THE CRITICAL TEMPERATURE FRANK BRESCIA College of the City of New York, New York City Most of our recent textbooks on general and physical chemistry refer to the temperature at which the meniscus between liquid and vapor phases disappears as the critical temperature. It is the purpose of this paper to show that this classical and simple concept is most likely erroneous and to propose a more accurate presentation.
THEcritical phenomenon was fir& described by de La Tour in 1822 when he observed that upon heating a liquid in a stationary sealed tube, a t a certain temperature the meniscus between the liquid and vapor phases disappears without ebullition, yielding what appears by ordinary light to be one homogeneous phase. Upon cooling the tube, the meniscus, of course, again appears but the temperature of reappearance does not coincide exactly with the temperature of disappearance. This disappearance of the meniscus was used by Thomas Andrews (1869-76) as the criterion for the critical temperature. He determined i t to be 30.92"C. for carbon dioxide. He concluded (upon the disappearance of the meniscus) that "no separation of the carbonic acid into two distinct conditions of matter occurs, so far as any indication of such a separation is afforded by the action of light" (1). From his studies on the gaseous and liquid states of carbon dioxide under various conditions of temperature and pressure, he coucluded that above this critical temperature, a gas phase exists which cannot be liquefied by pressure; hut below this critical temperature, the vapor is condensable by pressure. Using the average temperature of disappcarance and reappearance of the meniscus, he also determined the critical temperature of nitrogen and carbon dioxide mixtures (1887). Thus in terms of Andrews' classical experiments, the critical temperature may be defined as the temperature a t which the meniscus disappears (it being understood that experimentally i t is the average of the temperatures a t which the meniscus disappears and reappears), or as the minimum temperature above which a gas cannot, as evidenced by an appearance of a meniscus, be liquefied. For a description of an actual determination of the temperatures at which the meniscus disappears and reappears in a stationary sealed glass tube, reference (3) should be consulted. Van der Waals proposed in 1879 his now famous equation of state from which i t follows that there is but one temperature a t which the pressure and the volume of the gas equal those of the liquid. Besides its success
.
in explaining the deviation of gas behavior from the ideal gas law, the isothermal lines plotted from this equation reproduce remarkably well the experimentally determined isotherms. Successful and widely accepted, the van der Waals equation has been the starting point for most subsequent papers dealing with equations of state (5). It was therefore concluded, on the basis of this theory, that a t the critical point no discontinuity exists, both liquid and gas phases becoming identical in all properties. I n terms of this theory, the critical temperature, the temper+ture a t which the meniscus disappears, may he defined or rather interpreted as the temperature a t which the density of the liquid equals the density of the vapor, or as the tcmperaturc a t which the properties of the liquid and gas become identical. The critical temperature may therefore be determined from a series of pressure-volume measurements made a t a series of fmed temperatures extending above the critical point. The minimum tcmperature for which the P-V curve possesses a horizonta tangent (an inflection point for which the change in pressure with volume is zero) is taken as the critical temperature. Apparatus for such measurements with high precision is described and used by Beattie (4) and Michaels (5). Evidence which conflicted with the van der Waals continuity theory was obtained, however, over the turn of the century by several investigators, and Claik and Trauhe have more recently written of their experiences (6). Traube (7) found, for example, a difference in density between the lower and upper portions of a tube containing the carbon tetrachloride system above the temperature a t which the meniscus disappeared. Small calibrated glass floats within the experimental tube were used, instead of reading the position of the meniscus, for density measurements. Eversheim (8) measured the dielectric constant of liquid and vapor hydrogen sulfide as a function of temperature and found that the difference persisted beyond the temperature a t which the ~peniscusdisappeared. Such evidence which indicated a persistence of the liquid state above the temperature a t which the meniscus disappeared was dis-
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counted when it was shown that small amounts of impurities exerted a large influence on the critical phenomena. Particularly influential in this respect was the work of Young (9) who made density measurements of the liquid and saturated vapor phases of normal pentane to a temperature (197.1°C.) just below the temperature at which the meniscus disappeared (197.2"C.) by ohserving the position of the meniscus. It was very evident that the short extrapolation over a smooth parabola of the two curves (density of liquid and saturated vapor against temperature) would yield identical densities for both phases at the critical temperature. From such experiments it was concluded that the temperature at which the meniscus disappears is really the temperature at which the densities of liquid and saturated vapor become equal. The van der Waals theory of the liquid state has since crystallized solidly into our textbooks. While investigating the kinetics of the addition reaction between hydrogen chloride and propylene over a wide temperature range, about -80°C. to over 100°C., Sutherland and Maass (10) found that in the neighborhood of the critical temperature of the mixture under investigation, about 70°C., the temperature coefficient became negative and the velocity of the reaction became zero upon increasing the temperature above the critical point. This led to an assumption involving a discontimuity in state a t the critical temperature and to a series of careful investigations of the critical phenom-
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or
search. 9. 233 (19331.
