Vapor-Liquid Equilibria from Total-Pressure Measurements. A New Apparatus Richard E. Gibbsl and Hendrick C. Van Ness* Fluid, Chemical, and Thermal Processes Division, Rensselaer Polytechnic Institute, Troy, N . Y . 12181
A new apparatus for the measurement of vapor pressures of liquid solutions i s described. Liquid solutions of known composition are prepared in a test cell by volumetric metering of degassed liquids from accurate piston-injectors. Once the injectors are charged, vapor pressures for a binary system at constant temperature over the entire composition range are measured in a day. Solution of the coexistence equation provides the isothermal va por-liquid equilibrium relationship,
T h e measurement of heats of mixing with a n isothermal dilution calorimeter developed in our laboratory (Winterhalter and Van Ness, 1966) has proved so advantageous as to prompt application of the same basic idea to the determination of vapor-liquid equilibria (VLE) , Our earlier work with VLE (Ljunglin and Van Ness, 1962; Van Ness, et al., 1967a,b) convinced us of the desirability cf exploiting the route to VLE through total-pressure measurements. However, the experimental technique employed, though sufficiently accurate, did not produce data with the desired rapidity. A separate experiment was required for each measured vapor pressure because pure degassed liquids were distilled directly into the test cell, which then had to be emptied and evacuated after each such measurement. In the new method described here, pure degassed liquids are first transferred into evacuated piston-and-cylinder devices, where they are stored for subsequent injection into the vaporpressure test cell. Solutions of known composition are formed in the test cell and the composition is varied by metering the pure liquids volumetrically from these piston-cylinder injection devices. The entire composition range for a binary system is covered in two runs, and it is entirely practical to produce a complete pressure trace based on 20 to 30 vapor pressure measurements in one day. A schematic diagram of the major components of the new apparatus appears in Figure 1. Operation of the apparatus starts with the introduction of pure liquids into the two degassing units, where dissolved gases are removed over a period of time. After evacuation of the system, the degassed liquids are transferred to the piston injectors, where they are stored under positive pressure. With the test cell submerged in the constant-temperature bath, the cell is half-filled by metering in one of the pure liquids. After equilibration, the vapor pressure is recorded, and a small amount cf the second liquid is metered into the cell. The vapor pressure of this dilute solution is recorded, and the process is repeated for increasingly concentrated sclutions until the cell is nearly full. The cell is then emptied and evacuated, and a second run is made with the components added in the reverse order. The compositions in the cell are calculated from the accurately measured volumes injected. Vacuum is produced by combination of a mechanical pump and a n oil diffusicn pump, and the system is evacuated to a Present address, Rensselaer Research Corporation, Troy,
N. Y. 12181.
410 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 3, 1972
pressure below 10 p . The constant-temperature water bath, which is easily raised to submerge the cell and lowered to expose it, maintains a set temperature to ~kO.006~C without attention over the period of a run. The temperature range with a water bath is from 0 to about 75OC, and temperature is measured with an absolute accuracy of =tO.0loC. Vapor pressures are measured with a. thermosta ted Texas Instruments Co. fused quartz precision pressure gauge. Experimental Details
A proportioned drawing of the degassing apparatus is shown in Figure 2. Compartment C holds up to 300 om3 of sample; compartment A has a n external diameter of about 15 cm, and the cold finger B has a diameter of about 6 cm. The sample to be degassed is charged to C through the opening made by removal of the stem of needle valve E. This valve is then closed, and A is evacuated through stopcock D. The cold finger B is filled with a n ice-water mixture, E is opened, and heat is applied to C. Gentle refluxing follows. After 1 hr or so, the heater is removed, E is closed, and A is evacuated. This sequence is repeated a number of times until the liquid is judged to be sufficiently degassed. This process may be followed by a vacuum sublimation in the manner described by Bell, et al. (1968). In this event B is filled with a suitable coolant, such as liquid nitrogen, and D is opened to the vacuum system. The rate of sublimation onto