Liquid-vapor equilibria in binary systems containing 4He or 3He with nH2 or nD2

Fluid

Phase Equilibria,

Elsevier Scientific

6 (1981)

Publishing

203-227

Company,

203

Amsterdam

-- Printed

in The Netherlands

LIQUID-VAPOR EQUILIBRIA IN BINARY SYSTEMS CONTAINING 4He OR 3He WITH nH, OR nD, *

M.J. HIZA Thermophysical Properties Division, National of Standards, Boulder, CO 80303 (U.S.A.)

(Received

August

llth,

1980; accepted

Engineering

Laboratory,

in revised form December

National

Bureau

15th, 1980)

ABSTRACT Hiza, M.J., 1981. Liquid-vapor equilibria in binary systems nHz or nDz. Fluid Phase Equilibria, 6: 203-227.

containing

4He or 3He with

Equilibrium liquid and vapor compositions are reported at 2 K intervals for binary systems containing 4He or 3He with nHz or nDz between 20 and 30 K at pressures up to 20.3 x lo5 Pa (20 atm). Vapor pressures measured at 1 K intervals are also reported for nHz from 20 to 30 K and for nDz from 20 to 34 K. A vapor-recirculation apparatus was used with equilibrium compositions determined by gas chromatographic analysis. The results show that, at the same temperature and partial pressure, (1) 4He and 3He are three to five times more soiuble in liquid nH2 than in liquid nDz, (2) 4He is slightly more soluble than 3He in either liquid solvent, and (3) within the precision of measurement, vapor compositions are independent of the helium isotope present. Comparisons are made with corresponding liquid-vapor equilibria and vapor pressure data reported in the literature.

INTRODUCTION

The present investigation was the first phase of a comprehensive experimental study on the liquid-vapor equilibria of binary systems composed of 4He or 3He with nHa, nDa, or nT,. The purpose of this phase of the study was to design and construct an equilibrium apparatus capable of continuous operation between the triple point and critical point temperatures of the isotopes of hydrogen, and to measure by chromatographic analysis the equilibrium distribution of 4He and 3He between the liquid and vapor phases of nH, and nD,. The next phase of the study, measurement by mass spectrometer analysis of the equilibrium distribution of 4He and 3He between the liquid and vapor phases of nD, and nT, with the same basic apparatus, will be discussed in a future paper by R.H. Sherman.

* Contribution of the National Bureau of Standards (U.S.), not subject paper supersedes Natl. Bur. Stand. (U.S.), Tech. Note 621 (1972). 03783812/81/0000-0000/$02.50

@ 1981 Elsevier Scientific

Publishing

to copyright.

Company

This

204

Several investigators have determined compositions of the equilibrium liquid and vapor phases for 4He + nH2 (Smith, 1952; Roellig and Giese, 1962; Streett et al., 1964;Sneed et al., 1968) and 4He + pH2 (Sonntag et al., 1964; Sneed et al., 1968). In addition, some measurements were made to determine the three phase locus (S-L-V) (Sneed et al., 1968; Greene and Sonntag, 1968), the critical locus (Streett et al., 1964;Sneed et al., 1968) and the barotropic locus (Sneed et al., 1968), i.e. the density inversion locus of the liquid and vapor phases. Observation of the barotropic effect was first reported by Onnes (1906). Compositions in all of the investigations noted above (1952-1968) were determined by mass spectrometer analysis. In a recent study of high pressure phase equilibria for 4He + nH,, Streett (1973) included a few low pressure points at one temperature for comparison with his earlier measurements. In this later study, compositions were determined from static thermal conductivity measurements. Preliminary results of equilibrium vapor phase measurements in the solid-vapor region for 4He + H2 and 4He + Ne have been reported graphically by Berman et al. (1979). Concentrations of the minor vapor phase constituent (Hz or Ne) in this study were determined by low temperature freeze out and pressure measurement of the evaporated species. Matyash et al. (1966) report the only data for the solubility of 3He in liquid nHz. These measurements were made “in situ” using a nuclear magnetic resonance technique. Prior to the present investigation, there were no liquid-vapor equilibria data reported for 4He + nD, and 3He + nD%. The most apparent discrepancy is in the liquid phase data for 4He + Hz. The data of Roellig and Giese, comprised of nine independent data points, suggests that the solubility of 4He in liquid nH, decreases with increasing temperature at constant 4He partial pressure. The only other data available at the time were those of Smith, which indicated the opposite temperature dependence. In addition, the liquid phase 4He concentrations of Roellig and Giese are as much as an order of magnitude larger than those of Smith. Eckert and Prausnitz (1963) showed that the ideal vapor computation method used by Roellig and Giese to determine their temperatures could result in an error as large as 2.7 K, although this does not alter the above disagreement. In an attempt to assess the plausibility of each set of discrepant data, Corruccini (1964) compared the 4He K-values and derived heats of solution from each set of data with the corresponding solubility properties deduced from theory, and concluded that the data of Roellig and Giese must be invalid. Corruccini also noted that consistency tests operating solely on the hydrogen fugacities, i.e. the method used by Brazinsky and Gottfried (1962) to evaluate Smith’s data, are ineffective in the analysis of this type of problem. Wilson (1964), prior to the availability of the data of Roellig and Giese, showed that the Redlich-Kwong equation, with modified temperature dependence of the Q parameter, predicted the temperature dependence of *He solubility observed by Smith. The subsequent experimental results from the University of Michigan (Streett et al., K964; Sonntag et al., 1964; Sneed et al., 1968) provided proof of Corruccini’s conclusion and qualitative support of Wilson’s calculations. The data of Matyash et al. for 3He + nH also support the temperature dependence and order of magnitude of the liquid phase a He compositions of Smith. Staveley (1970) noted, however, that even with the newer and more consistent 4He + Hz liquidvapor equilibria data, heats of solution derived from infinite dilution Henry’s constants are less certain than for other low temperature systems he examined.

