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NBS TECHNICAL NOTE 621

Liquid-Vapor

Equilibrium in the Binary Systems

of He

4

and He

3

with nD2 and nH2
NATIONAL BUREAU OF STANDARDS

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. BUREAU Of SftiiGfigBS

2

Q(LI0C

UNITED STATES DEPARTMENT OF COMMERCE

Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb. Director

NBS

-t-TECHNICAL NOTE 621

ISSUED JULY 1972

Nat. Bur. Stand. (U.S.), Tech. Note 621, 66 pages (July, 1972)

CODEN: NBTNAE

Liquid-Vapor

Equilibrium in the Binary Systems

of He 4 and He 3 with nD2 and nH 2

M. J. Hiza

Cryogenics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

-,.<°>*.

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide

a means for making available scientific data that are

of transient or limited interest. Technical Notes may

be listed or referred to in the open literature.

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

(Order by SD Catlog No. 013.46:621), Price 65 cents

TABLE OF CONTENTS

Page

List of Figures ti List of Tables m

Nomenclature i v Abstract 1

1. Introduction i

2. Experimental Method 5

3. Experimental Results 10

A. Vapor Pressure of nD and nH 10

4 3 B. Solubility of He and He in Liquid nD and Liquid nH 13

4 3 C. Vapor Phase Saturation Limits of nD and nH in He and He 23

4. Discussion 28

A. Maxima in Gas Solubility at Constant System Pressure 28

B. Deficiency of Predictions from Regular Solution Theory 31

C. Comparisons of the Liquid Phase Data for the He-H Systems 34

4 D. Comparisons of the Vapor Phase Data for the He -H Systems 39

5. Summary 42

6. Acknowledgements . 44

7. References 45

Tables 48
LIST OF FIGURES

1. Estimated barotropic loci 4

2. Schematic diagram of the experimental apparatus 6

3. Details of the equilibrium cryostat 7

4. Deviations of vapor pressure data for nD from equation 1 11

5. Deviations of vapor pressure data for nH from equation 1 12

4

6. Solubility of He in liquid nD 14

3 7. Solubility of He in liquid nD 15

4

Z 8. Solubility of He in liquid nH 16

3 9. Solubility of He in liquid nH 17

4

10. Henry's law values for He in liquid nD 18

3 11. Henry's law values for He in liquid nD 19

4

12. Henry's law values for He in liquid nH 20

3 13. Henry's law values for He in liquid nH 21

14. Infinite dilution Henry's constants 22

4 3 15. Isothermal enhancement factors for the He - nD and He - nD systems .... 24

4 3 16. Enhancement factors for the He - nD and He - nD systems at constant. . . . system pressure 25

4

17. Isothermal enhancement factors for the He - nH system 26

4

18. Enhancement factors for the He - nH system at constant system pressure ... 27

4 3 19. Solubility of He and He in liquid nD at constant system pressure 19

4 3 20. Solubility maxima for He and He in liquid nD 30

4 3 21. Solubility of He and He in liquid nH at constant system pressure 32

4

22. Henry's law values from the He - nH data of Smith compared with those of this investigation 35

4

23. Henry's law values from the He - pHn data of Roellig and Giese compared

with those for He'* - nH from this investigation 36

2 4

24. Henry's law values from the He - nH, data of Streett et al. and Sneed et al.

4- and from the He* - pH^ data of Sonntag et al. compared with those for the

He^ - nH data from this investigation 37

Z

3 25. Henry's law values from the He - nH data of Matyash et al. compared with

those of this investigation 38

4

26. Enhancement factors from the He - nH data of Smith compared with those of

this investigation 40

4

27. Enhancement factors from the He - nH, data of Streett et al. and from the

He* - pH^ data of Sonntag et al. and of Roellig and Giese compared with those

for He 4 - nH from this investigation 41
LIST OF TABLES

1. Vapor pressure of nD 48

2. Vapor pressure of nH 48 V 3. Experimental liquid phase compositions for the He - nD system 49

3 4. Experimental liquid phase compositions for the He - nD system 50

4

5. Experimental liquid phase compositions for the He - nH system 51

3 Z

6. Experimental liquid phase compositions for the He - nH system 52

4

7. Experimental vapor phase compositions for the He - nD system 53

3 8. Experimental vapor phase compositions for the He - nD system 54

4

9. Experimental vapor phase compositions for the He - nH system 55

4 3 10. He and He K-values for the nD systems 56

4 3 11. He and He K-values for the nH systems 58

12. Heats of solution 60
NOMENCLATURE

A, B, C = constants of the Antoine equation (eq„ 1)

f = fugacity

CO H = infinite dilution Henry's law constant

AH = heat of solution

s K = ratio of the mole fraction of a component in the vapor

to its mole fraction in the liquid

P = pressure

P = partial pressure

P* = reference pressure (1 atm =0.101325 MN/m )

p

= vapor pressure

R = gas constant

T = absolute temperature, Kelvin

AU = change in internal energy from a specific state to the ideal

gas state v = molar volume

v = partial molar volume

x = mole fraction in the liquid phase

y

= mole fraction in the vapor phase

Greek Letters

1 /2

6 = solubility parameter, (AU/v)

TT = isometric mixing pressure

cp = volume fraction, x v /(x v. +x v )

Subscripts

1 = less volatile component (e.g., H )

2 = more volatile component (e.g., He)

nbp = normal boiling point

B = barotropic
4 3 Liquid-Vapor Equilibrium in the Binary Systems of He and He with nD and nH

M. J. Hiza

Cryogenics Division

Institute for Basic Standards, National Bureau of Standards

Boulder, Colorado

Abstract

Experimental data are reported for the equilibrium liquid and vapor phase com4 3 4 3 positions of the He -nD and He -nD systems from 20 to 30 K and the He -nH and He -nH

systems from 20 to 28 K. The maximum experimental pressures were 20 and 16 atm (2.0

2 4 3 and 1.6 MN/m ) for the He and He systems, respectively. In addition, vapor pressures were measured from 20 to 34 K for nD and from 20 to 30 K for nH .

Values of Henry's constants, enhancement factors, K-values, and heats of solution were derived from the experimental data for each system. The derived properties are

4 4 3 compared with those derived from previous data for the He -nH , He - pH , and He -nH

systems

4 3 4 3 Key Words: Binary systems, gas solubility, He -nD , He -nD , He -nH , He -nH

liquid-vapor equilibrium, nD vapor pressure, nH vapor pressure.

1 . Introduction

The purpose of the present investigation was to obtain a consistent set of experi4 3 mental data on the equilibrium distribution of He and He between the liquid and vapor

phases of nD and nH . It is hoped that this information will help resolve some of the discrepancies of the earlier investigations on the ,4He -H_ system and also provide additional

information for evaluation of predictive methods for systems composed of the molecular

species exhibiting strong quantum effects.

In a recent review paper, a detailed discussion was given on the contribution

of consistent sets of phase equilibrium data on binary systems of cryogenic interest, and

related pure fluid data, to an improvement of prediction methods for mixture properties.

[21 The subsequent paper of Sikora is an excellent example of related advancement in fundamental theory. Though the emphasis in both was on systems containing He, H , and Ne as one component, the systems and regions covered allowed simplified theoretical treatment.

However, theory becomes considerably more complicated and uncertain for binary systems,

such as He-Ne, Ne-H , and He-H , with the various isotopic modifications, in which one or

* This study was carried out at the National Bureau of Standards under the sponsorship of

the U. S. Atomic Energy Commission.
both components exhibit strong quantum effects. Reliable experimental data representative

of each type of the three systems is indispensible to the theoretical development.