the cold finger is regulated by the setting of needle valve E. Following degassing, the liquid is brought up into compartment A by sublimination or by freezing onto the cold finger B. Valve E is then closed; once thawed, the liquid is drawn through port F into one of the piston injectors. Figure 3 shows a semi-schematic drawing of the essential features of one piston-injector and the vapor-pressure test cell. The piston-injector is a Ruska Instrument Corp. Model 2200, stainless steel, 100-cm3 capacity, liquid-metering pump. The piston M is advanced by a precision lead screw D, and displaced volume is indicated by a traveling marker on a hub graduated to 0.01 cm3. The test cell F is a stock end piece of Corning industrial glass pipe with a capacity of about 100 cm*. For pressures much above atmospheric it would be replaced by a metal cup. The lid E is a square metal plate that supports all components within the cell, namely, a stirrer shaft and paddle, the magnet G, and a set of stationary baffles. The stirring is actuated by a n external rotating magnet. Custom-machined
needle valves I are integral with the cell lid so as to eliminate dead space. The cell, injection lines, and piston-injectors are evacuated through a 1-cm port H in the cell lid. This port is closed by a swivel-mounted piston which makes an O-ring seal when drawn up into the polished port opening. The cell is connected through line J to the Texas Instruments fused quartz pressure gauge L. Line J is insulated and heated to a temperature above the cell temperature so as to prevent condensation in the line. The pressure gauge is internally thermostated and calibrated for operation a t 49°C. Since the vapors from the cell act directly on the interior of the fused-quartz helical sensing element of the ga.uge, the bath temperature is limited to temperatures below 49°C for the mode of operation shown in Figure 3. Direct exposure of a T I gauge to other than inert gases has previously been reported by Singh and Benson (1968). Nevertheless, some question remains as to whether the gauge calibration is affected by this practice. In order to circumvent this possibility and to allow operation of the bath a t temperatures above 49OC, we have modified the design by interposing a Ruska Instrument Corp. differential pressure null indicator between the cell and the pressure gauge. Dry nitrogen is then used in the pressure gauge, and the null device and the line leading to the cell are heated to a temperature such that condensation of vapor cannot occur. The reference side of the pressure gauge is connected tc the vacuum system through line K, and the gauge therefore provides readings of absolute pressure. Once a component has been drawn into its piston-injector from a degassing cell, the piston M is advanced to put the liquid under pressure. This reference-point volume is recorded. The stop-point for advancing the piston is in all cases determined by an accurate break-point torque wrench, set to overbalance the frictional effect of the packing around the piston. By this technique volume differences read from the injector represent volume of liquid passed through needle valve I. After the cell is submerged in the constant-temperature bath, port H is closed and about 25 cm3 of one component is injected into the evacuated cell. The vapor pressure of this pure component is recorded, and if possible compared with values from the literature. An additional 25 cm3 of the same component is then added to the cell and the vapor pressure is again recorded. Experience has shown that when a liquid is not sufficiently degassed these two vapor-pressure readings will not agree. If adequste degassing is indicated, a run proceeds by injection of a quantity of the second component into the cell. The cell is stirred during an equilibration period. When no pressure change with time (usua,lly after 10 to 15 min) is noted, stirring is discontinued, and the quiescierit cell is allowed to stand for an additional 5 to 10 min. If the pressure is stable, it is recorded as the vapor pressure. Successive increases in composition of the second component are generated in like fashion until about 50 cma of the second component have been injected. The other portion of the composition range is covered by a second run, made with the materials remaining in the piston-injectors. Additional detsils are given by Gibbs (1971). Experimental Results and Discussion
Measurements of va.por pressures for the ethanol-nheptane system a t 30°C were used to test the apparatus. This system was chosen because of its highly nonideal behavior and because of the availability of extensive data reported earlier from this laboratory (Van Ness, et al., 1967a).