The objective of the present investigat:ion, established with due consideration of the above discussion, was to obtain a consistent set of vapor pressures for nHs and nDs and low pressure liquid-vapor equilibria data for 4He + nHa, 3He + nHn, 4He + nD,, and 3He + nD, between 20 and 30 K at closely spaced temperatures to facilitate analysis of the results and direct comparison with data of other investigators. The maximum pressure of the liquid-vapor equilibria measurements was intentionally established below

205

the barotropic locus of 4He + nH2 to avoid density instabilities, possible liquid entrainment, and complications in apparatus design and experimental procedures. At pressures above the barotropic locus, for example, it would be necessary to reverse the normal direction of vapor recirculation and to withdraw liquid samples from the top of the equilibrium cell. The barotropic effect, which results when the molecular weight of the more volatile component is greater than that of the less volatile component, would thus occur at higher pressures for 3He + nHz than for 4He + nH2. Pressures at which the densities of the liquid and vapor phases would be the same were estimated for 4He + nHz, 3He + nHz, observations for 4He + and 4He + nD 2, and are compared in Fig. 1 with the experimental nHz (Sneed et al., 1968). To make these estimates, the mass density of the vapor was assumed equal to that of pure liquid nHz or nD2 (Goodwin et al., 1961; Prydz, 1967). The vapor molar volume was then calculated from the average molecular weight based on the equilibrium vapor compositions given by Sneed et al. The barotropic pressure was obtained by assuming that the vapor molar volume of each mixture is approximately equal to the molar volume of pure 4He (McCarty, 1972) or pure 3He (Gibbons and Nathan, 1967) at the same temperature. With these assumptions, best agreement with experiment would be expected at the lower temperatures where the vapor phase is nearly pure He and the liquid phase is nearly pure nHz or nDx. This is apparent for 4He + nHz in Fig. 1. The barotropic locus for 4He + nDp was estimated to show the relative effect of nD2 vs. nH, in the mixture and the position or even the existence of this locus is speculative.

‘lie+ “D-2 ________-______

I

T. K

Fig. 1. Estimated barotropic pressures for 4He + nHz, 3He + nH2, and 4He + nD2 compared with experimental values for 4He + nHz.

206 EXPERIMENTAL

METHOD

The apparatus used in this investigation is a modified design of the vapor-recirculation apparatus of Duncan and Hiza (1970). A schematic flow diagram is shown in Fig. 2 and the arrangement of components within the cryostat is shown in Fig. 3. The equilibrium cell, made of electrolytic tough pitch copper, has an internal volume of 19.8 cm3, with an i.d. of 2.48 cm and an o.d. of 6.35 cm. The closure is a threaded copper plug soft-soldered in place. A double layer of fine mesh screen covers the vapor exit to serve as an entrainment separator. The platinum resistance thermometer (PRT) well parallels approximately the top two-thirds of the equilibrium cavity. At the temperatures of this study, differential temperature measurements between the top of the cell and the bottom of the equilibrium cavity were not considered necessary. The PRT, calibrated on the IPTS-68 kelvin scale, is secured in place with Wood’s metal. The temperature of the equilibrium cell is controlled by balancing refrigeration provided by cold hydrogen vapor from the refrigerant liquid reservoir (2.25 1 capacity) with an automatically regulated 120 ohm heater noninductively wound on the cell just below the equilibrium cavity. At a selected temperature, the unbalance from the corresponding voltage drop across the PRT at 1 mA constant current is sensed by a potentiometer, am-

-39Bcm

3.IBmm

Tuber

Coil ho

Llqu,d

Sample

Line t-l

-Vapor Bulb Lquld Level Indicator

Fig. 2. Schematic

of the experimental

Fig. 3. Details of the phase equilibria

apparatus. cryostat.

207 plified, and fed back to a custom-built power regulator for heater control. With this arrangement, the temperature can be maintained constant within about + 0.005 K during a single experimental run. The maximum imprecision in temperature measurement is believed to be about ?Z0.01 K. The liquid hydrogen refrigerant reservoir was sized to provide continuous refrigeration for about 12 h exclusive of cool-down. Though not shown in Figs. 2 and 3, the cryostat was immersed in a liquid nitrogen bath during all experimental runs. The cell pressure was measured with a 300 p.s.i.a., double-revolution Bourdon tube gage. Though the smallest scale division of this gage is 0.5 p.s.i.a. (0.0345 x lo5 Pa), a finely divided machinist rule was used to estimate lower subdivisions to approximately + 0.05 p.s.i.a. (f0.003 x lo5 Pa). The maximum uncertainty of the gage reading is claimed to be + 0.1 % of full scale with a repeatability of + 0.066 % of full scale. With the gage set at atmospheric pressure, readings checked against a laboratory dead-weight gage were well within the accuracy claims of the manufacturer. At 50 p.s.i.a. (3.45 X lo5 Pa), no difference in readings could be detected, The Bourbon tube gage readings at 150 p.s.i.a. (10.3 x lo5 Pa) were 0.065 % low with increasing pressure and 0.032 % low with decreasing pressure, based on the actual reading. At 300 p.s.i.a. (20.7 x lo5 Pa), the Bourdon tube gage reading was 0.089 % low. Pressures reported here were not corrected for these discrepancies. All fluids introduced into the equilibrium cell were purified with a small, liquid nitrogen cooled, silica gel adsorber (not shown in Fig. 2) between the feed cylinders and the thermal booster/ballast cylinder. The thermal booster/ballast cylinder was used to conserve 3He available for the experiment. By purifying the feed gases, only the He and H, isotopes and Ne impurities are introduced into the equilibrium system. The 4He was standard U.S. Bureau of Mines Grade-A He and the Hz was obtained from the NBS liquid and gas distribution facility. Since the Hz cylinders are often filled with boil-off gas, a cylinder which had been filled several months earlier was selected so that normalization would not be required. The 3He and D2 and the analysis of each were supplied originally by the U.S. Atomic Energy Commission. The 3He contained 1.4 mole % 4He and the D2 contained 1.12 mole % HD and 0.02 mole % Hz. These isotopic impurity levels in the 3He and Dz are significantly higher than the natural abundance of isotopic impurities present in the 4He and Hz, but their contribution to the phase equilibria properties measured here would not be detectable. Liquid samples were withdrawn directly from the bottom of the cell through a 0.178 mm i.d. stainless steel capillary. This capillary is joined to a tube of 1.19 mm i.d., also of stainless steel, about 15 cm above the top of the cell. The internal volume of the larger tube is filled with a copper wire slightly smaller in diameter and about 50 cm in length. Vapor samples were withdrawn from the recirculation pump cavity, which was isolated during sampling. In both cases, the recirculation pump was turned off during sampling. Due to excessive analysis time and to the large difference in compositions of the two phases, it was more convenient to determine liquid and vapor compositions in separate runs. A vapor pressure check at the beginning of each run was used to confirm the reproducibility of experimental conditions within the precision of pressure measurement. Compositions were determined chromatographically using thermistor detectors. To avoid the well known peak-folding phenomenon due to thermal conductivity reversal of He + H2 mixtures (Madison, 1958; Pietsch, 1958; Liebenberg and Edeskuty, 1964; Purcell and Ettre, 1965), Ar was used as the carrier gas at 50-55 cm3 min-l. The mixtures were separated at ambient temperature with a 12 m column, 3.18 mm i-d., packed with 80 mesh molecular sieve 5A. The pressure drop through the column was approximately 1.3 x lo5 Pa. Sample pressures, measured with a mercury in glass manometer, were generally between 0.6 and 0.8 X lo5 Pa and the sample loop volume was 0.3 cm3. With this arrangement, there was no separation of isotopes and the time lapse between sample injection and the start of the He and H2 peaks was approximately 15 and 23 min, respectively. Chromatographic peaks were recorded with a strip chart, particularly for the