[31 The liquid-vapor equilibrium data for the Ne-nH system of Streett and Jones 1

[41 and Heck and BarrickL together cover the liquid range of Ne and are in excellent agreement1- where comparisons can be made. Similarly, the Ne-nD data of Streett appear

[51 to be internally consistent and are in qualitative agreement with the Ne-nH data. The

4 [71 , He -Ne system was investigated by Heck and Barrick over the entire Ne liquid range up

2 T 81 to 200 atm (20 MN/m ). Subsequent measurements reported by Knorn between the triple

. 2 point and boiling point temperatures of Ne up to 50 atm (5 MN/m ) qualitatively confirm

the Heck and Barrick data, but do not appear to be as consistent. Nevertheless, the data

4 for the Ne-nH , Ne-nD , and He -Ne systems are reasonably complete and consistent.

4

Several investigators determined the equilibrium distribution of He between the

liquid and vapor phases of nH and pH ' In addition, some measurements

were made to determine the three phase locus (S-L-V) L

' and the barotropic locus,

i.e. , the density inversion locus of the liquid and vapor phases. Observation of the baro-

[151 tropic effect was first reported by H. Kamerlingh Onnes in 1906.

Matyash, Mank, and Starkov report the only data for the solubility of He in

*- 2 liquid H These data provide essentially one isotherm at 20.4 K up to 9.2 atm (0.92 MN/m ) 3 He partial pressure with a few points at higher and lower temperatures to indicate tempera4 ture dependence. There are no published liquid-vapor equilibrium data for the He -D and

3 L He -D systems

.

The most significant discrepancy in the He-H systems data is found in the data for

[121 the liquid phase. The data of Roellig and Giese, comprised of nine independent data

points, suggest that the solubility of He in liquid H decreases with increasing temperature

at constant He partial pressure. The only other data available at the time of the above

[91 investigation were those of Smith, which indicated the opposite temperature dependence.

In addition, the liquid phase He compositions of Roellig and Giese are as much as an order

of magnitude larger than those of Smith.

Eckert and Prausnitz showed that the temperatures reported by Roellig and

Giese could be in error by as much as 2. 7 K, although this correction does not alter the

above disagreement. In an attempt to assess the plausibility of each set of discrepant data, _ .[18] torruccim compared the He 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

[ 1 9] Gottried to evaluate Smith's data, are ineffective in analysis of this particular type of
problem. Wilson, prior to the availability of the data of Roellig and Giese, showed that

the Redlich-Kwong equation, with modified temperature dependence of the 'a' parameter,

predicted the temperature dependence of He solubility observed by Smith. Subsequent

experimental data from the University of Michigan1-

' provided the proof of

Corruccini's conclusion and at least qualitative support of Wilson's calculations. Later,

[21] Staveley1 J noted that, even with the newer data, heats of solution derived from infinite 4 dilution Henry's constants for the He -H ? system are less certain than for other low temperature systems he examined.

The objectives of the present investigation, established with due consideration of

the above discussion, were to obtain a consistent set of liquid-vapor equilibrium data in 4 3 4 3 the low pressure region for the He - nD , He -nD,, He - nH , and He -nH systems, and

to provide a comparative reference with previous data. This investigation includes measurements on:

(a) the vapor pressures of nD from 20 to 34 K and of nH from 20 to 30 K;

4

(b) the compositions of the equilibrium liquid and vapor phases of the He - nD

4 system from 20 to 30 K and the He - nH system from 20 to 28 K up to 20 atm

,2 L

(2 MN/m );

and

3

(c) the compositions of the liquid and vapor phases of the He - nD system from

3 20 to 30 K and the He - nH system (liquid phase only) from 22 to 28 K up to

, 2 16 atm (1.6 MN/m ).

The maximum pressure was intentionally established below the barotropic locus

4

of the He - nH, system to avoid density instabilities, possible entrainment, and the necessity to reverse the direction of recirculation, as would be the case above the barotropic

locus. The density inversion, 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

3 4

pressures for the He - nH system than for the He -nH., system.

The pressures at which the densities of the two phases would be the same were

4 3 4 estimated for the He -nH., He -nH , and He - nD systems, and were compared with

a riii

the experimental observations for the He -nH. system. These are shown in figure 1. 4 The barotropic locus for the He -nD. system is of academic interest only since the actual

density inversion may not appear below the locus of critical pressures. In these calculations, the density was assumed to be that of pure, saturated liquid; the molar volume of

the vapor phase, calculated from the average molecular weight for the equilibrium vapor

phase composition taken from Sneed et al. and the corresponding liquid phase den-

[22, 231 4 ("241 sity, was assumed to be equivalent to the molar volume of pure He L or

3 [25] He at the same temperature.
5xicr

(•P* - I atm 0.101325 MN/m2

)

He

A-nD2

10

a. |0-

*. ntf2

O Sneed, et al Calculated

10 16 18 20 22 24

TEMPERATURE, K

26 28

Figure 1. Estimated barotropic loci.
4

In contrast, for the He - nH system at 20.4 K and at the same vapor phase composition used above, the barotropic pressure calculated from the mixutre virial equation of

state, truncated after the second term, is significantly lower than that estimated above

(approximately 25%). The interaction second virial coefficient of Knaap et al. * was

used in determining the mixture second virial coefficient at the subject vapor phase composi4 tion. Since the second virial coefficient alone is inadequate to reproduce the pure He

[241 properties at this temperature and pressure, it appears that the mixture third virial

coefficient, which is usually not available, is required for this calculation.

2. Experimental Method

The apparatus used in these measurements is a modified design of the apparatus of

T27l T 281 Duncan and Hiza with the same type of pumpL J for recirculation of the vapor. A

schematic flow diagram of the apparatus is shown in figure 2, and the arrangement of the

components within the cryostat is shown in figure 3.

The equilibrium cell, made of electrolytic tough pitch copper, has an internal

3 volume of 19.8 cm , an internal diameter of 2.48 cm, and an outside diameter of 6.35 cm. The closure is a threaded copper plug soft-soldered in place; a double layer of fine

mesh screen covers the equilibrium vapor exit in the center of the plug to serve as an entrainment separator. The platinum resistance thermometer (PRT) well extends from

the top of the cell to a point approximately one -third of the distance from the bottom of

the equilibrium cavity. Thus, differential temperature measurements from the top of

the cell to 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 reservoir (of 2. 25 1 capacity) with an automatically regulated 120 ohm heater, noninductively wound on the cell just below

the equilibrium cavity. The heater power regulator is a transistorized unit designed by

[29] Jellison. J The desired temperature is obtained by controlling the voltage drop across

the PRT; the unbalance from the selected voltage drop, as sensed by a potentiometer, is amplified -with a breaker amplifier and fed to the power regulator for heater control.

With this arrangement, the experimental temperature could be maintained, generally

within ± 0.005 K, for any desired length of time. The maximum uncertainty in temperature is thought to be ± 0.01 K.

The cell pressure was measured with a 300 psia, double-revolution, Bourdon

tube gauge. Though the smallest scale division of this gauge is 0.5 psia (equivalent to 0.034 atm), a finely divided machinist rule was used to estimate lower subdivisions to approximately + 0.05 psia. The maximum uncertainty of the gauge is claimed to be

5
7T\ RECIRC.

PUMP

f

VENT —

M

VAC. - 1

ROTAMETER

El—t>0- v*\

X

-<gHXH

C*H

1

75 cm*

BOOSTER/

BALLAST

He

VAR

SAMPLE

rOOVAC.

CHROMATOl

k

GRAPH

LIQ.

i

«v

SAMPLE

CAL.

GAS

PURGE

I ROTAMETER ROTAI

REE

CONTROL

VEJJJ

I

LH,

1

5 psi RELIEF! CO—

I

| IX] VAC.

