satellites in the future is an intriguing prospect (8).
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VOLUME 34. NO. 10, OCTOBER, 1951
BINARY MIXTURES
In this discussion we shall deal only with mixtures of substances which are completely miscible in the liquid state. Figure 3 is a plot of data (9, 10) on a particular mixture of methane and butane (25% methane by weight). This figure is analogous to Figure 1 for a pure substance. No longer is there a simple vaporpressure line. In general the coexisting liquid and vapor phases are of different composition. I t is this difference in composition of the two phases which permits fractionation by distillation. Any point within the loop represents a combination of temperature and pressure which results in two phases of differing composition and properties. The upper boundary aP,..C is the bubble-point locus of the saturated liquid. The lower boundary bT,,C is the dew-point locus of the saturated vapor. The orientation of constant-density lines in the single-phase region outside the loop would he quite similar to that of pure butane in Figure 1. From the information given in Figure 3, one cannot calculate either the composition or the density of the liquid and of its coexisting vapor phase for points within the two-phase loop. However, this information can be obtained from the data published for this system. From those data it is evident that the two coexisting phases d i e r in both composition and density a t all points within the loop and on its boundary except a t the single point C . We may plot densities of the two phases as functions of any path within the twwphase loop. If that path crosses the boundary a t any point other than C, one of the two phases will disappear by vaporization or condensation before the two phases become equal in density. I n Figure 4 we have plotted temperature versus density of the bubble-point liquid and of its vapor phase along the line aP,..C. Along this path the liquid always contains 25% methane by
2 5 7 . METHANE - 7 5 % BUT&NE AT BUBBLE POlNT
temperature a t which. . ." may ask whether it is not possible t o continue to use this idea of maxima in temperature and pressure. It can be shown that if one knows the position of the critical point C relative t o P,, and , . T (in Figure 3), some such statements can be made. First, however, one should perhaps consider the nature of the material in the critical region and also the retrograde behavior within the loop near the critical point. DESCRIPTION OF FLUID PHASES
DENSITY, G/ML
Figure 4.
Density of c.,exi.ting
Flvid Phases at Bvhhle point
weight. It is noticed that a t 190°F. the densities become identical. The plot along a different path is shown in Figure 5, where pressure is plotted versus the phase densities a t the constant temperature of 190°F. If a plot of the type shown in Figure 5 had been attemped a t any lower temperature, the vapor phase would have disappeared before the two phases became equal in density. For this particular mixture, there is one temperature, 190°F., and one pressure, 1698 p.s.i.a., a t which the two phases assume the same density. The critical point for this mixture then is a t this temperature and this pressure. The critical point is seen not to lie a t either the maximum temperature T , or the maximum pressure P,., on this twwphase envelope. Liquid and vapor can coexist a t temperatures more than 30°F. above the critical temperature or at pressures more than 60 p.s.i. above the critical pressure. For binary systems we cannot associate the critical state with either the maximum pressure or the maximum temperature a t which two phases can coexist. We are left with the general definition of the critical state as being that state in which the two phases become so alike in properties that they merge in a single phase. One who has always thought in termb;of "the highest
The definition of the critical temperature as "the highest temperature a t which.. ." not only restricts the student t o consideration of one-component systems, but also tends to give him a false impression of the nature of the material in the single-phase region. In Figure 1 at point x along the vapor-pressure curve of a pure substance two fluid phases can coexist. The more dense of these two is customarily called liquid, and the less dense, vapor or gas. Suppose the pressure is increased isothermally; the vapor phase condenses and the liquid phase alone remains. If the pressure is increased still further, t o the pointy, we generally say the material is a liquid. If it is then heated a t constant pressure from y to z, the system expands considerably, but a t no time does a new phase appear, and we might say a t z the material is presumably still liquid. On the other hand, starting a t x, we may heat the material a t constant pressure and cause all liquid to disappear. At u the system is thus said t o he gaseous. Iscthermal compression from u to z causes considerable decrease in volume but no separation of a new phase. So we might think of z as representing a gaseous statein contrast to our earlier experiment which led us to think of z as a liquid. The point is that when one deals with systems a t pressures and temperatures in the critical region, one must be cautious in designating the nature of a fluid phase in common terms. When a student has been subjected to "the highest temperature a t which.. ." concept, he frequently visualizepor even draws-an isotherm upward from the critical point to demarcate the liquid and gas regions. Some writers arbitrarily divide the pressuretemperature plot into four arbitrary regions labeled liquid, vapor, gas, and fluid, with the four regions having corners a t the critical point. However, others consider such division as not only unnecessary but actually misleading. The only real phase boundary, the only locus along which two phases of a pure substance can coexist a t equilibrium, is the liquid-vapor equilibrium line mC. All properties of the material change continuously along any smooth curve except when the path crosses the liquid-vapor locus. If for a mixture we should divide the area around the critical point into the four arbitrary regions of liquid, vapor, gas, and fluid, we could have (if the system is such as t o allow thecritical point t o fall a t point C,,, in Figure 7 below) the following designations for equilibrium between a denser and a lighter phase: liquid-vapor, liquid-gas, and liquid-fluid. RETROGRADE BEHAVIOR IN MIXTURES