208 base line profile. The peak areas were determined by electronic integration, with a voltage to frequency converter and an electronic counter, and those for the liquid phase were corrected for base line offset with planimeter measurements using the strip chart records. The peak area determination is discussed in more detail later. The chromatograph was calibrated with the pure components and five reference mixtures prepared on a partial pressure basis appropriately corrected for nonideality. Excess interaction second virial coefficients from Brewer and Vaughn (1969) with selected values of second virial coefficients for 4He (McCarty, 1972), Ar (Gosman et al., 1969), nH2 (Michels et al., 1960), and nDz (Prydz, 1967) were used to correct for nonideality. For lack of experimental data, it was assumed that the excess interaction second virial coefficients for 4He + nDz and nD2 + Ar were the same as those for 4He + nH2 and nH2 + Ar, respectively. Compositions of three of the mixtures determined by Sherman (see Table 1) from mass spectrometer analysis were in excellent agreement with the calculated values. The calculated compositions of the reference mixtures and results of the analyses are given in Table 1. Since the isotopes were not chromatographically separated, the sum of D2, HD, and Hz concentrations were considered as Dz in the calibrations without response factor corrections. Normalized, this would result in effective Dz concentrations of about 50.14 vs. 50.09 mole % in mixture (4) and about 4.98 vs. 4.97 mole % in mixture (5), which are not significant changes. For ,3He analysis, in lieu of 3He reference mixtures, the peak area was adjusted to the equivalent 4He response for comparison with the appropriate 4He reference mixture. The ratio of integrated peak areas of 4He 3He was found to be 0.858 f 0.004 by of pure at the by analysis of the He peaks to mixture of as the in the of nHz or nD2

1 Composition

of

in chromatographic

As prepared

*

Mass spec. analysis

(1)

4He Ar

5.22 94.78

Not analyzed

(2)

4He

10.08 89.92

10.03 89.97

49.86 50.14

49.86 50.14 49.75 49.82 0.43

H2

49.91 49.52 0:56 *** 0.01 ***

D2 HD Ar

4.91 0.06 95.03

Not analyzed

H2 (3)

4He H2

(4)

4He D2 HD

(5)

l

**

* Corrected for nonideality. * Analysis by R.H. Sherman, Los Alamos Scientific Laboratory. *** Estimated from HD and H2 impurity levels in Dz. l

l

*

209

bration time. With this mixture, there was no base line drift, the 4He peak was nearly symmetrical, and electronic peak area integration was easily reproduced within about 0.05 mole%. However, in comparing mixture (2), 10.08 mole % 4He in nHp, with mixture (l), it was noted that the presence of nH, had some effect on base line stability though good peak separation was obtained. After sample injection, the base line exhibited a slow positive drift, a small positive peak and a negative deflection in advance of the 4He peak, and a negative deflection between the 4He and nH, peaks. The bottom of the negative deflections were approximately the same as the base line before injection and the tail of the large nH2 peak returned slowly but smoothly to the same original base line. The negative deflections before and after the He peak presented the main problem in obtaining a true area for He by electronic integration apart from base line offset. By rezeroing the chromatograph just before the small positive peak, the 10.08 mole % of 4He in mixture (2) was reproduced for several samples, relative to mixture (l), within about 0.1 mole % on the high side. Unfortunately, this agreement was misleading and the contribution from base line offset in all liquid phase He concentrations similarly measured turned out to be larger and less consistent than the above comparisons indicated. Assuming a linear relation between He content in the liquid and partial pressure, all of the liquid phase isotherms obtained from electronic integration alone (i.e. the preliminary values reported by Hiza in 1972) extrapolated to positive zero pressure intercepts, generally between 0.3 and 0.6 mole %. The linear dependence of He concentration on partial pressure and, consequently, the existence and approximate magnitude of systematic error were verified independently by Sherman from his initial measurements on 4He + nD2. Due mainly to higher He solubility limits, the discrepancies were not nearly as apparent for the nH2 systems. As a result, the He peaks for mixtures (1) and (2) were again compared using both planimeter area measurements and electronic integration with and without rezeroing the chromatograph before the positive deflection ahead of the 4He peak in mixture (2). Briefly, it was found that the total area from electronic integration of the 4He peak in mixture (2) minus the area from planimeter measurements between the true base of the 4He peak, defined by a small inflection on each side, and the chromatograph zero provided the most consistent means of reproducing the He concentration of mixture (2), as prepared, with random scatter of less than * 0.1 mole %. The area from electronic integration of the 4He peak from mixture (1) was again used as the reference. All of the liquid phase He concentrations reported here were determined in this manner. Vapor phase compositions were determined by analysis of the chromatographic peaks of both components in the mixture, referenced to either mixture (3) or (4), and the mole fractions were normalized to sum to unity. Mixture (5) was prepared to verify the reliability of analysis of low D2 concentrations using mixture (4) as the reference. For the vapor phase, compositions were determined from electronic peak area integration without planimeter area measurements to correct for base line offset. Contributions from base line offset at these generally larger component concentrations were not as significant and were accounted for in the calibration and normalization procedures used.

RESULTS

AND DISCUSSION

Experimental vapor pressures for nH2 and nD2 are given in Tables 2 and 3. Included are the correlating equations, the differences between experimental and calculated values, the calculated change in vapor pressure at each temperature for a change in temperature of 0.01 K, and the normal boiling point temperature derived from the correlating equations. Experimental liquid-vapor equilibria data for 4He + nH2, 3He + nH2, 4He

210 TABLE Vapor

2 pressures of nH,

In Po(Pa)

= 7.987749

(standard

deviation

-

219.6811/(7.127745

= 0.00478)

APO (exp. -talc.)