TABLE 1 Distribution of Densities i n a Sealed Tube a t Various Tern. peratures Temperature,
"C.
Density, float at Density, fiat at 88 cm. from 8 m.from bottmn of tube bottom of tube
125.5 0.2200 0.3360 0.3010 126.7 0.2390, , 126.9 Meniscus invlslble to the eye at 18 cm. 127.1 0.2450 0.2940 128.9 0.2580 0.2800 132.3 0.2650 0.2730 135.1 0.2680 0.2720
.
Diffmnee 0.1160 0.0620 0.0490 0.0220 0.0080 0.0040
ena extending over a period of years by Maass and his coworkers. The measurement of surface tension as a function of temperature was the first investigation undertaken. The capillary rise method was applied to methyl ether and to propylene. The measurements extended t o within 1.5'C. of the temperature a t which the meniscus disappears. The results (11) do not extrapolate t o zero at the latter temperature. A direct method of measuring the density of a liquid and of the vapor phase in equilibrium with it, at temperatures extending from below to above the temperatures at which the meniscus disappears, was then undertaken (19). A glass float of known weight (W, g.) and volume (V, cm.9 was suspended from a quartz spiral in a sealed tube containing the liquid under investigation. The sensitivity (8)of the spiral balance was calibrated in g./cm. by determining the variation in length with suspended known weights. Its normal length (L, cm.) was, of course, also measured. At known fixed temperatures, the float was placed a t different positions in the tube and the length of the spiral (LI, em.) measured. Using Archimedes' principle, W- (L- LI) X S equals the weight of the medium in grams displaced by the float. The weight of the medium so determined divided by the volume of the float yields the density of the medium. Typical results for methyl ether, given in Table 1 and plotted in Figure 1, show a persistence of a definite differencein the density of the medium above and below the position at which the meniscus disappears, although the medium appears as a homogeneous phase to the eye. Stirring the tube contents at constant temperature for short or long periods of time has no effect on the measured density differences. Temperature gradients across the length of the tube of the order of 0.1-O.Z°C. are required to remove or increase the density difference. If the bottom is maintained at the higher temperature, density differencemay be reduced to zero and even reversed. warming the upper portion increases the density difference. Maximum temperature difference, observed while the recorded data were obtained, is O.OZ°C. Precision of the density measurements is 0.3 per cent. These results with methyl ether were duplicated. S i a r measurements made with propylene yielded identical behavior (18). Illustrative results for propyl-
MARCH, 1947
TABLE 2 Density of Propylene as a Function of Float Position a t 93.4OoC. -~ ~~~~~
..
1 1
I 1
Meniscus disa~~eared at the 28.50 cm. wsitiou at 91.9-C. Position of float./ em. 19.875 20.350 26.020 27.850 31.870 35.060 Densitv.~./cm.~ 0.2142 0.2145 0.2145 0.2150 0.2056 0.2056
ene a t 93.40°C., above the temperature a t which the meniscus disappears, are given in Table 2. Good agreement was found between the propylene density measurements obtained with the float method and those dilatometrically determined (14). Above 87.5OC., however, the dilatometric method is uncertain because of the difficulty in reading the position of the meniscus which becomes diffuse. Further evidence that a "liquid" phase of methyl ether and propylene may persist above the critical temperature was obtained from a determination of the dielectric constants of the liquid and saturated vapor of these compounds (16). The dielectric constants (Table 3) do not become equal a t or several degrees beyond the temperature of meniscus disappearance. , TABLE 3 Dielectric Constant of Liquid and Gas Phase Temp., "C.