.J

Figure 2. Schematic diagram of the experimental apparatus.
J_J

Inlet

Vapor

Vacuum Line

Refrigerant Fill & Vent Line

Equilibrium

Vapor

Refrigerant

Exhaust

PRTLiquid

Sample LineScreen

Copper

Shields

Refrigerant

Liquid —

\>>>>»>> ;>>>/»>>>>>>; w>»>7*

3- 3.18 mm Tubes

9.8cm Coil Dia.

14.3 cm 66 cm

Vapor Bulb

Liquid Level

Indicator

Figure 3. Details of the equilibrium cryostat.
± 0.1% of full scale and repeatability within ± 0.066% of full scale. The gauge was set at atmospheric pressure with a barometer reading corrected far temperature and gravity.

Gauge readings were then checked against a laboratory dead-weight gauge and were found

to meet the accuracy claims of the manufacturer. At 50 psia no difference in readings

could be detected; at 150 psia the Bout don tube gauge reading was 0.065% low; and at 300 psia the Bourdon tube gauge reading was 0.089% low.

All fluids introduced into the equilibrium cell were purified with a small, liquid

nitrogen cooled, silica gel adsorber (not shown in figure 2) on the feed cylinder side of

the booster volume. Thus, only the level of impurities of He or H isotopes or Ne in the

4 feed gas are of significance. The He was standard U.S. Bureau of Mines Grade-AHe,

and the H was purified gas obtained from the NBS liquid and gas distribution facility.

Since the H cylinders are often filled with boil-off gas, a cylinder which had been filled

several months prior to use was selected so that normalization would not be required.

3 4 Thus, He and higher hydrogen isotopes would be present in the He and H_ in natural

3 3 abundance. The He and D and the analyses were supplied by the U.S.A.E.C. The He

contained 1.4 mole % He4

, and the D£ contained 1.12 mole % HD and 0.02 mole % H2.

3 These isotopic impurity levels in the He and D? gas were not expected to produce detectable differences in the phase equilibrium properties measured here.

Compositions of the equilibrium phases were analyzed by gas chromatography with

thermistor detectors. To avoid the well known peak-folding phenomenon, due to thermal

[301 conductivity reversal of He -H mixtures, the mixtures were separated with an 11.9

meter column of 3.18 mm I. D. tubing packed with 80 mesh molecular sieves 5A. Ar was

3 used as the carrier gas at 50 to 55 cm /min flowrate. Pressure drop through the column

2 was approximately 1.3 atm (0. 13 MN/m ). Samples were injected at various pressures,

2 3 generally between 0.6 and 0.8 atm (0.06 and 0.08 MN/m , respectively), using a 0. 3 cm

sample loop on the injection valve. With this arrangement, the time lapse between injection and the start of the He and H peaks was approximately 15 and 23 min, respectively.

Equilibrium liquid phase samples were withdrawn directly from the bottom of the

cell through a 0. 178 mm I.D. stainless steel capillary tube. This capillary tube 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, of slightly smaller

diameter, approximately 50 cm in length. Equilibrium vapor phase samples were withdrawn from the recirculation pump cavity, which was isolated with inlet bypassed to the

outlet during sampling. In both cases, the recirculation pump was turned off during

sampling. Due to the excessive analysis time (approximately 30 to 35 min) and to the
large differences in compositions of the two phases, it was more convenient to determine

liquid and vapor phase compositions in separate runs. A vapor pressure check at the

beginning of each run was used to confirm the reproducibility of experimental conditions.

These vapor pressure measurements were made in both static and recirculation modes

with no detectable difference in results.

The chromatograph was calibrated for liquid phase measurements with a mixture

4

of 5. 27 mole % He in Ar . This mixture was prepared on a partial pressure basis, as2 suming ideality, at a total pressure of 18 atm (1.8 MN/m ). The use of Ar as the second

component in the mixture in lieu of nH_, for example, eliminates the second peak, thus

significantly reducing the time required for calibration. However, a second mixture of 4 10.00 mole % He in nH? was prepared, also assuming ideality at a total pressure of

2 15 atm (1.5 MN/m ), to verify the primary reference mixture and to ensure that separation was adequate to avoid interference between a large nH? peak and a relatively small

He peak. An estimate of the nonideality of each mixture indicated that the actual compositions were 5. 22 mole % He^ in Ar and 10. 08 mole % He in nH . Interaction second

[311 virial coefficients from Brewer and Vaughn1 ' with selected values of the second virial

coefficients for He , Ar, and nH were used in these estimates. The relative

magnitude of the difference between the ideal and corrected compositions was approximated

in the comparative analyses. Since the uncertainty was no more than 1%, the ideal com4 position of the He - Ar reference was used as the basis of all liquid phase analyses.

The chromatograph was calibrated for vapor phase measurements with mixtures of 50.00 mole % He

4

in nD , prepared at 6 atm (0. 6 MN/m2/1 ), and 50 . 00 mole % He4 in nH

L

2 prepared at 9.5 atm (0.95 MN/m ), also using the ideal mixture compositions. Compara4 tive analyses of these mixtures were in agreement within less than 1% of the He content. Comparison of the nD and nH content with pure nD and nH , respectively, at the same

partial pressure verified this agreement.

3 , 4 For He analysis, the peak area was adjusted to the equivalent He response for

comparison with the appropriate standard. The ratio of integrated peak areas of He : He , for indentical samples of the pure species, was found to be 0.858 by repetitive chromatographic analyses.

The uncertainty in the compositions of the equilibrium liquid and vapor phases is thought to be ± 3% of the reported concentration of the minor component, or ±0.1 mole %,

whichever is greater.
3. Experimental Results

A. Vapor Pressure of nD and nH

Though vapor pressure measurements were intended only as verification of the

;ntal technique, discrepancies in published vapor pressure values for nD made

more detailed study of this property desirable. Measurements made generally at one K

increments for nD 1 equation of the form

experimental technique, discrepancies in published vapor pressure values for nD made a

t c increments for nD from 20 to 34 K and for nH from 20 to 30 K, were fitted to an Antoine

lnp (atm) = A - B/(T + C) (1). o This simple form allows convenient interpolation and evaluation of the normal boiling

point temperature of each isotope. At the normal boiling point, equation (1) reduces to

T = (B - AQ/A (2). nbp

The constants of equation (1) and vapor pressure values are given in table 1 for nD. and in

table 2 for nH .

[341 The normal boiling point of nD listed by Woolley, Scott, and Brickwedde1 J is almost exactly 0.1K lower than the value found in this investigation. The vapor pressure

, , r 3 51 of nD , upon which the equation of Woolley et al. is based, was measured1 J relative to

the vapor pressure of nH only up to 20. 4 K. Thus, the normal boiling point of nD re- ported was found by extrapolation. Subsequent measurements on uncatalyzed D reported

ro/i r o -7"] " by Hoge and Arnold and Grilly give normal boiling points of 23.666 K and 23.665 K,

respectively. Deviations of the four sets of nD vapor pressure values are shown in figure 4 relative to equation (1) fitted to the present data. The larger deviations at the low

temperature end result from weighting the data for uncertainty in pressure measurement

during curve fitting. The remarkable agreement of the normal boiling point (23.666 K)

obtained from the fit of the present data with those resulting from the measurements of

Hoge and Arnold and of Grilly is somewhat fortuitous, since the fit of the data is obviously

not that good and the apparatus used in this investigation was not specifically designed for

precise vapor pressure measurement.