PO

( lo5

20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 (20.375 * lo5

Pa = 1 bar = 0.98692

Pa) *

-0.0008 -0.0002 0.0000 0.0049 -0.0042 0.0025 -0.0003 -0.0028 -0.0’086 0.0067 0.0026

MO (lo5

(AT = 0.01 K) Pa) *

0.0027 0.0034 0.0041 0.0049 0.0058 0.0068 0.0079 0.0090 0.0102 0.0115 0.0128

atm.

3 pressures of nD2

In Po(Pa)

= 7.987864 deviation

-

221.2539/(4.032572

20.00 21.00 22.00 23.00 24.00 25.00 26.00 27.00 28.00 29.00 30.00 32.00 34.00

+ T) + In 101325

= 0 -0111) PO (lo5

k)

* lo5

(lo5

nbp)

(standard

(23.666

Pa) *

0.9067 1.2100 1.5824 2.0374 2.5648 3.2026 3.9334 4.7746 5.7295 6.8293 8.0393

TABLE Vapor

+ T) + In 101325

Pa) *

0.2945 0.4275 0.6082 0.8412 1.1204 i.4624 1.8892 2.3822 2.9820 3.6784 4.4678 6.4190 8.9045

-0.0051 -0.0052 0.0005 0.0090 0.0060 -0.0001 0.0043 -0.0078 -0.0038 -0.0018 -0.0129 -0.0089 0.0268

nbp) Pa = 1 bar = 0.98692

APO (exp. -talc.) * (lo5 Pa)

atm.

APO (AT = 0.01 K) ( lo5 Pa) * 0.0011 0.0015 0.0020 0.0025 0.0031 0.0038 0.0046 0.0055 0.0064 0.0075 0.0086 0.0110 0.0136

211 TABLE4 4He+nH2 data P

x2

(lo5Pa)* 20.00

22.00

24.00

26.00

28.00

0.9067

6.233 10.414 15.062 19.281 7.346 11.208 15.965 20.112 1.5824 5.861 9.777 14.655 20.623 2.5648 6.726 10.852 15.517 20.202 7.388 10.908 16.547 20.067 3.9334 8.735 12.186 16.289 19.960 8.481 10.925 12.490 13.959 16.024 18.050 20.257 5.7295 8.749 11.931 16.095 20.343 8.356 11.707 11.793 17.020 19.981

YzPlX,

Yl

YlP/POl

1.0 0.1891 0.1348 0.1094 0.1026

1.0 1.300 1.548 1.817 2.182

1.0

1.0

1.0 0.4695 0.3402 0.2776 0.2503

1.0 1.231 1.439 1.679 1.971

1.0

0.5650 0.4572 0.3911 0.3583

1.0 1.255 1.416 1.620 1.818

1.0

1.0

0.7576 0.6311 0.5392 0.4881

1.157 1.314 1.515 1.733

(lo5Pa)* 0

0.0064 0.0125 0.0165 0.0208 0 0.0075 0.0132 0.0220 0.0305 0

954 781 863 869

0.0099 0.0175 0.0287 0.0365 0

424 413 420 412

0.0114 0.0192 0.0237 0.0261 0.0327 0.0384 0.0425 0

0.0095 0.0221 0.0218 0.0412 0.0520

* lo5 Pa=lbar= 0.98692atm.

523 568 542 564

319 290 289

307 296 294 307

197 193 198 196 196

212 TABLE5 3He + nH2 data P

x2

(lo5Pa)* 22.00

24.00

26.00

28.00

1.5824 8.298 10.601 13.724 15.134 2.5648 7.967 10.374 12.790 14.979 3.9334 7.825 10.435 13.621 15.375 5.7295 9.301 11.700 13.172 15.406

Y2PIX2

Yl

YlP~POl

1.0

1.0

1.0

1.0

I.0

1.0

1.0

1.0

(lo5Pa)* 0 0.0085 0.0113 0.0153 0.0172 0 0.0101 0.0145 0.0190 0.0229 0 0.0097 0.0162 0.0245 0.0291 0 0.0112 0.0187 0.0240 0.0312

723 731 724 718 465 467 467 469 321 321 316 314 227 227 221 221

l lO5Pa=lbar= 0.98692atm. + nD2, and 3He + nD2 are given in Tables 4-7. For the vapor phase, mole fractions (yr) of nH, or nD, and the equivalent enhancement factors (yrP/P,,,) are tabulated. For the liquid phase, mole fractions (x2) of 4He or 3He and the ratios of He partial pressures to mole fractions are tabulated. The He partial pressures were obtained by graphical interpolation of the

TABLE6 4He+nD2 data P

TK)

(lo5Pa)*

20.00

0.2945 6.832 10.042 13.696 18.254 9.846 13.420 16.941 19.450

x2

YzP/Jc, (lo5Pa)*

0

0.0021 0.0028 0.0035 0.0041

4470 4610 4670 4580

Yl

YlP/POl

1.0 0.0603 0.0458 0.0392 0.0349

1.0 1.399 1.562 1.823 2.164

213 TABLEfS(continued) P

x2

(lo5 Pa)*

22.00

24.00

26.00

28.00

30.00

0.6082 8.515 10.363 14.093 17.285 20.063 1.1204 4.037 8.453 J.4.221 20.439 8.712 10.639 13.841 17.127 20.257 1.8892 8.643 9.329 12.069 13.983 17.375 19.664 20.154 2.9820 8.098 10.642 15.744 19.291 6.805 7.112 10.294 15.461 18.795 19.153 20.016 4.4678 7.243 10.556 15.431 20.274 8.943 11.604 14.210 16.493 20.670 20.684

YePlX2

Yl

YlPIPOl

1.0

1.0

1.0 0.3143 0.1773 0.1254 0.1013

1.0 1.132 1.338 1.592 1.848

1.0

1.0

1.0 0.4463 0.3672 0.2836 0.2525

1.0 1.212 1.310 1.497 1.633

1.0 0.6888 0.5263 0.4103 0.3512

1.0 1.117 1.243 1.417 1.594

(lo5Pa)* 0

0.0036 0.0043 0.0070 0.0073 0.0091 0

2130 2200 1860 2210 2070

0.0061 0.0078 0.0107 0.0130 0.0150 0 0.0073 0.0082 0.0109 0.0127 0.0152 0.0192 0.0187 0

1190 1160 1130 1180 1220

0.0055 0.0061 0.0100 0.0188 0.0230 0.0229 0.0244 0

609 593

0.0084 0.0140 0.0197 0.0238 0.0315 0.0310

438 420 409 419 428 436

* lo5 Pa= lbar= 0.98692atm.