Liquid
Gas
Methyl Ether
...
1.903 1.899
... ...
1.878
91.9 93.1 96.4
1.860 Propylene 1.331 1.318 1.314
1.279 1.292 1.310
X-ray data obtained in the critical range of isopentane and ethyl ether substantiate this type of evidence obtained by Maass and his coworkers. Characteristic liquid scattering curves, plotted from the measurement of the ionization current produced by the scattered X-rays as a function of angle, are found to persist above the critical temperature (16). With ethyl ether, the scattering curve obtained a t 210°C. has the typical shape of a gas difhaction curve. The diffraction pattern for isopentane changes from one typically liquid to one typically gaseous with patterns in between having similarities to both liquid and gas curires. Further, a theoretical basis for a critical region instead of a critical point is furnished by Porter (17),who showed that a surface tension may become zero before the densities of a liquid and its saturated vapor are the same, and by Mayer, who has calculated on a statisticalmechanical basis (18) the general form of the pressurevolume curve for a number of temperatures in the region
of the critical temperature. The type of P-V diagram obtained for a pure liquid-saturated vapor system is given in Figure 2. Two critical or characteristic temperatures, T, and T,, may thus exist. T , is interpreted to correspond to the temperature at which the meniscus disappears and the surface tension becomes zero. This temperature is lower than the true critical temperature, T,, the temperature a t which the P-V curve has an inflection point for only one volume. At and above T, no differences exist between gas and liquid. Below T, a definite meniscus exists, and the condensed phase has a surface tension. Between T, and T , the P-V curve is horizontal over a finite volume, and no surface tension exists. The magnitude of the temperature interval between T, and T , has not been theoretically calculated. According to the van der Waals equation, this interval is zero. The more recent, careful determination of the isotherms of carbon dioxide in the neighborhood of the critical phenomena by Michaels and his coworkers (6) does not show the existence of a critical region, so that if for carbon dioxide a difference does exist between T, and T,, it is too small to be experimentally detected. It is of interest to note that the critical temperature of carbon dioxide, 31.04°C., as determined by Michaels, agrees, within the probable error of both types of determinations, with the value 30.96°C., determined (19) by the criteria of the meniscus disappearance. Again, although the critical temperature of pentane was carefully determined ($0) from P-V cnrves to only three significant figures, 197.OC., it should be noted that this value agrees with Young's value of 197.2"C., a t which temperature the meniscus disappears and presumably the densities of both phases become identical,
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On the other hand, a definite temperature interval TABLE 4 has been measured for the ethylene system by Maass System Ethylene. Constancy of P r e s s u ~ ewith Varying and his coworkers, who also successfully reproduced Volume a t 9.80°C. the theoretical P-V diagram shown in Figure 2. Merpcus disappears at 9.50PC. Temperature control An apparatus, represented diagrammatically in +0.001 C. Absolute temperature determined to +O.Ol°C. Figure 3, was constructed (21) in which any ?ne of the Specific volume Pressure, atmowheres three variables-P, V, or T-may he kept constant while the other two are varied. The pressure of the system under investigation in bomb B, of calibrated capacity, is balanced by the pressure in bomb B1,maintained and controlled by a known vapor pressure of liquid carbon dioxide thermostated at a known temperature. Density measurements of condensed and low- or high-pressure side. T, was determined to be noncondensed phases are made by the float balance 9.5OoC.; and T,, the temperature for which the change method. To obtain P-V at constant temperature, bomb in pressure with volume was.zero for one volume only, B is maintained at a fixed temperature while the tem- was determined to be 9.90°C. The temperature interval appears to be of the order of magnitude of ten deperature of bomb BIis varied, thereby changing P and V in bomb B. To obtain V-T at constant pressure, grees for methyl ether and of five degrees for propylene bomb B1 is kept at constfmt temperature while the tem- from the data given in Tables 1and 3. This conclusion perature of bomb B is varied. To obtain P-T at con- for propylene is, however, in conflict with the data stant volume, the temperature of both bombs is varied given in Table 5. in such a manner that the mercury level in bomb B is TABLE S constant. Results obtained (22) confirm the existence Determined from Meniscus Disof a region, above the temperature at which the menis- Critical Temperatures appearance and P - V Isotherms in 'C. cus disappears, in which the change in pressure with Stetionmy Shaken volume at cpnstant temperature is zero. This is illusRef. Bomb Ref.Isotherm' Ref. System Bomb trated by the data given in Table 4 for an isotherm. A (19) . . . . . . 31.04 (5) similar type of isotherm obtained at 9.60°C. was shown Carbondioxide 30.96 ... ... Ethane 32.23 (SO) 32.27 (4) to be approachable and reproducible from either the Propane 96.85 ($71 ... ... 96.81 (4) Butane Pentane Ethylene Propylene
$8) (3) (IS) (13)
9.21
Ethyl ether 192.3 Methyl alcohol 240.6
($6) (85)
... ... ...