Whereas the low temperature portion of the present nD vapor pressure measurements tend to reflect the lack of precision of pressure measurement, the present nH vapor

pressure measurements are generally more indicative of the precision of temperature

measurement in the range of investigation. The normal boiling point of nH. reported by

T3 71 Woolley et al. is 0.014 K higher than that found from this investigation. Grilly and

[381 Vanltterbeek et al. also report vapor pressure data for nH in the region of interest.

Deviations of these sets of nH vapor pressure values are shown in figure 5 relative to equation (1) fitted to the present data.

10
+ 3

+ 2

+ 1

CMO

o

o

Ol

Q.X

a> a.

D

o

a.

-I

-2

nD2

• This Investigation

A Woolley, Scott, and Brickwedde

V Hoge and Arnold

Grilly

+ 0.01 K ° •-V

•

D

SZ-V« D U V t

2" D • V V • _

-0.0IK D

A

A

20 22 24 26 28 30 32 34

TEMPERATURE, K

Figure 4. Deviations of vapor pressure data for nD from equation 1.

11
+ 2

CVJO

o

o

Q.

'aX

a> a.

8

Q.

nH : • This Investigation

A Woolley, Scott, and Brickwedde

O Van Itterbeek.et al. Grilly

+ 0.01 K A

-•- o

oo

• i>o ^-^

0.01 K

S

<h a

D

20 22 24 26 28 30 32

TEMPERATURE, K

Figure 5. Deviations of vapor pressure data for nH from equation 1,

12
The agreement of the present vapor pressure measurements for nD and nH

with other measurements for these fluids is considered adequate for present purposes.

The only significant discrepancy, i.e. with the nD vapor pressure values of Wooley et.

al. above 21 K, clearly is the result of error in the extrapolation of Wooley et al based

on rather limited data.

4 3 B. Solubility of He and He in Liquid nD and Liquid nH .

Results of the measurements on the equilibrium liquid phase compositions of the

4 3 4 3 He - nD , He -nD„, He -nH,, and He -nH systems are given in tables 3-6. These

2 2 2 4 3 results are plotted in figures 6 - 9 as mole % of He or He as a function of the total

system pressure minus the vapor pressure of the liquid solvent, which is roughly equivalent to the He partial pressure. The actual He partial pressure would be given by the

product of the total pressure and the mole fraction of He in the equilibrium vapor. At

each temperature, P - p was determined using the experimental vapor pressure. The

form of representation used in figures 6-9 avoids crossing of the isotherms but retains

the original curvature of the composition versus total system pressure isotherms.

4 3 In all four systems, the solubility of He or He increases with increasing temperature at constant He partial pressure. At the same temperature and partial pressure,

4 3 the solubility of He or He in liquid nH is approximately twice as large as that in liquid

4 nD In addition, the solubility of He is approximately 10 - 20% larger than the solubility

1

3 of He in either solvent. It should be noted that the 26 K isotherm for nH ? systems is approximately at the same reduced temperature (of the solvent) as the 30 K isotherm for

the nD systems. Even then, the solubility in nH. is still somewhat larger.

Solubility data also are often represented as Henry's law diagrams. These

normally consist of the ratio of the fugacity of the solute in the vapor to its mole fraction

in the liquid plotted as a function of the solute fugacity in the vapor. For the systems

and conditions under consideration, the solute fugacity is not greatly different than the

solute pressure. Thus, the Henry's law diagrams for the liquid phase data of this investigation, as given in figures 10 - 13, are based on pressure. The dashed curves

represent isotherms determined by extrapolation. These diagrams more clearly expose

experimental discrepancies and are a valuable aid in smoothing the liquid phase data.

The intercepts of the curves at zero solute fugacity are also of great interest in correlation attempts and theoretical analysis. The intercepts are commonly referred to as the infinite dilution Henry's constants, that is

lim (f 2 /x

2

, = H*

(3) _

f 2-°

13
O

E 2

I

1 He4 -nD21 1 \/\

— —

^-^ A ^-

— ^y—-^—

jC

^—-—c>=

( P*= 1 atm := 0.101325 MN/m2)

2 4 6 8 10 12 p -Poi

14 16 18 20

4 Figure 6. Solubility of He in liquid nD

14
3 —

a>o

E 2

roX

He3 -nD2

so

— ^__?2 p- _

3Z —o——

^^%^o^ ^

~ 20 '

r\

^

(P*=latm = 0.101325 MN/m2

)

I —

2 4 6 8 10

P-Poi

12 14 16 18

Figure 7. Solubility of He in liquid nD

15
18 20

Figure 8. Solubility of He in liquid nH.

16
3 Figure 9. Solubility of He in liquid nH

17
5 x10s

He*-nD2

(P*= latm =0.101325 MN/m2

)

10*

2 4 6 8 10

p-Poi

12 14 16 18 20

Figure 10. Henry's law values for He in liquid nD,

18
5x10*

He3 -nD2

(P*= I atm = 0.101325 MN/m2

)

10' 2 4 6 8 10 12 14 16 18

p -Poi

3 Figure 11. Henry's law values for He in liquid nD,

19
5xlOc

He^-nH2

(P* = I atm = 0.101325 MN/m2

)

10'

2 4 6 8 10 12

P-Poi

14 16 18 20

Figure 12. Henry's law values for He in liquid nH,

20
5xlCr

He3 -nH 2

10* o

a. *

Q.

CVJ

(P*= I atm = 0.101325 MN/m2

)

I0< 2 4 6 8

P-Poi

10 12 14 16

Figure 13. Henry's law values for He in liquid nH,

21
22 24 26 28

TEMPERATURE, K

Figure 14. Infinite dilution Henry's constants.

22
The difficulty of obtaining infinite dilution Henry's constants is quite obvious; the necessary

extrapolation is strongly affected by the degree of nonlinearity of the curves, the precision of the data, and any systematic errors. Infinite dilution values were obtained for the

four systems studied here using both the curves in figures 6-9 and those in figures

10-13. The results, shown in figure 14, reflect the fact that the solubility of He is sig4 nificantly greater in nH than in nD and the fact that He is slightly more soluble than

3 He . It should also be noted that the infinite dilution Henry's constants for the two He

isotopes are also somewhat lower for the nH. systems at 26 K than the corresponding

4 3 values for the nD systems at 30 K. The fact that He and He have identical values with

nD rather than reflecting the slight difference in solubility as with nH , is related to the

difficulty of the extrapolation and is not considered significant.

4 3 C. Vapor Phase Saturation Limits of nD and nH in He and He .

Results of the measurements on the equilibrium vapor phase compositions of the

4 3 n 4 He -nD , He -nD , and He - nH. systems are given in tables 7-9. Measurements were

not made for the He - nH system when no significant difference was found in the vapor

4 3 phase compositions between the He - nD and He - nD systems within the pressure limits

of the measurements.

The vapor phase data are best evaluated by examination of enhancement factors,

i.e. , the ratio of partial pressures of the condensible component to its normal vapor

pressure at the same temperature. Enhancement factors are a direct indication of the

non-ideality of the vapor phase, and at least in the low pressure region (removed from

the critical region of the condensible component) can be represented by a rigorous theoretical model.

4 3 Enhancement factors for both the He -nD and He - nD systems are shown in figure 15. Within the pressure and temperature limits of this investigation, no significant difference is indicated in the vapor phase properties due to the isotopic differences

4 3 of He and He . This is not entirely surprising -when a comparison of enhancement factors

is made for systems such as H~- ArL J and Ne - Ar, near the normal boiling point of

2 Ar, up to 10 atm (1 MN/m ) or so. Even though the major components interact quite

differently with the common condensible component, Ar, the difference reflected in the

enhancement factors only becomes apparent as the pressure is advanced.

