532
D. ATACK AND W. G . SCHNEIDER
THE COEXISTENCE CURVE OF SULFUR HEXAFLUORIDE I N THE CRITICAL REGION D. ATACK'
AND
W. G. SCHNEIDER
National Research Council, Ottawa, Canada Received April 10, 1960 INTRODUCTION
I n the thermod.ynamic equilibrium diagram for a two-phase, liquid-vapor, one-component system, the coexistence curve bounds the two-phase region. According to the van der Waals theory, the shape of the coexistence curve in the immediate vicinity of the critical point is roughly parabolic when the phase relationships are represented on a diagram of density, or specific volume, versus temperature. The apex of the parabola corresponds to the critical state, which is therefore a unique state of the system. The coexistence curve in the critical region is defined in terms of the temperature of disappearance or reappearance of the visible meniscus between the two phases. The statistical theory developed by Mayer (4) suggests that the coexistence curve, defined in terms of menisrus separation, becomes flat and parallel to the density, or specific volume, axis a t some temperature, T,. The temperature T,, according to Mayer, is lower than the true critical temperature T,, the conventional critical temperature, which is defined as the unique temperature at which both a p l a u = 0 and a 2 p / B v 2= 0; between the two temperatures the system is composed of more than one stable phase, whereas above T, only one stable phase, the gas phase, may exist. There is a finite range of specific volumes over which the meniscus disappears and reappears at the same temperature T,. Thus, as applied to the coexistence curve, the classical theory would indicate a unique critical point, whereas the theoretical approach of Mayer would lead to a critical region. These controversial views have recently been discussed with reference to the experiments of several investigators (6, 7). It mas considered that more accurate experimental data concerning the shape of the coexistence curve in the critical region were necessary, and would have an important bearing in elucidating the nature of the phase change. The results of several investigations on one-component systems, quoted and reported by Schroer (lo), indicate that the coexistence curve has a flattened part in the neighborhood of the critical point. However, the experimental data cannot be considered sufficiently accurate to justify this conclusion. More precise measurements were recently obtained by Naldrett, Mason, and Maass (3, 5 ) on ethane and ethylene systems, respectively, which substantiate the previous findings within the limits of experimental error. These latter data, which are summarized in figures 1 and 2, show considerable scatter, and can quite well be represented by smooth rounded curves as we have indicated. I t would seem that 1
National Research Laboratories Post-Doctolate Rrsearcll Fellon, 1949-50
COEXISTESCE CURVE O F SULFUR HEXAFLVORIDE
533
two main factors are responsible for this scatter. In the first place, each euperimental point is determined on a different sample and with a different amount of component, thus giving rise to n larger relative error in the density value than if all observations were made upon the same sample in the same containing. bomb. This procedure also admits of different relative amounts of impurities in the system, should any impurity be present in the original sample. Secondly, and probably more important, the feasibility of reproducing temperature measurements to 0.001”C. on a Beckmann thermometer over a period of days is to be questioned. In this investigation, using sulfur hesafluoride as the pure component, we have employed a somewhat more refined technique in an effort to eliminate these sources of error.
0 Z403
0 230C
.