852 836 861 878 940 854 902

643 587 609 625 618

P

x2

(lo5Pa)* 20.00

22.00

24.00

26.00

28.00

30.00

0.2945

5.286 5.664 8.553 12.604 15.844 3.496 6.244 9.418 11.859 14.637 0.6082 5.078 7.553 9.722 12.432 16.338 1.1204 3.682 8.343 12.504 16.044 4.071 5.730 6.578 8.840 9.219 9.342 11.301 13.769 13.927 1.8892 5.816 7.040 8.718 11.348 15.651 2.9820 8.808 12.404 14.603 9.467 11.876 15.010 4.4678 7.501 10.035 13.321 17.161 9.105 10.656 13.534 17.816

Y2WX2

Yl

(lo5Pa)* 0

0.0012 0.0010 0.0012 0.0030 0.0033 0 0.0018 0.0029 0.0032 0.0051 0.0064 0

2620 5850 7470 3790 4270

0.0009 0.0022 0.0040 0.0046 0.0055 0.0057 0.0062 0.0066 0.0072 0 0.0033 0.0048 0.0064 0.0084 0.0117 0

3110 1990 1300 1590 1400 1370 1560 1820 1690

0.0072 0.0108 0.0137 0

791 725 775

0.0070 0.0095 0.0140 0.0205

544 536 536 541

* lo5 Pa=lbar= 0.98692atm.

1.0 0.0725 0.0694 0.0512 0.0403 0.0359

1.0 1.302 1.335 1.487 1.725 1.932

1.0

1.0

1.0 0.3465 0.1778 0.1346 0.1148

1.0 1.139 1.324 1.502 1.644

1.0

1.0

1.0 0.4216 0.3307 0.2936

1.0 1.245 1.376 1.438

1.0 0.6731 0.5460 0.4505 0.3833

1.0 1.130 1.226 1.343 1.472

2410 2320 2770 2250 2380

1090 988 983 1030 1080

215

enhancement factors. The appropriate experimental and nD, from Tables 2 and 3 are also included. Vapor pressures

vapor pressures of nHz

of nH, and nD,

Each set of vapor pressures in Tables 2 and 3 was obtained in a single day after careful purging and evacuation of the system. The vapor pressures measured periodically before a set of binary mixture measurements were compared with the corresponding values in these tables to verify control and repeatability of experimental conditions. To obtain an indication of the uncertainty in vapor pressure due to the imprecision of temperature control and to facilitate comparisons with data from other sources, these data were fitted to an Antoine equation of the form In Pe(Pa) = A - [B/(C + T)] + In 101325

(1)

At the normal boiling point, eqn. (1) reduces to T nbp

=

(B

--AC)/-4

(2)

Equation (2), with the constants given in Tables 2 and 3, was used to calculate the normal boiling point temperatures given in those tables. The nH, vapor pressures are generally more indicative of the precision of temperature measurement of this study. Deviations of these values and those of Woolley et al. (1948), Grilly (1951), and Van Itterbeek et al. (1964) from values calculated with eqn. (1) and the constants in Table 2 are shown in Fig. 4. Compared with 20.375 K, the normal boiling point temperature in Table 2, the value listed by Woolley et al. is 20.390 K and that by Van Itterbeek et al. is 20.389 K; the value calculated from the equation given by Grilly for his data is 20.402 K. Deviations of the nD2 vapor pressures and those of Woolley et al., Grilly, and Hoge and Arnold (1951) from values calculated with eqn. (1) and the constants in Table 3 are shown in Fig. 5. The larger deviations at the low temperature end are a result of weighting for uncertainty in pressure measurement. Compared with 23.666 K, the normal boiling point temperature given in Table 3, the value listed by Woolley et al. is 23.573 K. The vapor pressures of nD2, upon which the value of Woolley et al. is based, were measured (Brickwedde et al., 1935) relative to vapor pressures of nH2, but only up to 20.4 K. Thus the normal boiling point temperature they list was obtained by extrapolation. The subsequent measurements of Grilly and of Hoge and Arnold yield values in much better agreement with the value in Table 3. The value calculated from the equation given by Grilly is 23.665 K. The value from the data of Hoge and Arnold is 23.661 K obtained from a fit of seven of their data points between 22.6 and 24.6 K. Since the fit of the present data is not that good, the agreement of the value in Table 3 with the values from Grilly and from Hoge and Arnold is somewhat fortuitous. For example, a fit of only the data points between 22 and 25 K yields a normal boiling

216

Fig. 4. Deviations

of vapor pressures

for nH, from eqn. (1).

Fig. 5. Deviations

of vapor pressures

for nDz from eqn. (1).

point temperature of 23.645 K, which is more consistent with the differences observed for nH,. Since the lowest imprecision of pressure measurement in this study, kO.003 X lo5 Pa, is roughly equivalent to the uncertainty associated with kO.01 K uncertainty in temperature at pressures below about 1.5 X lo5 Pa, the agreement between the measured vapor pressures with the results from the sources cited is quite satisfactory. The only significant discrepancy, i.e. with the vapor pressures of nD, from Woolley et al. above 21 K, is apparently the result of uncertainty in the extrapolation of Woolley et al. Vapor phase saturation

limits of nH, and nD, in 4He and 3He

The equilibrium vapor phase compositions for systems of this type are best evaluated by examination of pressure and temperature dependence of the enhancement factors. The enhancement factor is defined as the ratio of the partial pressure (y,P) of the condensible component (nH, or nD,) to its vapor pressure (Per) at the same temperature. To be consistent, enhancement factors at constant temperature must extrapolate smoothly to unity at

He+nDn

t

0

%e

Fig. 6. Enhancement nDp.

factors

of nDz at constant

temperature

Fig. 7. Enhancement nD2.

factors

of nDz at constant

total pressure

for 4He + nDz and 3He +

for 4He + nD* and 3He +

the vapor pressure; or at constant pressure, below the critical pressure, to unity at the temperature for which the vapor pressure is equal to the pressure of the isobar. The enhancement factors in Tables 4-7, when plotted as a function of pressure and cross-plotted at even pressures as a function of temperature, satisfy these tests for consistency. The isothermal curves for the *He + nD, and 3He + nD, values are shown in Fig. 6 and are cross-plotted at constant pressure in Fig. 7. The intercepts in Fig. 6 are the experimental vapor pressures and those in Fig. 7 were determined from the vapor pressure equation. The broken curves in Fig. 6 were interpolated from Fig. 7. It is apparent from Fig. 6 that the vapor phase nonideality is independent of the He isotope present in this pressure region. This is not surprising when one compares enhancement factors below 20 X lo5 Pa for systems such as Hz + Ar (Mullins and Ziegler, 1965) and Ne + Ar (Streett, 1965) near the normal boiling point temperature of Ar. Even for these systems, the difference reflected in the Ar enhancement factors only becomes apparent as the pressure is advanced to 20 X lo5 Pa and above. As a result, the vapor phase data obtained for 4He + nH, were considered sufficient to represent 3He + nHz without additional measurements.