4 3 The enhancement factor curves for the He -nD and He - nD systems are crossplotted in figure 16 at constant system pressure. A property of the enhancement factor,

which should be apparent in figures 15 and 16, is that its value must approach unity as the

system pressure approaches the vapor pressure of the condensible component. As defined here, enhancement factors less than unity have not been observed (outside the

23
/ (P* = latm = O.IOI325MN/m 2

)

2 4 6 8 10 12 14 16 18 20

P. p*

4 3 Figure 15. Isothermal enhancement factors for the He -nD and He -nD systems.

24
18 20 22 24 26 28 30 32 34

TEMPERATURE, K

Figure 16. Enhancement factors for the He -nD and He -nD systems at constant

system pressure.

25
2.5

Figure 17. Isothermal enhancement factors for the He -nH system.

26
18 20 22 24 26 28 30 32 34

TEMPERATURE, K

Figure 18. Enhancement factors for the He -nH system at constant system pressure.

27
uncertainty" in the measurements and the knowledge of the vapor pressure), though there is no theoretical reason why values less than unity cannot occur.

4 Enhancement factors for the He - nH system are shown in figure 17, and crossplots are shown in figure 18. The 29 K isotherm shown in figure 17 was determined by

extrapolation. Based on the experimental results of the nD systems, these enhancement

3 factors also are considered representative of those for the He -nH. system within the

pressure and temperature limits of this investigation.

D. Derived K-values and Heats of Solution.

The graphs of Henry's law values and enhancement factor values provide a convenient form for smoothing and interpolating the experimental data. These graphs were

used to obtain smoothed liquid and vapor phase compositions and K-values, i.e., ratios

of vapor phase to liquid phase mole fractions for each component, at even increments

of system pressure. The essential values for He are given in tables 10 and 11 for the

nD and nH systems, respectively.

The heat of solution for He dissolving in liquid nD or nH can be calculated

4 3

d. 2 . directly from the He and He K-values from the integrated expression1-

AH = R[T ! T/(T'- T)] ln(K/KJ) (4) postulating ideal solution. These values are listed in table 12 for all four systems.

4 The heats of solution for He in liquid nH , with the exception of those at the

highest temperatures, all fall within 400 - 800 J/mol (endothermic) in the agreement with

r y 81 the estimate of Corruccini. The increase in heat of solution with temperature for all

t 42] [431 four systems is also consistent with the behavior of the He - CH , H - C H , and

[441 4 2 2 6 H - C H systems studied earlier. It should be noted that the sign of heat of solution

2 2 4

' b values for the He - CH , and H„- C„H. were erroneously reported as negative; i.e. , heats

4 2 2 6

i

. r f of solution for all of these systems are endothermic.

4. Discussion

A. Maxima in Gas Solubility at Constant System Pressure.

In systems of the type studied here, the solubility of the gas in a liquid solvent can pass through a maximum at constant system pressure (below the solvent critical pressure) as temperature is increased; thence the solubility must decrease toward zero as

the temperature approaches the saturation temperature of the solvent at the subject pres4 3 sure. Liquid phase compositions for the He - nD and He - nD systems at constant

system pressure are shown in figure 19.

28
20 22 24 26 28

TEMPERATURE, K

4 3 Figure 19. Solubility of He and He in liquid nD at constant system pressure.

29
10

(P*=l atm =0. 101325 MN/m2

)

3~ 6 o

w

<D X

E

£

X

o

E

INCREASING

SOLUBILITY

a-i£

22 24 26 28 30 32 34

TEMPERATURE, K

4 3 Figure 20. Solubility maxima for He and He in liquid nD

30
Maxima are apparent in all of the isobars with the exception of that for P/F*

= 0.6, even though the data are extrapolated to the triple point temperature of nD . Though the temperatures associated with the maxima cannot be determined with a high

3 degree of certainty, it appears that the He maxima occur at slightly higher temperatures,

but are essentially the same at the lowest temperature. The loci of solubility maxima for

4 3 the He - nD and He - nD systems are shown in figure 20 along with the vapor pressure

curve for nD . This figure serves as a 'map' for regions of increasing and decreasing

solubility. A significant point worth noting is that the region below P/P'|C = 0.75, bounded

by the three phase locus (melting line) and the vapor pressure curve of nD , is one in

which no solubility maxima exist; i.e. , solubility always decreases with increasing temperature at fixed system pressure in this region.

4 3 Similarly, the He - nH and He - nH systems exhibit maxima in gas solubility

at constant system pressure. Liquid phase compositions at constant system pressure for

these systems are shown in figure 21. Since the data of the present investigation do not

extend much below the normal boiling point of nH_ complete information on solubility

[101 maxima cannot be obtained. The data of Streett et al. are included in figure 21 below

the lower temperature limit of the present measurements to indicate the qualitative dependence of solubility in this region and to provide a comparison between the two sets where

the largest disagreement was found. This disagreement is about twice the estimated un- certainty of the present data.

B. Deficiency of Predictions from Regular Solution Theory.

It would be desirable, of course, to find the source of the discrepancy between

the data of Streett et al. and the present data or to show, through sound theoretical

argument, which data are closer to the true values. The method of calculating gas solubility in a liquid solvent used by Corruccini, 'which was adapted by Prausnitz1- J from regular solution theory, provides a good example of the difficulty one encounters in applying theory

to evaluate such discrepancies. The steps followed in the solution process are: (1) compression of the solute gas from its partial pressure to an isometric mixing pressure at which its molar volume is equivalent to its partial molar volume in solution, (2) dissolving the gas in the liquid at the isometric mixing pressure, and (3) decompression of the

liquid solution to the final system pressure. The equation for this process is P

- In x

2 =ln[f2

(TT)/f 2 (P

2

)] +^2^(62-6^ /RT+ ( 1 /RT)J v"2 dP . (5)

In the second term, the volume fraction, cp , for these systems is quite close to unity, and

the product of the partial molar volume and the square of the difference of solubility parameters is representative of the heat of solution.

31
2.4

2.2

2.0

1.6

1.4

55

°> 1.2 o

E

4 1.0

0.8

0.6

0.4

0.2

He-nH2

He4, This Investigation

He3

, " He4

, Streett.et al.

(P*= I atm = O.IOI325 MN/m2

)

14 16 18 20 22 24

TEMPERATURE, K

26 28

4 3 Figure 21. Solubility of He and He in liquid nH at constant system pressure.

32
Equation (5) was used in this study to determine v , the partial molar volume of

4 He , and TT , the related isometric mixing pressure, needed to reproduce the present ex4 perimental mole fraction of He in liquid nH at 20 K for P/P'' = 10. With this informa3 4

tion, an attempt was made to estimate the relative solubility of He in nH. and He in nD

at the same conditions of temperature and pressure. The necessary PVT and thermo4 3 [24] dynamic properties for He , He , D and H were taken from McCarty, 1 J Gibbons and

[251 [231 [461 Nathan, Prydz, and Roder, Weber, and Goodwin/ J respectively. The latter

reference is a convenient source of pH rather than nH properties; but, as will be shown

later, the difference has no significant effect on the phase equilibrium properties of these

systems in the region of consideration.