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3 g
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0 2000
Ol800 32200
32 210
32220
32230
32
T E Y P L I A T Y R E *:
F I G . 1 (Left). Coexisteiice curve of ethane plotted from d a t a of reference 1 FIG.2 (Right). Corxistence curve of ethylene plotted from h t : i of reference 6 EXPERIS1EST.iL
A . Method and procedure Aidiagram of the apparatus is shoxn in figure 3. Sulfur hesafluoride, which had kindly been prepared and purified by Mr. J . UT.Dale, was introduced into the 2-1. bulb A. It \vas subsequently fractionated several times between the two bulbs B and C, one bulb being held at -78°C. and the other at -180°C. An amount of sulfur hesafluoride roughly 20 per cent by weight in excess of the maximum amount which \vas to be employed in subsequent measurements was condensed into the brass bomb E, which was fitted with n small high-pressure valve. The remainder of the gas, apart from a few centimeters which were left in bulb B, was pumped out of the system. The bomb \vas then detached. from the manifold and weighed. The weight, which was of the order of 230 g., could be reproduced to 1 part in IOs after repeated immersion in liquid air. The bomb \vas replaced on the manifold, stopcock .\ \vas opened. and the trapped air ~ m s
534
D. ATACK A S D W. G . SCHNEIDER
pumped out of the system, after which the manifold was thoroughly flushed by sulfur hesafluoride from B. Sulfur hesafluoride \vas then condensed from E into the glase bomb B, which was 12 cm. long and 1 cm. in internal diameter, to a density of 0.1 g./ml. in ex* cess of the critical density. Valve G was closed and the remainder of the gas was condensed back into the brass bomb. The weight of sulfur hexafluoride transferred into the glass bomb was obtained by difference. The assembly D, F, G was then immersed into an oil thermostat. After observations had been made upon the sample of this density, F mas closed, and by opening G a small amount of gas was expanded into the steel capillary J. Valve G was then closed, and the expanded gas was drawn off through H and
MsLEOD GAUGE AND VACUUM PUMPS
FIG.3. Diagram of the apparatus
condensed into the brass bomb, which was reweighed. In this manner, observations could be made upon the same sample through a whole range of densities. The volume of the glass bomb and the capillary had been previously determined by a gas-expansion method (2). The volume between valves G and F was about 0.05 ml. and the volume of the glass bomb approximately 10 ml., so that an expansion in the critical region brought about a decrease in density of the order of 0.0030 g. ml. The rate of condensation of the expanded gas into the brass bomb was accelerated considerably by reducing the dead space of the manifold to as small a value as possible. After all observations were completed, the remainder of the sample was condensed into the brass bomb in order to ascertain whether there had been a loss in weight.
COEXISTENCE CGRVE OF SULFUR HEXAFLUORIDE
535
B. Temperature measurements The thermostat, which has been described previously, was tapable of control to ~0.0005"c.(1). A Leeds and Northrup platinum resistance thermometer, calibrated by the U. S. Bureau of Standards, was used for the absolute temperature measurement in conjunction with a Leeds and Korthrup Type G-2 Mueller bridge. The ice point of the thermometer, which was checked after each temperature measurement, showed variations of only 1-2 X l(r ohm over a period of weeks. C. Observation of the meniscus Previous investigations have shown that the temperature of reappearance of the meniscus, unlike the temperature of disappearance, is a reproducible and characteristic reference point in the critical reg,ion (3, 5). However, it is necessary to make a further differentiation with regard to the reappearance temperature, according to whether or not the system has been stirred before the obser-
(0)
(b)
m (e)
FIG.4 . Stages in the physical appearance of meniscus formation in an unstirred system
vation is made. The form of the meniscus reappearance is different in the two cases. In addition, an unstirred system shows a lower temperature of reappearance than one which has been stirred. The difference between the two temperatures, both of which are reproducible, is of the order of 0.005°C. I t has been established that both the nature and the temperature of meniscus reappearance in an unstirred system are dependent upon the maximum temperature of the heating cycle and the time that the system is retained above T, (1, 3). Thus it is necessary to state the history of the system above T , in defining a characteristic point of reappearance without stirring. In the present experiments without stirring, the temperature was taken 0.50°C. above T , and retained there for 5 min. before the temperature was lowered. KOsuch information is necessary in the case of a stirred system. It should also be noted that all thc opalescent effects were observed by means of transmitted white light. The physical nature of the meniscus reappearance as the critical temperature is approached in the absence of stirring is shown diagrammatically in figure 4. At the position of reappearance a small diffuse opalescent band first appears (figure 4 (a)), which becomes increasingly more intense and sharply defined as
536
D. .4T.4CK A S D W. G. SCHNEIDER
the temperature is sloivly decreased (figure 4 (b)). The meniscus finally appears m a very distinct white line through the middle of the sharply defined dark band (figure 4 (e)). In figure 5 the sequence of observations is depicted when vigorous stirring takes place between each observation. As the temperature is slowly decreased, faint brown opalescence appears dispersed throughout the length of the tube (figure 5 (a)); it becomes increasingly more intense, yet remains dispersed throughout the tube, with a further decrease of temperature (figure 5 (b)). Finally, a greyish “wet mist” appears, accompanied by a distinct brown line of demarcation as the mist settles down (figure 5 (c)). At densities higher than the critical density, the brown opalescence becomes more intense at the top of the tube just prior to meniscus formation (figure 5 : (e), (d), (c)); the volume occupied by the mist is small and localized to the ultimate position of reappear-
FIG.5 . ( a ) ,( b ) , ( c ) : stages in the physical appearance of meniscus formation in a stirred system. ( d ) , (e): gradation of opalescent intensity in a stirred system a t a density higher than the critical density, (e) being a t a slightly higher temperature than ( d ) .