218 The enhancement factors are quite linear for 4He t nH, at 26.00 and 28.00 K. Linear regression of these values at each temperature as a function of (P -Pa,), the difference between total pressure and nH, vapor pressure, results in a standard deviation of 0.0060 with a maximum deviation of 0.009 at 26.00 K; at 28.00 K, the standard deviation is 0.0017 with a maximum deviation of 0.005. Enhancement factors at the respective nH, vapor pressures from the resulting equations are 1.0029 at 26.00 K and 1.0028 at 28.00 K. For the nD, systems, only the enhancement factors at 24.00 K up to about 15 X lo5 Pa appear to be linear. Linear regression of the combined values from the 4He and 3He data results in a standard deviation of 0.0089 with a maximum deviation of 0.017 for the 3He point at 3.6 X lo5 Pa. The enhancement factor at the nD, vapor pressure from the resulting relation is 1.0089. Based on the 30 values, the maximum deviations, and the difference from unity of enhancement factors calculated at the vapor pressures, the uncertainty of enhancement factors from the vapor phase data reported here is thought to be about + 0.03. Enhancement factors from the three vapor phase isotherms of Smith (1952) for the 4He + nH, system and corresponding isotherms taken from the present study are compared in Fig. 8. The 17.40 K curve was obtained by extrapolation, but the low pressure region shown should be reasonably correct. If the enhancement factor of 0.74 at about 2 X lo5 Pa is disregarded, the 20.39 K isotherm of Smith would be fairly well behaved. Similarly , Smith’s 17.40 K isotherm is reasonable if one disregards the low pressure enhancement factors of about 1.5 and 1.55. His vapor phase data at 21.70 K are the least consistent of his results. Enhancement factors representative of the vapor phase data of Streett et aI. (1964) and Streett (1973) for 4He + nHn, of Sonntag et al. (1964) for 4He t pHa, and corresponding isotherms taken from the present study are compared in Fig. 9. Agreement is excellent with all of the nH, data of Streett. Differences are generally less than 3% with a maximum difference of 5% for one point at 26.00 K. Though agreement with the pHa data of Sonntag et al. is comparable with that for nHz at 29.00 K, the differences at the lower temperatures are systematic and appear to increase, from about 3 to lo%, with a decrease in temperature. Due to the difference in vapor pressures between pHa and nHn, the intercepts for 4He + pHa should be higher in pressure by about 0.04 X lo5 Pa at 20.40 K, 0.10 X lo5 Pa at 26.00 K, and 0.15 X lo5 Pa at 29.00 K. If the slopes of the enhancement factor curves are about the same for the two H, forms, one would expect the enhancement factors for pHa to be slightly smaller than those for nHa, at least at the lower pressures. Sneed et al. (1968) report data for both nHs and pHa with 4He, though predominantly for nH,, extending from the higher pressures of Streett et al. (1964) and Sonntag et al. (1964) up to about 100 X lo5 Pa. At 20.40 K between 51 and 103 X lo5 Pa, where data for both forms of H2 are given, there is no systematic difference in enhancement factors up to about 75 X lo5 Pa. At about 34 X lo5 Pa, where they meet the two sets of lower pres-

.

07 0

2

I

I

I

I

I

I

/

I

4

6

8

10

12

14

16

IS

Fig. 8. Comparison for 4He + nHz.

P,PC

I

20Kl0’

with the enhancement

Fig. 9. Comparisons with the enhancement Streett et al. (1964) and of Streett (1973) al. (1964) for 4He + pH,.

factors

IO

0

2

4

6

8

10

P, PO

12

14

16

I8

20x10$

of nH2 from the data of Smith (1952)

factors of nH, and pH, from the data of for 4He + nH, and from the data of Sonntag

et

sure data, the nH, enhancement factors are about 0.2-0.25 higher than those of Streett et al. and they extrapolate to values consistent with those of Sonntag et al. between 15 and 25 X lo5 Pa. However, below 40 X lo5 Pa at 29.00 K, where the enhancement factors from the two sets of lower pressure data are in good agreement, the nH, enhancement factors of Sneed et al. are higher than those of either set by about 0.1-0.15. At both temperatures, all other things being equal, the vapor phase nH, mole fractions of Sneed et al. are systematically higher than those of Streett, et al. by about 5-10s. Since the enhancement factors from the data of Streett et al. extrapolate smoothly to the nHp vapor pressure at each temperature, it is probable that the vapor phase data from that source are the more reliable. Similar comparisons cannot be made with the vapor phase data of Roellig and Giese (1962) and Matyash et al. (1966) since they report He partial pressures only. Roellig and Giese give sufficient information regarding their method of data acquisition from which vapor phase compositions can be derived indirectly. But, it was felt that uncertainty introduced in the process would preclude meaningful comparisons.

220

Solubility

of 4He and 3He in liquid nH, and liquid nD,

The liquid phase He mole fractions (3t.J given in Tables 4-7 at each temperature show linear dependence on He partial pressure (y,P) within the precision of composition measurement. Since the liquid and vapor phase compositions were not measured at the same total pressures, the He partial pressure corresponding to the experimental temperature and pressure of each liquid point was obtained by interpolation from the vapor phase enhancement factor curves discussed in the previous section. As a result, the variations in the ratios of He partial pressures to mole fractions (i.e. the Henry’s law proportionality constants) given in Tables 4-7 are due mainly to the scatter in the liquid phase mole fractions. To obtain an estimate of the uncertaimy in the He solubility data and to facilitate comparisons, the He concentrations at each temperature were fitted to a linear equation of the form 100~~ = A + B(y,P)

(3)

The constants obtained for each temperature and system are given in Table 8. The results of statistical analysis for the following three isotherms are considered most representative of the consistency of the liquid phase data. At 26.00 K, the standard deviation in 100 x2 for 4He + nHz is 0.0737 with a maximum deviation of 0.097, and for 4He + nDz it is 0.0469 with a maxiTABLE

8

Constants for eqn. (3) 100 x2 = A + B(y2P) where P is in Pa * 4He * nD2

3He + nDz

0.0099 0.0211

0.0006 0.0223

-0.0174 0.1399

-0.0033 0.0483

-0.0136 0.0431

-0.0264 0.2429

0.6155 0.2119

0.0469 0.0814

0.0093 0.0609

0.0205 0.3314

-0.0392 0.3215

0.0634 0.1081

0.0407 0.0903

-0.0034 0.5124

-0.0631 0.4614

0.0084 0.1623

0.0047 0.1307

0.0438 0.2304

0.0019 0.1852

Constant

*He + nHz

20.00

A B x 105

0.0020 0.1165

22.00

A B x 105

0.0513 0.1753

24.00

A B x 105

26.00

A J3 x 105

28.00

A

3He + nH2

TK)

B x 105 30.00

* lo5

A B x 105 Pa = 1 bar = 0.98692

atm.