Under the more usual conditions for mixtures, as a t point d in Figure 3, isothermal increase in pressure JOURNAL OF CHEMICAL EDUCATION
ture a t which the gas phase can undergo complete condensation; the critical pressure is the highest pressure a t which the liquid phase can undergo complete vaporization. For C,,,: the critical temperature is the highest temperature a t which the liquid phase can undergo complete vaporization; the critical pressure is the highest pressure a t which the liquid phase can undergo complete vaporization. I t is obvious that to use any of the definitions of critical pressure and temperature in the preceding paragraph requires information about the location of the critical point relative to P,., and T,.,. Certainly, this is no way t o introduce the concept of the critical state. SUMMARY
causes condensation (e.g., from 30y0 liquid to 40% liquid in the container) whereas isobaric increase in temperature causes evaporation (e.g., from 30% to 20970). This normal type of behavior may not be the case in binary (and more complex) mixtures near the critical point. For example, in Figure 6, isothermal increase in pressure from j t o h does cause partial condensation in the normal fashion, but further pressure increase from h to g causes this liquid to revaporize. This is an example of isothermal retrograde vaporization. The opposite path from g to h is one of isothermal retrograde condensation. Similarly, the path from n to m is normal isobaric vaporization, but from m to k is isobaric retrograde condensation, and from k t o m is isobaric retrograde vaporization (11). The critical point of a mixture of methane and butane of the given composition lies between the points P,., and T,. . Not all systems exhibit this hehavior. For present purposes we may recognize three cases, as shown in Figure 7. If the critical point falls a t C,, both P,. and T,. lie on the dew-point locus; if at C,,, P,., is on the bubble-point locus, while T. is on the dew-point locus; if at C,,,, both lie on the buhblepoint locus. For each of these three cases we can give different definitions of critical temperatures and critical pressures in terms of "highest value a t which. . . ." For C,: the critical temperature is the highest temperature at which the gas phase can undergo complete condensation; the critical pressure is the highest pressure at which the gas phase can undergo complete condensation. For C,,: the critical temperature is the liighest tempera-
The purpose of this discussion has been to point out that the common definition of the critical state given in most general chemistry texts is inadequate to describe other than a pure substance and that attempts to retain the phrases "highest temperature" and "highest pressure" lead to undue complications. It is not proposed that an attempt he made to discuss critical behavior of mixtures in the general chemistry course or perhaps even in the first course of physical chemistry. However, it is suggested that the common practice of giving a definition of critical temperature or pressure that applies only to a pure substance instills into the student a false impression that he has some idea of the critical state for fluid systems in general. Even if the instructor states that what he has told the student applies only to a pure substance, that restriction may well be soon forgotten since the student has no alternative definition to which to turn. Is it not preferable to emphasize the increasing similarity between coexistent liquid and gas as a certain combination of pressure and temperature is approached, and the ultimate limit of the loss of distinction between the two phases? This is the critical state. This is true for a pure substance or for a mixture of any number of components. The student then has this broad definition from which he may later specialize to the one-component system if he wishes; he will not automatically think of a highest temperature of coexisting phases whenever he thinks of the critical state. LITERATURE CITED (1) See letter by M. E. Lase, J. CHEM.EDUC.,31, 102 (1954). (2) OLDS, R. H., H. H. REAMER, B. H. SAGE,A N D W. N. LACEY,Ind. Eng. Chem., 36, 292-4 (1944). (3) SAGE,B. H., AND W. N. LACEY,"Volumetric and Phase (4)
(5)
(6)
(7) (8) (9)
TEMPERATURE
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Figur. 1. Three Posdbl. Losation. of th. Clitic.1 Point
VOLUME 34, NO. 10, OCTOBER, 1957
(10) (11)
Behavior of Hydrocarbons," Stanford University Press, Stanford, California, 1939, p. 34. AMERICANINSTITUTE OX. PHYSICS, "Temperatu-Its Measurement and Control in Science and Industry," Reinhold Publishing Corp., New York, 1941, p. 1084. STRONG, R. K., Edifor, "Kingaetts' ChemicalEncyelopedia," 7th ed., D. Van Nostrand Co., Inc., Nem York, 1946, p. 266. HIRSCHFELDER, J. O., C. F. CURTISS,A N D R. B. BIRD, "Molecular Theory of Gases and Liquids, John Wiley & Sons, New York, 1954, p. 382. For example, pp. 357-63 of Reference ( 8 ) . PALMER, H. B., J. Chem. Phys., 22, 62534 (1954). SAGE,B. H., B. L. HICKS,A N D W. N. LACEY,Ind. Eng. Chem., 32, 1085-92 (1940). SAGE,B. H., R. A. BUDENHOLZER, AND W. N. LACEY, Ind. Eng. Chem., 32, 126S77 (1940). KATZ,D. L., AND F. K U R ~ T A Ind. , Eng. Chem., 32, 817 (1940).