ance, and the line of demarcation appears quite rapidly. As the critical density is approached, the opalescent intensity becomes more uniformly intense and the volume of mist becomes larger. -4very much longer time is required for the line of demarcation to appear. When the density becomes less than the critical density, the opalescence is more intense at the bottom of the tube, and the time required for meniscus separation to occur decreases. The position of reappearance of the meniscus is above or below the JTertical center of the tube, at densities respectively higher or lower than the critical density. A t the critical density, taken as that corresponding to the highest temperature a t which two visible phases can exist, the position of meniscus reappearance coincides approximately with the center of the tube. The difference between any two positions of reappearance, separated by equal density steps and measured as a distance along the tube, becomes increasingly great as the critical density is approached.
537
COEXISTESCE CURVE OF SULFUR HEXAFLUORIDE
I
TEYPEMTUPE
~
T.
45.440 45.444 45.449 45.451 45.453 45.454
TEXPEPAIURE
f.lml.
~
I 1
TEMPEUTUPE
DEXSITY
0.7813 0.7759 0.7697 0.7644 0.7580 0.7527
DENSITY
~
~
#./ml.
45.455 45.454 45.452 45.4505 45.453
1
DENSITY
'C.
TEbIPEPATUPE
0.7465 0.7412 0.7357 0.7304 0.7245 ~
1
DENSITY
OC.
f./ml.
"C.
g.lml.
45.538 45.543 45.548 45.5505 45.552 45.5535 45,555
0.7879 0.7816 0,7764 0.7706 0.7642 0.7580 0.7516
45.554 45.552 45,5505 45,549 45.546 45.5415
0.7456 0.7393 0.7333 0.7265 0.7201 0.7138
was suspected. This lack of symmetry may be due to fractionation of the sample upon withdrawal of small amounts. Such fractionation, though small in amount, is definitely possible if the expansion is made from a two-phase system. This fact may be used to advantage in detecting impurities. Confirmation of the presence of impurities was obtained when the whole of the sample was withdrawn from the bomb and refractionated between liquid carbon dioxide and liquid air. The refractionated sample gave a slightly higher temperature of reappearance at a given density (approximately 0.7698 g./ml.) than had been obtained with the previous sample. This procedure waa repeated until the temperature of reappearance a t this density remained constant after further fractionation. It was assumed that the system then contained no im-
5.38
D. ATACK AND W. G. SCHNEIDER
purities. Moreover, a mass spectrogram of this final sample showed no trace of water, air, or sulfuryl fluoride. The latter had been regarded as a probable impurity, arising from the method of preparation of the sulfur hexafluoride. The results in table 2, graphically represented in figure 7, were obtained for this sample, which was taken to be the pure component. It is to be emphasized that all the results given in both tables refer to states of the system in which the meniscus reappeared within the confines of the tube. The critical temperature of sulfur hexafluoride was found to be 45.555”C. and the critical density 0.7517 g./ml.