Ethyl alcohol 241.7 243.6
Figure 3. Diaplam of Bomb Assembly. Bomb6 Contains t h e S ~ t e m Under Investigation. Bomb h Contain. Liquid-Vapor .Carbon Diorids. M is a Msgn-tic Stirrer. F the Float. D the OuartzSpird. and N the Holder. Taken from 0. Maul. and A. L. Gedd... rrlm.. Ray. Sea. London, AZ3B. 307 (1937).
...... ... ...
152.2 197.2 , 9.50 91.4 91.9 Methyl ether 126.9
(88) (9)
($5) (8g)
- ..
... ...
,,,
152.01 197 (51) 9.90 ... 91.4 91.9 Not determined 194.6 Not deter-
... ... ... ...
...
...
-
m i.. n.d ....
...
243.6
(4) ($0)
($2) ($3)
($4)
...
($6)
...
... ($9)
It is thus presently evident that the interval between T, and T, is real, hut for some systems it is either too small to be measured or is nonexistent. This point is emphasized by the data given in Table 5. That the critical phenomenon is more complicated than is predicted by the van der Waals equation receives further proof from the study of the temperature at which the meniscus disappears as a function of density. The critical phenomenon is observable in a tube, according to the classical equation, only when the tube contents conform to one volume (or density)-that is, the critical volume (or the critical density). Actually, the phenomenon has been observed for a range of densities. The temperature a t which the meniscus disappears was obsemed using bombs of known capacity (about, 4 cm.9 and varying known amounts of ethane. Typical results (SO) are given in Table 6. Similar results have been obtained with ethylene and with ethylene-propylene mixtures (31). This evidence substan-
TABLE 6 Disappearance of Meniscus at 32.230eC. + O.OISDC. for Different Densities of Ethane Precision of density measurements. 1/3000 Densitg, g./m.a
T,, "C.
,
not always identical a t the temperature a t which the meniscus disappears. At this temperature the liquid and vapor states may he regarded as miscible, the lower phase in the sealed tube consisting of the liquid molecular species saturated with the vapor molecular species and the upper phase consisting of the vapor saturated with the liquid, the line of demarcation between the two phases not being visible with ordinary light. Since a liquid possesses a more definite structure (order) than a gas (58), this structure persists beyond T , and is not completely broken (disorder) until T, is reached, a t which temperature the complete disorder, or complete ramdon molecular arrangement, characteristic of the gas state, is finally attained. One would thus expect associated liquids to have larger intervals between T,,, and T, than the nonassociated liquids. And in this connection it is interesting to note (Table 5) that carbon dioxide and the saturated lower hydrocarbons, typical unassociated liquids, possess, within the errors of the data, a practically zero interval, whereas the more strongly associated lower ethers and alcohols appear t o have measurable intervals. Strongly associated water has an interval of 6'C. Its meniscus disappears at. 374.2"C. 0.20°C. (59, 40, 41) but the density of the saturated vapor does not equal that of the liquid (59, 40) until the temperature 380°C. (40) is reached. A quantitative relationship between the degree of association and magnitude of the interval cannot, however, be deduced from the presently available data. I n teaching freshmen students, critical temperaturemay be defined as a temperature, characteristic for each gas, above which liquefaction is impossible, irrespective of the applied pressure. It may also be stated that a t this temperature, properties of the liquid and gaseous. states are indistingu~shable. These statements, however, should not be associated with the disappearanceof a meniscus. If i t is desirable to discuss the deter-. mination of a critical temperature in terms of the disappearance of the meniscus in a shaken bomb, the student should be further informed that this phenomenon does not always occur a t the critical temperature as. above defined. For students of physical chemistry, i t is desirable to. discuss the inability of the van der Waals equation to. describe the critical phenomenon and to emphasize t h e existence of two characteristic temperatures for certain. liquids, the so-caUed critical dispersion temperature and the true critical temperature. The uncertainties of t h e data in Table 5 will serve to illustrate to our students: that "classical" chemistry is not yet "solid" or deador even "solved in principle" as several theoretical: physicists have claimed.