221

IO

8

y*p,

PO

He

Fig. 10. Solubility of 4He and 3He in liquid nH2 and In liquid nDz at 28.00 K as a function of partial pressure.

mum deviation of 0.089. The 30 values are 0.222 and 0.141 (mole % He), respectively. At 24.00 K, the standard deviation in 100 x2 for 3He + nDz is 0.0644 with a maximum deviation of 0.090. The 30 value is 0.193 (mole 5% He). From these results, the maximum uncertainty in the liquid phase He mole fractions reported here is thought to be about kO.002 (kO.2 mole 5%). Comparisons of the values of B in Table 8 are indicative of the relative solubilities. From these values at corresponding temperatures, it is apparent that 4He is about 3-5 times more soluble in liquid nHz than in liquid nDz, and that 4He is generally about 1.1-1.3 times more soluble than 3He in either liquid solvent. It is noted that He is still significantly more soluble in liquid nH2 at 26.00 K than in liquid nD2 at 30.00 K where both liquid solvents are at the same reduced temperature, 0.78. The liquid phase He concentrations at 28.00 K for the four systems are compared in Fig. 10 as a function of partial pressure. It can also be seen from the values of B in Table 8, that at any partial pressure, the solubility of He in the liquid increases with temperature. However, at constant total pressure, the solubility of He in the liquid can go through a maximum. At total pressures below the solvent critical pressure as the temperature is increased, the solubility of the gas in the liquid must decrease toward zero as the saturation temperature of the solvent is approached at the subject pressure. In Fig. 11, this temperature dependence is shown for the nD, systems at constant total pressures below 16.43 X lo5 Pa, the critical pressure of nD,. The data were not at sufficiently high temperatures to define the maxima at 10 X lo5 Pa total pressure. Calculated gas solubilities at a total pressure of 10 X lo5 Pa for the four systems at 20.00 K and the nDz systems at 23.00 K qualitatively verify the relative solubilities observed. The method was that used by Corruccini

222

I IS

20

22

24

28

26

30

32

T, K Fig. 11. Solubility

of 4He and 3He in liquid nDz at constant

total pressure.

(1964), adapted from regular solution theory by Prausnitz (1958). The model defines the solution process as (1) compression of the solute gas from its partial pressure P, to an isometric mixing pressure 7~where the molar volume of the gas is equivalent to its partial molar volume in solution, (2) dissolving the gas in the liquid at 71,and (3) decompression of the liquid solution to the final system pressure. The equation for the process is V2@W2 --In

x2

= WLV62)

+

RT

4)”

+ A_

pv

dp

s 2 RT n

The PVT and thermodynamic properties of 4He, 3He, D2 and H, were taken from McCarty (1972), Gibbons and Nathan (1967), Prydz (1967), and Roder et al. (1965). The latter reference is a convenient source of pH2 properties but the difference from those of nH, would have little effect on the calculated results. At 20.00 K, the value of v2 of *He and the corresponding isometric mixing pressure needed to reproduce the experimental mole fraction of 4He in liquid nH, were determined and these were used to calculate the solubility of 4He in liquid nD, at the same conditions. With the values of v2 = 37.05 cm3 mole-l and x = 56 X lo5 Pa, x2 calculated for 4He + nH2 is 0.0108 compared with 0.0102 from experiment. The value of x2 calculated for 4He + nDz with the same 4He parameters is 0.00033 compared with 0.0021 from experiment. The isometric mixing pressure for 4He + nD, would have to be about 95 x lo5 Pa to obtain agreement with experiment. The solubility of 3He in both solvents was calculated with an isometric mixing pressure of 56 X lo5 Pa and the corresponding value of v2 = 39.52 cm3 mole-’ for 3He. This resulted in calculated values of 3c2= 0.0034 vs. 0.0073 from experiment for 3He + nH, and 3tz = 0.000070 vs. 0.0021 from experiment for 3He +

223

nD,. The isometric mixing pressure for 3He + nHs would have to be about 101 X lo5 Pa and that for 3He + nD, about 274 X lo5 Pa to obtain agreement with experiment. At 23.00 K, where the reduced temperature of nD, is the same as that for nHs at 20.00 K, i.e. 0.60, the isometric mixing pressure needed for 4He + nD, is about 122 X lo5 Pa, while that for 3He + nD, is about 284 X lo5 Pa. The liquid phase He concentrations at 23.00 K were obtained by interpolation. The ratio of these pressures is roughly the same as those for the nHz systems at 20.00 K and the isometric mixing pressures for 4He + nD, and 3He + nD2 at 23.00 K are both a little higher than those at 20.00 K. The higher isometric mixing pressures for 3He relative to 4He and for both at the higher temperature are consistent with the differences in reduced temperatures. Probably the most meaningful results of the calculations are those for the same gas with the different solvents at the same isometric mixing pressure., The calculated values of x2 for 4He in nD2 compared with that for 4He in nH2 indicates that it is more difficult to dissolve 4He in nD2 than in nH,; and, though not in quantitative agreement, that the experimental observations are consistent with the thermodynamic properties of the liquid solvents. Experimental liquid phase He concentrations as a function of partial pressure for He + H2 from the literature are compared in Figs. 12-15 with corresponding isotherms taken from the present study. In all cases, the partial pressures were taken from the reported vapor phase data. Of the three iso-

Fig. 12. Comparison

of the solubility

of 4He in liquid nHz with the data of Smith (1952).