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T IYIIRATURI
FIQ.6 (Left). Coexistence curve of sulfur hexafluoride containing a small amount of air
FIQ.7 (Center). Coexistence curve of pure sulfur hexafluoride FIG.8 (Right). The superposition of the two coexistence curves of figures 6 and 7 DISCUSSION
The improved technique employed in the present experiments has greatly reduced the scatter of the experimental points, and the shape of the coexistence curve seems to be roughly rounded. The actual deviation from constant temperature at the top of the coexistence curve over the density range 0.74560.7580 g./ml. is extremely small and, moreover, is of the same order as the error in the temperature measurements. Thus, until more accurate temperature measurements are available, it is difficult to say whether or not the curve is “mathematically flat” over the density range 0.7456-0.7580 g./ml. I t has been suggested (8) that there may still be traces of impurity in the final sample and that the curve may flatten out somewhat if these were eliminated. In figure 8 we have superimposed the two curves of figures 6 and 7, and there would seem to be little
COEXISTENCE CURVE OF SULFUR HEXAFLUORIDE
539
difference in curvature in the two cases, indicating that traces of impurity do not have such a profound effect upon the curvature. In this figure we have also indicated by the dimensions of the plotted points the error in the temperature measurement. If we consider that the imposition of the gravitational field causes a uniform pressure gradient throughout the tube, then the fact that meniscus reappearance occurs at different heights in the tube over a range of overall densities is not incompatible with classical theory. If such were the case, it would be reasonable to assume that the density a t the point in the tube at which the meniscus separates corresponds in every case to the critical value. However small the bombs may be, it is important to note that the relative density gradient would therefore be exactly the same in the region of the meniscus. In this respect one may reasonably assume that the density range over which the meniscus reappears within the confines of the bomb will be a function of the length of the bomb. It would be interesting to test this experimentally. Owing to the effect of gravity, one would expect the curve to have a flattened part whether the transition takes place according to classical theory or whether it involves molecular clustering. On this basis it would seem difficult to explain a coexistence curve which has a curved part at the top. We may thus conclude that with all factors favorable to the observation of a flat top the result is inconclusive. Yet the indications are that if such a flat part does occur, it is over a very small density range and certainly much smaller than would be indicated from the results on ethane and ethylene. SUMMARY
The coexistence curve of sulfur hexafluoride has been determined in the critical region by a more refined technique than has been used heretofore. The shape of the curve in the critical region may be flat over the very small density range 0.745647580 g./ml. The critical temperature of sulfur hexafluoride waa found to be 45.555% and the critical density 0.7617 g./ml. The authors are indebted to Professor 0. K. Rice for reading and criticizing the manuscript prior to publication. REFERESCES (1) ATACK,D., A ~ SCHNEIDER, D W . G . : J. Phys. & Colloid Chem. 64, 1323 (1950). (2) KAMINSKY, J., A N D BLAISDELL, B. E . : Rev. Sci. Instruments 10, 57 (1939). (3) MASON,S . G., SALDRETT, S. S . , A N D MAASS,0.: Can. J. Research 18B, la3 (1940). (4) MAYER,J. E., A N D HARRISON, S. F . : J . Chem. Phys. 6, 87, 101 (1938). ( 5 ) XALDRETT, S. K.,A N D MAASS,0: Can. J . Research 18B, 118 (1940). (8) RICE,0. K . : J . Chem. Phys. 16, 314 (1947). (7) RICE,0. K . : Chem. Revs. 44, 69 (1919). (8) RICE,0. K . : Private communication. (9)RUEDY,R . : Can. J. Research 9B,637 (1933). (10) SCHRBER, E . : Z . physik. Chem. 129,79 (1927).