tiates the existence of the flat portion a t TT,of the P-V-T diagram demanded by Figure 2. Prior to this latter work, critical temperature determinations based on the disappearance of the meniscus were made in stationary bombs. Shaking the bomb vigorously, however, bas a profound effect not only on the temperature a t which the meniscus disappears, but it also increases greatly the precision with which such measurements may be made (50). The meniscus disappears so sharply in a shaken bomb, rather than the usual fade-out, that reproducibility of the temperature a t which this occurs becomes practically dependent only upon the limits of temperature control. Shaking the bomb causes the meniscus to disappear a t a lower temperature. Thus with ethylene, T , is 9.50°C. in a 0.015'C. in a shaken stationary bomb and 9.21%. bomb. The possible effect of this phenomenon upon the data in Table 5 should not be overlooked. It is suggested (51) that the "temperature a t which the meniscus disappears in a bomb that is vigorously shaken" be known as the "critical dispersion tempers, ture." The critical temperature so determined in a stationary bomb is therefore a comparatively indefinite point between the "critical dispersion temperature" and the true critical temperature. It is further suggested that the determination of the critical temperature in stationary bombs be eliminated as a physical measurement, since it is not a definite temperature, and that the classical definition of critical temperature in terms of a disappearing meniscus in a stationary bomb be dropped. Evidence for heterogeneity a t T,, or the persistence of the "liquid" phase above T,, is also obtainable from solubility (52), heat capacity a t constant volume (55), adsorption (54), and viscosity (56) measurements made through the region of the critical temperature. The viscosity measurements with the carbon dioxide system, however, again indicate no measurable difference between T, and T , (56). A heterogeneous ethylene system, detected by density difference, was produced by cooling $0 a temperature just above the temperature a t which the meniscus disappeared, after the system had been made homogeneous by heating i t 5°C. above the temperature where the m e ~ s c u sdisappeared (57). LITERATURE CITED Heterogeneity is not so restored for all systems. (1) ANDREWS, T., Trans. Roy. Soc. London, 159, 575 (1869). ( 2 ) BENNING,A. F.,AND R. C. MCHARNESS, Ind. Eng. Chem.,. Although i t is not universally accepted that T, and 32, 814 (1940). T , are two distinct and separate characteristic tem( 3 ) 'WOOLSET, G., J. CHEM.EDUC., 16, 60 (1939). peratures~ sufficient and ( 4 ) BEATTIE,J. A,, Proc. Am. Acud. Arts S d . , 69, 389 (1934); sults are available to substantiate the view that the BEATTIEETAL., J. Am. C h m . Soe., 59,1586,1589 (1937);. 61, 24, 924 (1939). molecular state of the liquid and the vapor is certainly
+
~ ~ I C H A EA,, L S B. , BLAISSE,AND C. MICHAELS, Proc. Roy. Soc. L m d m , 160A, 358 (1937). TRAURE,I., Trans. Faraday Soc., 34, 1234 (1938); A. L. CLARK,Chem. Revs., 23, 1 (1938); see also G. BRUHAT, Chaleur et ind., 11, 263 (1930). TRAURE, I., Z. anorg. allgem. Chem., 38, 399 (1904). EVERSHEIM. P.. Ann. Phvsik. 8. 539 (1902): 13.492 (1904). . . YOUNG,s . , ' P ~ ~~La g .53 , (51,' 153 ii8gij; ~ . ' c h e m SOC., . London, 71,446 (1897). SUTHERLAND, H. S., AND 0. MAASS,Can. J. Research, 5.48 (1931).