4 _ 3 Briefly, it was found that for the He - nH system, v = 34.67 cm /gmol and TT 2 2 2

= 60 atm (6.0 MN/m ) resulted in x = 0. 0145 at 20 K for P/P:;: = 10, compared to the

experimental value of x = 0.0153 from the present measurements. Using v = 39.20

3 2 cm /gmol and rr = 50 atm (5 . MN/m ) resulted in x = 0.0109, in closer agreement with

the experimental value of Streett et al. of x =0.0121. Corruccini's estimate of 4 v from the volume of solid He would fall between these values, but probably closer to the value needed to reproduce the data of Streett et al. However, the uncertainty in Corruccini 1 s data possible

Corruccini's estimate of v is at least ± 10%, which makes agreement with either set of

3 For the He - nH system, a partial molar volume was estimated by adjusting

4 3 3 4 the He molar volume of 34. 67 cm /gmol with the ratio of He to He liquid phase molar

3 volumes. This results in a value of about 54.00 cm /gmol and an isometric mixing pres2 sure of 35 atm (3.5 MN/m ) . The result of x = 0. 00074 obtained with these parameters

L 4

is quite disappointing. Using the same isometric mixing pressure as that for He and the

3 3 corresponding molar volume for He , 37. 24 cm /gmol, results in x = 0.0044; alterna4 3 tively, using approximately the same molar volume as for He , 34.06 cm /gmol, and

3 2 the corresponding isometric mixing pressure for He , 70 atm (7.0 MN/m ), results in x = 0.0058. The experimental values are x = 0.0114 from the present investigation at

r i a l 20 K for P/P* = 10, and x = 0.0103 from the measurements of Matyash et al. at 20.4 K for P/P* = 10. 2.

3 . , Though the prediction of He solubility was not successful, one might expect to 4 obtain better results in predicting the solubility of He in nD using the parameters that

4 seem to work for He in nH_. The solvent effect is only introduced in the solubility

parameter term. However, x = 0.00077 is obtained with these parameters compared to

the experimental value of x = 0.0086 at 20 K for P/P''~ = 10. This strongly suggests that

Z 4 Corruccini's success in estimating reasonable solubility limits for the He - nH system was fortuitous. Further discussion or development of theory for systems of this type is 33
beyond the scope of this paper. It is hoped that this subject can be explored in more detail

in the near future. The remainder of the discussion in this paper will be restricted to comparisons with data of previous investigators through Henry's law values from the liquid

phase data and enhancement factors from the vapor phase data, in that order.

C. Comparisons of the Liquid Phase Data for the He - H Systems.

[91 Henry's law values from the three liquid phase isotherms of SmithL for the

4

He - nH system are compared in figure 22 -with those for two isotherms, 20.4 and

21.7 K, interpolated from the present data. The 21.7 K isotherm of Smith is quite erratic

and is in poor agreement with the present data, as well as being inconsistent with his other

two isotherms. The 20 . 4 K isotherm, on the other hand, appears well behaved and is in

reasonable agreement at the higher pressures with the comparable isotherm taken from

the present data. Smith's 17.4 K isotherm is difficult to compare directly with the data

of the present investigation in other than a qualitative way. However, a comparison can

be made relative to the data of Streett et al. The He compositions in the liquid phase

at 17.4 K reported by Smith are lower than those reported by Streett et al. by 30 - 50%,

in the pressure range of the present investigation, the worst agreement being at the lower

4 pressures. As shown in figure 21, the He compositions reported by Streett et al. are

4 about 20% lower than those of this investigation at 20 K; on the other hand, Smith's He

compositions are a few percent higher than those of Streett et al. at 20.4 K, particularly

at the higher pressures.

Six of the liquid phase data points of Roellig and Giese for the He -H system,

approximately equivalent to two isotherms, are compared in figure 23 with corresponding

isotherms taken from the present investigation. The temperatures for the Roellig and

eJ

47J IT

[171 Giese data are those calculated by Eckert and Prausnitz. It is presumed that these

data are for pH_, since the authors used the vapor pressure curve of Chelton and Manr

in calculating the temperatures they originally reported. The same pH vapor pressure

curve also was used here to determine the Henry's law values of the Roellig and Giese

data shown in figure 23. Though it is not possible to draw reasonable curves through the

data points of Roellig and Giese, it is clear that both partial pressure and temperature

dependence of their Henry's law values are exactly opposite to the partial pressure and

temperature dependence of those from this investigation.

Three liquid phase isotherms, representative of the data reported in separate

University of Michigan investigations, are compared in figure 24 with corresponding

isotherms taken from the present investigation. For practical purposes, the University

4

of Michigan data can be taken as one complete set for the He - nH system, covering a

4 - wide range of pressure, and for the He - pH system, covering the lower pressure range,

34
1

1

1 1 1 1 1

<

< —

—

CM X

c

1 X

o

o

<

<M<w<

*\

1

CME

v.z

m

CO

roO

d

MEo

—

oo

<a

n *

Qc

< oo *

.EP O

ro

o o

Inve; h,

17. b

CO CO

11

col

•"" o o < h-

'Z E E E

1- CO CO CO o o — o <

< —

CO

1

1

1 1 1 ! ! ! 1 \\ ! O

oo

CO

toCO

CO

COCOoCO

GO

(X)

COO

O

Cl

i Q_

*

Q_

CO

00

UD

CO

o

TSu

nia,s

o

u

g

COo

ni

X

a

X

<u XI

a

o

h

0)3

i—

i

>

Pi ID

00

00

35
icr

o|» 'O2 -

Q. CL _ I CM CL IX —

10'

He4 -pH 2

20.6 K

26.0 K

20.6

O

20.9

O

O A Roellig and Giese — This Investigation, nH 2

( P* = I atm = 0.101325 MN/m2

)

6

P-Poi

10

Figure 23. Henry's law values from the He -pH2 data of Roellig and Giese compared

with those for He^-nH from this investigation.

36
CM -*— X a> Q. a>o

sr c

<u c X o

<oco

•— CM o o X +- ^_ o c1 a>>

<U

<v c

sr •—»

<D •o

<v

W 0)

X 1c

%_

H CO CO

-3-O o

CDOO

oc£ Oc\j

CMO

rfl £ ° S ,11 w S

XI o R X

cd +"

<D X)

+• £

<U cd

0) ft

CO

a. £ <d

cd -j->

(M

M - +-> R3o

CO 0)D

X!

cd « K *>

en

a c

;-( -t o

i—(<u

h

cd>

ffi «4H

crt £

(D -M X crt

crt -4-> Tl i—i

CO CO X

>s

M

a

u

m i a Tl *

<u

R

cd

V

XX

-*"

<NJ

<Uh3

m>

37
5xicr

10'

o

a. *

Q.

\0'

He 3 -nH 2

20.4 K

O Matyash, et al.

Extrapolated from

This Investigation

(P* = I atm = 0.101325 MN/m2

)

2 4 6 8 10 12

P-Poi

P*

Figure 25. Henry's law values from the He -nH data of Matyash et al. compared with

those of this investigation.

38
The apparatus used in each was developed by Streett, and all compositions were analyzed

by mass spectrometry. Disagreement with the isotherms from the present investigation

4

is largest in the low pressure region where low He concentrations are encountered. It appears, however, that the isotherms of the present investigation would extrapolate to [11

T3]

higher pressures in reasonably good agreement with the data of Sneed et al. L J There

is no significant difference indicated between the pH_ data of Sonntag et al. and the

nH data of Streett et al. and Sneed et al.

One additional point to be noted in figure 24 is the steep, downward curvature

of the Henry's values of Streett et al. as infinite dilution is approached. In fact, the

lowest pressure values are in excellent agreement with those taken from the present investigation. With such extreme curvature, it is not clear how one should extrapolate the

[21] values of Streett et al. to infinite dilution. This is precisely the reason Staveley's

heats of solution, calculated from the infinite dilution Henry's constants, were less certain

4 for the He - H_ system than for other systems examined. In essence, Staveley, as well

as Solen, Chueh, and Prausnitz, 1- disregard the lowest pressure values in making this

extrapolation. The paper of Solen et al. presents a correlation of He solubility in several

cryogenic solvents, with special attention to predicting He solubility in mixed solvents.