Vacuum
Q Figure 1. Schematic diagram of equipment
Figure 2. Degassing apparatus: A, reflux chamber; B, cold finger; C, liquid-storage bulb; D, vacuum stopcock, E, Teflon needle valve; F, port to piston-injector
Figure 4 shows a comparison of the new data with those reported earlier. The solid line is an analytic representation of the earlier data resulting from the extended spline-fit technique (Klaus and Van Ness, 1967). Similar representation of the present data (Gibbs, 1971) and interpolation allows direct comparison of results. The average deviation between vapor pressures from the two sets of data is less than 0.3%. The dashed line of Figure 4 is the dew-point curve computed by the coexistence equation (Van Ness, 1964) from the earlier data. Similar results calculated from the present data are compared on the y os. z plot of Figure 5 with the earlier results. The excellence of agreement is evident. The earlier VLE data a t 30°C were combined with heat of mixing data to yield VLE results a t a constant pressure of 760 mm (Van Ness, et al., 1967a). These results are in close agreement with data recently reported by Raal, et al. (1972), who measured both y and z with a recirculating equilibrium still. Of the possible sources of error, incomplete degassing is undoubtedly the most important. No general test for completeness of degassing is available, and one must rely on experience, on repeatability tests, and on comparison of pure-component vapor pressures with literature values when they are available. I n any event thorough degassing is essential, and if it is not attained, large errors can result. Vapor pressures are highly temperature dependent. Thus errors in temperature translate into errors in vapor pressure, Ind. Eng. Chcm. Fundam., Vol. 1 1, No. 3, 1972
41 1
Figure 5. Vapor composition y vs. liquid composition x for ethanol (1)-n-heptane (2) at 30°C. The solid line is from Kochar ( 1 966), and the triangles are from the present work
Figure 3. Piston-injector and test cell: A, line to degassing vessel; B, piston-injector body; C, packing nut; D, lead screw; E, cell cover; F, glass cup; GI Teflon-coated magnet; HI port to vacuum system; I, needle valves; J, heated line; K, line to reference vacuum; L, Texas Instruments pressure gauge; MI piston
XI 2Yl
Figure 4. Vapor pressures for ethanol (1)-n-heptane (2) at 30°C:0, data of Van Ness, et a/.,( 1 967a); A, present work
and the magnitude depends on the temperature and on the substrance. For ethanol and n-heptane at 30°C an error of 0.01"C results in errors in vapor pressure of 0.04 and 0.03 mm, respectively. A systematic error is introduced in calculated liquid compositions if no account is taken of the material in the vapor phase. Since the cell is initially filled with liquid to only half its volume, some of the injected liquid vaporizes. When the composition in the vapor phase is different from that in the liquid phase, as is usually the case, direct calculation of composition from known volumes of injected liquids gives not the composition of liquid in the cell but the overall composition. At pressures below atmospheric, the great differences in density between liquid and vapor phases almost always 412
Ind. Eng. Chern. Fundarn., Vol. 1 1 , No. 3, 1972
makes a correction for the amount of material in the vapor phase entirely negligible. For the ethanol*-heptane data reported here the maximum error introduced is 0.0005 in the mole fractions. Where a correction is required, it can easily be made by a simple iterative calculation. One first ignores the effect of vapor space on the liquid composition and solves the coexistence equation for an initial estimate of vapor compositions. These are used together with known volumes of the vapor space for each datum point to correct the liquid compositions, and the coexistence equation is again employed to find a new set of vapor compositions. The process may be repeated if necessary. Calculation of the masses of injected liquids from the measured volumes requires knowledge of the densities of the liquids a t the temperature and pressure in the injectors. The temperature of the injectors is controlled through air-conditioning of the laboratory, and the pressure in the injectors is controlled through use of a torque wrench, as already described. Since the injectors have a very large heat capacity jn relation to the heat capacity of the stored liquids, fluctuations in room temperature have little effect on the liquid densities. The stored liquids are in a compressed state, and the correct liquid density for calculation of an injected mass is the compressed density. However, if both injectors are subject to approximately the same conditions and if a consistent injection technique is employed, negligible error is introduced by use of densities measured a t atmospheric pressure. The data described here were taken with the injectors under a pressure of about 5 atm, and calculations show that this compression causes a density increase of only about 0.5% in each liquid. It is readily shown that if the densities of both liquids are in error by the same fractional amount, then no error results in calculated mole fractions. Since most organic liquids well below the critical temperature have densities and isothermal compressibilities of the same order of magnitude, similar treatment of the two injectors usually ensures that errors introduced by use of densities for atmospheric pressure are inconsequential. If in some case this is inappropriate, the required refinements in technique are obvious. It is, of course, essential that all volume measurements be made a t the same pressure. Inconsistencies in procedure during a run can well lead to unacceptable errors. Conclusions
The apparatus described provides the means by which accurate isothermal VLE data may be accumulated very rapidly. Use of such data a t a single temperature in conjunction with
heats of mixing allows calculation of VLE behavior for the system over a wide range of temperatures and pressures. Isothermal VLE data taken a t several temperatures also permit the same calculations. The addition of a third pistoninjector to the apparatus would expand its capabilities to the study of multicomponent systems. Acknowledgment
Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for support of this research.