Fig. 13. Comparison Giese (1962).

of the solubility

of 4He in liquid nHz with the data of Roellig and

~2 P, Pa ‘He

Fig. 14. Comparison of the solubility of 4He in liquid nH2 with the data of Streett et al. (1964) and of Streett (1973) for 4He + nH2 and of Sonntag et al. (1964) for 4He + pH2.

therms for 4He + nHa from Smith (1952) (Fig. 12) his data at 21.67 K are the least consistent with the present results, as were his vapor phase data at this temperature. The differences at the other two temperatures are no more than 0.2 mole %. The inconsistencies in the 4He + nHz data of Roellig and Giese (1962) relative to the present data are shown in Fig. !3. The tempera-

Fig. 15. Comparison (1966).

of the soluhility

of 3He in liquid nH2 with the data of Matyash

et al.

225

tures assigned to each data point are those calculated by Eckert and Prausnitz (1963). Although differences approach 1 mole %, the three data points at approximately 26 K are the most consistent with the present results. The 4He + nH, data of Streett et al. (1964) and Streett (1973) and the 4He + pH, data of Sonntag et al. (1964) are compared in Fig. 14 at two temperatures with isotherms from the present results. The agreement is better with the more recent measurements of Streett than with his earlier measurements, though the differences of all of his data from the present data are generally within 0.2 mole %. The differences from the pH2 data of Sonntag et al. at the higher temperature are generally larger. In Fig. 15, the data of Matyash et al. (1966) are compared with corresponding isotherms from this study. Their data are generally within 0.2 mole % of the present results. At 20.40 K and below, their data are generally higher, but -the data point at 24.00 K is lower by about 0.2 mole %. At 20.40 K and a partial pressure of 10 X lo5 Pa, the 3He concentration from Matyash et al. is about 1.10 mole % compared with the 4He concentration of about 1.4 mole % from Streett et al. (1964) and about 1.25 mole % from the present results. This difference between the solubility of 3He and 4He is consistent with that observed in this study. With the noted exceptions, the differences in liquid phase He concentrations between the literature data and those reported here for the He + Ha systems are within the estimated maximum uncertainty of about + 0.2 mole %. ACKNOWLEDGEMENTS Partial funding was provided initially by the U.S. Atomic Energy Commission through the Lawrence-Livermore Laboratory. Useful discussions with W.J. Hall, H.H. Otsuki, W.R. Parrish, and R.H. Sherman are gratefully acknowledged. The contributions of N.C. Winchester during construction of special instrumentation and the assistance of W.H. German during assembly of the apparatus and experimental measurements were greatly appreciated. NOMENCLATURE

A, B, C f P Y2P

= p2

PO

R

&I v x Y

constants fugacity pressure partial pressure (e.g. He) vapor pressure gas constant absolute temperature, kelvin change in internal energy from a specific state to the ideal gas state partial molar volume mole fraction in the liquid phase mole fraction in the vapor phase

Greek letters solubility parameter, (AU/v)112 isometric mixing pressure volume fraction, xrVr/(xlV1 + X2V2)

226 Subscripts

1 2 nbp

less volatile component (e.g. Hz) more volatile component (e.g. He) normal boiling point

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227 Mullins, J.C. and Ziegler, W.T., 1965. Phase equilibria in the argon-helium and argonhydrogen systems from 68 to 108°K and pressures to 120 atmospheres. Adv. Cryog. Eng., 10: 171-181. Onnes, H.K., 1906. Contributions to the knowledge of the G-surface of Van der Waals. XI. A gas that sinks in a liquid. Commun. Phys. Lab’. Univ. Leiden, No. 96a. Pietsch, H., 1958. Die quantitative Bestimmung von Gasen mit hilfe der Chromatographie. Erdoel Kohle, 11: 702-705. Prausnitz, J.M., 1958. Regular solution theory for gas--liquid solutions. AIChE J., 4: 269-272. Prydz, R., 1967. The thermodynamic properties of deuterium. MS. Thesis, University of Colorado. See also Prydz, R., Timmerhaus, K.D. and Stewart, R.B., 1968. The thermodynamic properties of deuterium. Adv. Cryog. Eng., 13: 384-396. Purcell, J.E. and Ettre, L.S., 1965. Analysis of hydrogen with thermal conductivity detectors. J. Gas Chromatogr., 2: 69-71. Roder, H.M., Weber, L.A. and Goodwin, R.D., 1965. Thermodynamic and related properties of parahydrogen from the triple point to 100” K at pressures to 340 atmospheres. Natl. Bur. Stand. (U.S.) Monogr. 94. Roellig, L.O. and Giese, C., 1962. Solubility of helium in liquid hydrogen. J. Chem. Phys., 37: 114-116. Sherman, R.H., (in preparation). Liquid-vapor equilibria in binary systems containing 4He or 3He with nDz or nT2. Smith, S.R., 1952. I. Gas-liquid phase equilibrium in the system He-Hz. II. Development of mass spectrograph techniques for analysis of He--Hz and their isotopes. Ph.D. Thesis, Ohio State University. Sneed, C.M., Sonntag, R.E. and Van Wylen, G.J., 1968. Helium-hydrogen liquid-vapor equilibrium to 100 atm. J. Chem. Phys., 49: 2410--2414. Sonntag, R.E., Van Wylen, G.J. and Crain, R.W., Jr., 1964. Liquid-vapor equilibrium in the system equilibrium hydrogen-helium. J. Chem. Phys., 41: 2399-2402. Staveley, L.A.K., 1970. Hard-sphere model applied to the solubility of gases in low-boiling liquids. J. Chem. Phys., 53: 3136-3138. Streett, W.B., 1965. Liquid-vapor equilibrium in the system neon-argon. J. Chem. Phys., 42: 500-503. Streett, W.B., 1973. Phase equilibria in molecular hydrogen-helium mixtures at high pressures. Astrophys. J., 186: 1107-1125. Also private communication, Feb. 1973. Streett, W.B., Sonntag, R.E. and Van Wylen, G.J., 1964. Liquid-vapor equilibrium in the system normal hydrogen-helium. J. Chem. Phys., 40: 1390-1395. Van Itterbeek, A., Verbeke, O., Theewes, F., Staes, K. and De Boelpaep, J., 1964. The difference in vapor pressure between normal and equilibrium hydrogen. Vapor pressure of normal hydrogen between 20” K and 32” K. Physica, 30: 1238-1244. Wilson, G.M., 1964. Vapor-liquid equilibria, correlation by means of a modified Redlich-Kwong equation of state. Adv. Cryog. Eng., 9: 168-176. Woolley, H.W., Scott, R.B. and Brickwedde, F.W., 1948. Compilation of thermal properties of hydrogen in its various isotopic and ortho-para modifications. J. Res. Natl. Bur. Stand., 41: 379-475.