[161

Finally, the liquid phase isotherm at 20.4 K of Matyash, Mank, and Starkov

3 for the He -H_ system is compared in figure 25 with the corresponding isotherm extrapolated from the present data. The ortho-para form of H was not specified by the above

authors, but it was presumed here to be nH . As found in previous comparisons, the

largest disagreement occurs at the lower pressures, and the difference decreases as the

pressure increases. The largest disagreement is about twice that between the data of 4

Streett et al. and those of the present investigation for the He -nH, system. The data

of Matyash et al. indicate that the Henry's law values are essentially constant in this

pressure range and are equivalent to the infinite dilution value. Qualitatively, this be4

havior is not consistent with that for the He - nH system, and certainly is not in agreement with the behavior of the data from the present investigation. Their infinite dilution

Henry's constant would be about twice that obtained from the present investigation.

4 D. Comparisons of the "Vapor Phase Data for the He - H~ Systems.

[9] Enhancement factors from the three vapor phase isotherms of Smith for the

He

4

- nH system and corresponding isotherms taken from the present investigation ... are compared in figure 26. The 17.4 K curve taken from the present investigation is only an approximation; however, the extrapolation at the low pressures is not difficult and the

results should be reasonably correct. The 17.4 K isotherm of Smith, with the exception

of two low pressure points, appears to be consistent with the present data, but is somewhat higher. The tendency for the lower temperature enhancement factor curves to 39
2 4 6 8 10 12 14 16 18 20

_P

p*

4 Figure 26. Enhancement factors from the He -nH data of Smith compared with those of

this investigation.

40
Figure 27. Enhancement factors from the He -nH2 data of Streett et al. and from the

He4 -pH2 data of Sonntag et al. and of Roellig and Giese compared with those

for He^-nH2 from this investigation.

41
increase in slope as pressure increases, as Smith's 17. 4 K isotherm does, is consistent

with the behavior observed in this investigation. If the one point with an enhancement

factor, of 0. 74 were disregarded, the 20. 4 K isotherm of Smith would be fairly well behaved.

However, the behavior of his 21. 7 K isotherm is simply incorrect. Since the Henry's law

values for the liquid phase are high and the enhancement factors for the vapor phase are

low, Smith's reported temperature of 21. 7 K might be erroneously high.

Enhancement factors from vapor phase isotherms representative of the data of

Streett et al. ^ ' for the He -nH system, of Sonntag et al. ^ " for the He -pH system,

and the corresponding isotherms taken from the present investigation are compared in

r 1 2T figure 27. 'Enhancement factors from the six vapor phase points of Roellig and Giese,

equivalent to two isotherms at approximately 20. 6 and 25. 8 K, are also shown. Agreement

between the present data and those of the University of Michigan investigators is excellent;

differences in the enhancement factors are generally less than 3% at the higher temperatures. At the lowest temperature agreement is not quite so good; however, the largest

disagreement is less than 7%. With the exception of the one high pressure point at 20. 6 K,

the vapor phase data of Roellig and Giese appear to be in reasonable agreement with the

present data. Of the five remaining points the largest disagreement is about 8.. 4%.

There may be slight differences between the enhancement factors for pH and for

nH as indicated by an increasing difference between the data of Sonntag et al. and

Streett et al. with decreasing temperature. However, since the uncertainty also increases

with decreasing temperature, the apparent difference is not considered significant.

5. Summary

4 3 This investigation provides new data for two systems, He -nD and He -nD

which had not been studied previously. These data were extrapolated down to the triple

point temperature of nD 18. 72 K, and up to 32 K. Measurements in the liquid-vapor

3 region for the He -nH system, though not made to as low a reduced temperature as that

for the nD systems, provide the major portion of all data now available for that system.

2 4

The data obtained for the He -nH system serve as comparative reference to results of

several other experimental investigations covering a wide range of temperature and

pressure. The measurements of nD and nH vapor pressures not only provide verification of the experimental technique, but help to point out an explainable discrepancy in the

nD, vapor pressure values, a fact of which this author was previously unaware.

Based on the evaluation of these results and comparisons with other data, the

following conclusions can be drawn.

42
1) The present measurements provide a consistent set of data on the relative phase

4 3 4 3 equilibrium properties of the He -nD He -nD , He -nH , and He -nH systems.

Though efforts were made to avoid systematic errors, if such an error is present it will

be reflected in the data for all four systems. The uncertainty in composition determination, the largest source of error in this investigation, is estimated to be ± 3% of the

concentration of the minor component, or ± 0. 1 mole %, whichever is greater.

2) There is no apparent difference in the equilibrium vapor phase compositions

4 3 between the He -nD and He -nD systems, within the pressure and temperature limits

4 3 of this investigation. Thus, none is expected between the He -nH and He -nH systems.

£ 3 There is, however, a significant difference between the solubility limits of He and He

in the liquid phase, the ratio of which is about the same in both liquid solvents.

3) There is a significant difference in both the liquid and vapor phase compositions

between the nD and nH systems, even at the same nD and nH reduced temperature;

i. e. , 30 and 26 K, respectively. At the same absolute temperature, the differences

4 are quite pronounced. The solubility of He in liquid nD and the enhancement factor

4

of nD in He are both lower than the corresponding nH values. Data from the University of Michigan studies'- ' J indicate no apparent difference in the phase equilibrium

properties between the normal and para H forms; thus, none is expected between the

normal and ortho D forms.

4 4

4) Though the disagreement between the He -nH and He -pH liquid phase data

of the University of Michigan investigators'- J and comparable data from the

4

present investigation for He -nH is somewhat larger in the low pressure region than

the present estimates of uncertainty, these former measurements provide the most

h

4 complete and, for the most part, reasonably consistent set of data for the He -nH,

4 f 9"! and He -pH systems. The earlier data of Smith1 J

, though valuable as pioneering

f 1 21 work, and the subsequent data of Roellig and Giese are too limited and inconsistent

to be of further value.

5) The data of Matyash et al. L J for the solubility of He in liquid H in addition

4

to the University of Michigan data on the solubility of He in liquid H , support the

3 4

results of the present investigation; i. e. , the solubility of He is less than that of He . The disagreement between the data of Matyash et al. and the present data is significantly

larger in the lower pressure region than that observed between the University of

4 Michigan data and those of the present investigation for He . In each case, however,

the disagreement is in the same direction. Since Matyash et al. do not discuss the uncertainties in their measurements, it is not possible to further evaluate the disagreement

noted.

43
4 3 6) Finally, prediction of the solubility of He or He in liquid nD or liquid nH , using regular solution theory, is not promising. It is felt that the present data should

be first correlated, possibly with a technique similar to that used by Solen et al. The correlation could then be studied for clues to the nature of the deficiency of theory.

[49] In this respect, the prediction method discussed by Miller should be examined more

closely for possible application to quantum fluid mixtures.

6. ACKNOWLEDGEMENTS

Useful discussions with W. J. Hall, J. Hord, H. H. Otsuki, W. R. Parrish,

R. H. Sherman, and T. R. Strobridge at various times during the course of this study are gratefully acknowledged. In addition, the contribution of N. C. Winchester during

construction of the temperature controller and the loyal assistance of W. H. German

during all phases of the experimental program were greatly appreciated.

44
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46
33. A. Michels, W. De Graaff, and C. A. Ten Seldam, Virial coefficients of hydrogen

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to three atmospheres, J. Am. Chem. Soc. 73, 843-846 (1951).

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1238-1244 (1964).

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argon-hydrogen systems from 68° to 108°K and pressures to 120 atmospheres,

International Advances in Cryogenic Engineering, Vol. 10, 171-181 [ed. K. D.