Gibbs, R. E., Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, N. Y., 1971. Klaus, R. L., Van Ness, H. C., A.I.Ch.E. J. 13, 1132,(1967).
Kochar, N. K., Ph.D. Thesis, Rensselaer Polytechnic Institute, Trov. N. Y.. 1966. Ljungiin, J. J.,’VanNess, H. C., Chem. Eng. Sci. 17, 531 (1962). Raal, J. D., Code, R. K., Best, D. A,, J. Chem. Eng. Data 17, 211 /,nrro\ (1YtA).
Singh, J., Benson, G. C., Can. J. Chem. 46, 1249 (1968). Van Ness, H. C., “Classical Thermodynamics of Non-Electrolyte Solutions,” pp 136-148, Pergamon, Oxford, 1964. Van Ness, H. C., Soczek, C. A., Kochar, N. K., J. Chem. Eng. Data 12, 346 (1967a). Van Ness, H. C., Soczek, C. A., Peloquin, G. L., Machado, R. L., J. Chem. Eng. Data 12,217 (1967b). Winterhalter, D. R., Van Ness, H. C., J. Chem. Eng. Data 11, 189 (1966).
literature Cited
Bell, T. N., Cussler, E. L., Harris, K. R., Pepela, C. N., Dunlop, P. J., J. Phys. Chem. 72, 4693 (1968).
RECEIVED for review August 27, 1971 ACCEPTED May 23, 1972
A Small-Volume, Flow-Proportional Counter for Radioactive Tracers Eduardo Wolf and J. M. Smith* University of California, Davis, Calif. 96616
A-small-volume (-1 .O cms)counter for radioactive tracers, designed to give a minimum of dispersion, has been built and tested. Low dispersion is required if transient phenomena, such as adsorption rates on catalysts, are to be measured chromatographically using such a detector. The counter was tested by measuring peaks in the effluent when pulses of 14C0 are introduced into a helium stream fed to a column. Comparison of these peaks with those obtained using a thermal conductivity detector in series indicates that the counter does not cause appreciable dispersion.
A chromatographic method has been developed (Schneider and Smith, 1968) for measuring equilibrium constants and mass-transfer rate constants in a fixed-bed reactor. A pulse of adsorbing gas is introduced into the feed stream and the chromatographic peak of tracer is measured in a detector a t the exit of the bed. The retention time and dispersion of the peak are used to establish the equilibrium and rate parameters. To use the method for the determination of adsorption rate constants, i t is necessary to inject an isotope as the tracer into a carrier gas of unlabeled molecules. Padberg and Smith (1968) have measured chemisorption rates of hydrogen on a nickel catalyst in this way by introducing deuterium pulses into a stream of hydrogen entering the bed. A small-volume thermal conductivity detector was satisfactory for analyzing mixtures of hydrogen and deuterium. The method is rapid and conditions (temperature and pressure) in the catalyst bed can be changed easily. A critical requirement is that dispersion be minimal in the detector. Otherwise, the dispersion due to the catalyst bed cannot be determined accurately from the observed chromatographic peak. Application of the method to gases other than hydrogen would be valuable. Particularly, i t would be helpful to mea-
sure chemisorption rates of hydrocarbons on catalysts important for petrochemical reactions. To accomplish this requires a radioactive counter for the detector-a device capable of counting, for example, radiation from carbon-14. The two existing flow-proportional counters do not meet the low-dispersion requirement. The detector described here was developed to fulfill this need. Radioactive flow counters have been designed primarily for use in counting effluents from gas-liquid chromatographs (Lee, et al., 1962; Welch, et al., 1967; Wolfgang and Rowland, 1958). The objective was to obtain a high efficiency (fraction of radiation that is detected) in order to detect and count low-activity, radioactive substances separated in the chromatograph. I n one type, gc effluent is mixed with a filling gas and the mixture passed through the counter. I n the second type the gc effluent is maintained separate from the filling gas with a window. The efficiency of the first type is high, but the mixing with the filling gas increases the dispersion. Also the gases that may be employed are restricted to those that do not cause quenching problems. I n the existing window type, the volumes are large (-40 cm3 minimum) in order to obtain reasonable efficiencies. Dispersion in such a large volume would eliminate this form for use in measuring rate constants. Ind. Eng. Chem. Fundam., Vol. 11, No. 3, 1972
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