WINKLER,C. A,, AND 0. MAASS,ibid., 9, 65 (1933). TAPP,J. S., E. W. R. STEACIE, AND 0. MAASS,ibid., 9,217 (1933).
(23) VAUGHAN, W. E., AND N. R. GRAVES, Ind. Eng. Chem., 32, 1252 (1940). (24) SOUNDERS, ibid. (25) FlscnER, R., AND T. REICHEL,Mik~oehemiever. Mikmchim. Acta, 31, 102 (1943). (26) SCHROER, E., Z. phyaik. Chem., 140,379 (1929). Ind. E m". Chem.. 32. 127) . . DEscnaE~.W. W.. AND G. G. BROWN. 836 (1940). (28) KAY,W. B., Bid., 32, 358 (1940). W., AND S. YOUNG,Tram. Roy. SOC.London, 177, (29) RAMSAY, 123 (1886). (30) MASON,S. G., S. N. NALDRETT, AND 0. MUSS, Can. J. Research, 18B, 103 (1940). (31) NALDRETT,S. N., AND 0. MAASS,ibid., 18B, 118 (1940); W. G. SCHNEIDER AND 0. MAASS,ibid., 19B, 231 (1941). C. H., AND 0. MAASS,ibid., 18B, 293 (1940). (32) HOLDER, o ~ ,0. MAASS,ibid., 16B, (33) PALL,D. B., J. W. ~ R o u G n ~AND
, ~ .
WINKLER, C. A,, A N D 0.MAASS,ibid., 9, 613 (1933). WINRLER, C. A., AND 0 . MAASS,ibid., 9, 610 (1933). MARSDEN, J., AND 0 . MAASS,ibid., 13B, 296 (1935). 2.10 (1028) \----,. NOLL,F. H. W., Phys Rev., 42, 336 (1932); G. W. STEWART,Trans. Faraday Soc., 29, 982 (1933); C. A. BENZ, (34) MOR& H. E., AND 0. MAASS,ibid., 9, 240 (1933); W. A. PATRICK, W. C. PRESTON,AND A. E. OWENS,J. P h ~ s . Proe. Iowa Amd. Sci., 41, 249 (1934); W. A. BARNl38, Chem., 29, 421 (1925). . Chem. Reus., 23, 29 (1938). (35) MASON.S. G.. AND 0. MAASS.Can. J. Research. 18B. 128 PORTER,A. W., Phil. Mag., 7, 624 (1929). (1940). MAYER,J. E., AND S. F. HARRISON, J . Chem. Phys., 6,87, NALDRETP, S. N., AND 0. MAASS,ibid., 18B, 322 (1940). (36) 101 (1938). R. L., J. R. DACEY,AND 0. MAASS,ibid., 17B, (37) MCINTOSH, KENNEDY, H. T., J . Am. Chem. Soc., 51, 1360 (1929). 2.11 (1020). -.~ -...,. SAGE,B. H., AND W. N. LACEY, Ind. Eng. Chem., 34, 730 (38) STEWART, G W.. Chem. Revs., 6,483 (1929); Rev. Modern (1942). Phys., 2, 116 (1930). MAASS,O., AND A. L. GEDDES,Trana. Roy. Sac. London, (39) SCHROER, E., Z. physik, Chem., 129, 79 (1927). A236, 303 (1937). H. L., Proe. Roy. Soc. London. A12O. 460 (40) CALLENDAR, MCINTOSH, R. L., AND 0. MAASS,Can. J . Research, 16B, (1928). 289 (1938); J. R. DACEY,R. L. MCINTOSH,AND 0. (41) KHITAROV, N. I., AND L. A. IVANOV, Zentr. Mineral. Geol.. MAASS,ibid., 17B, 206, 241 (1939). 1936A, 46.