Timmerhaus, Plenum Press, 1965],

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Phys. 42, 500-503(1965).

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42. C. K. Heck and M. J. Hiza, Liquid-vapor equilibrium in the system heliummethane, A.I.Ch.E. J. 1_3, 593-600(1967).

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equilibrium in the system hydrogen-ethane, Advances in Cryogenic Engineering,

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equilibrium in the system hydrogen-ethylene, Chem. Eng. Progr. Symp.

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properties of parahydrogen from the triple point to 100 °K at pressures to 340 atmospheres, Natl. Bur. Std. Monograph 94 ( 1965)

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Lab. Report, UCRL-3421 (May 1956).

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solubility in cryogenic solvents at high pressures, Ind. Eng. Chem. Process

Res. and Dev. 9, 310-317(1970).

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hard-sphere model, J. Chem. Phys. 55, 1613-1616(1971).

47
Table 1. Vapor Pressure of nD

In p (atm) =7.987864211 - (221. 2539491)/ (4. 032572130 + T)

T PQ px CALC

o DIFF

K

atm atm atm

20.000 0.2906 0.2957 -0.00506

21.000 0.4219 0.4271 -0.00518

22.000 0.6002 0,5997 0.00046

23.000 0.8302 0.8213 0.00889

24.000 1. 1057 1.0998 0.00591

25.000 1.4433 1.4434 -0.00007

26.000 1.8645 1.8603 0.00421

27.000 2.3510 2.3587 -0.00775

28.000 2.9430 2.9468 -0.00377

29.000 3.6303 3.6321 -0.00180

30.000 4.4094 4.4221 -0.01274

32.000 6.3351 6.3438 -0.00869

34.000 8.7881 8.7616 0.02650

23.666 1.0000

Standard Deviat ion = 0. 010963

7 * 1 atm =0. 101325 MN/m

Table 2. Vapor Pressure of nH

In p (atm) =7.987748573 - (219. 6811229)/(7. 127745367 + T)

T Po p CALC

o DIFF

K

atm atm atm

20.000 0.8948 0.8956 -0.00079

21.000 1. 1942 1. 1944 -0.00018

22.000 1.5617 1.5617 0.00002

23.000 2.0108 2.0059 0.00490

24.000 2.5313 2.5354 -0.00408

25.000 3. 1607 3. 1582 0.00248

26.000 3.8820 3.8823 -0.00025

27.000 4.7122 4.7149 -0.00268

28.000 5.6546 5.6631 -0.00849

29.000 6.7400 6.7333 0.00665

30.000 7.9342 7.9316 0.00264

20.375 1.0000

Standard Deviation = 0. 0047181

1 atm =0. 101325 MN/m

48
4 Table 3. Experimental Liquid Phase Compositions for the He -nD System

T

K atm

20.00 0.2906

4

(He )

1 atm =0.101325 MN/m

atm

9.717 0.0085 5 1103

13.245 0.0092 6 1399

16.719 0.0099 7 1648

19.196 0.0101 1872

22.00 0.6002

8.404 0.0099 Z 787

10.227 0.0106 908

13.909 0.0133 1001

17.059 0.0136 1208

19.801 0.0154 1247

24.00 1.1057

8.598 0.0126 594

10.500 0.0143 659

13.660 0.0157 801

16.903 0.0195 809

19.992 0.0200 943

26.00 1.8645

8.530 0.0146 457

9.207 0.0142 519

11.911 0.0182 551

13.800 0.0200 596

17.148 0.0212 721

19.407 0.0252 695

19.890 0.0247 730

28.00 2.9430

6.716 0.0103 367

7.019 0.0109 373

10.159 0.0148 487

15.259 0.0236 521

18.549 0.0278 562

18.903 0.0277 577

19.754 0.0292 577

30.00 4.4094

8.826 0.0136 325

11.452 0.0192 367

14.024 0.0249 386

16.277 0.0290 409

20.400 0.0367 436

20.414 0.0341 470

49
3 Table 4. Experimental Liquid Phase Compositions for the He -nD System

T

K

20.00

22.00

24.00

26.00

28.00

30.00

p"~

atm

X

2 (He

3

)

P"Pol

atm

0.2906

3.450 0.0065 2 485

6. 162 0.0062 6 938

9.295 0.0065 3 0.0083Z 1379

11.704 1372

14.446 0.0086 3 1640

0.6002

5.012 0.0072 5 609

7.454 0.0083 5 821

9.595 0.00868 1036

12.269 0.0090 5 1289

16. 124 0.0104 1500

1. 1057

4.018 0.0060 5 481

5.655 0.0074 1 614

6.492 0.0091 5 589

8.724 0.0098 1 777

9.098 0.0107 744

9.220 0.0109 744

11. 153 0.0114 879

13.589 0.0118 1057

13.745 0.0124 1023

1.8645

5.740 0.0090 8 427

6.948 0.0106 481

8.604 0.0122 554

11.200 0.0142 659

15.446 0.0170 800

2.9430

9.343 0. 0122 525

11.721 0.0158 555

14.814 0.0187 634

4.4094

8.986 0.0130 353

10.517 0.0155 394

13.357 0.0192 466

17.583 0.0257 513

1 atm =0. 101325 MN/m

50
4

Table 5. Experimental Liquid Phase Compositions for the He -nH System

T

K

20.00

22.00

24.00

26.00

28.00

p*

atm

x

24

(He )

P"Pol

X

2 atm

0.8948

7.250 0.0110 580

11.061 0.0172 592

15.756 0.0211 703

19.849 0.0244 776

1.5617

5.784 0.0107 394

9.649 0.0204 397

14.463 0.0266 485

20.353 0.0343 548

2.5313

7.291 0.0155 307

10.765 0.0231 357

16.331 0.0333 414

19.805 0.0411 421

3.8820

8.370 0.0150 299

10.782 0.0238 290

12.327 0.0283 299

13.776 0.0307 322

15.814 0.0373 320

17.814 0.0430 324

19.992 0.0471 342

5.6546

8.247 0.0141 184

11.554 0.0267 221

11.639 0.0264 227

16.797 0.0458 243

19.720 0.0566 249

1 atm =0.101325 MN/m

51
3 Table 6. Experimental Liquid Phase Compositions for the He -nH_ System

T

K

22.00

24.00

26.00

28.00

P'" atm

X

2 (He 3

)

P"Pol

X

2 atm

1.5617

8. 189 0.0123 538

10.462 0.0151 589

13. 545 0.0201 597

14.936 0.0215 623

2.5313

7.863 0.0137 389

10.238 0.0176 439

12.623 0.0221 456

14.783 0.0285 430

3.8820

7.723 0.0113 339

10.299 0.0178 361

13.443 0.0285 336

15. 174 0.0331 342

5.6546

9. 179 0.0148 239

11.547 0.0227 260

13.000 0.0280 262

15.205 0.0368 260

1 atm =0. 101325 MN/m

52
Table 7. Experimental Vapor Phase Compositions for the He -nD System

T P* v, y P

K atm

Z0.00 0.2906 1.00 1.00

6„743 0.06029 1.399

9.911 0.0457 5 1.560

13.517 0.0392 2 1.824

18.015 0.03489 2.163

24.00 1.1058 1.00 1.00

3.984 0.3143 1.132

8.342 0.1760 1.328

14.035 0.1217 1.545

20.172 0.1005 1.833

28.00 2.9430 1.00 1.00

7.992 0.4436 1.205

10.503 0.3688 1.316

15.538 0.2884 1.523

19.039 0.2523 1.632

30.00 4.4094 1.00 1.00

7.148 0.6905 1.119

10.418 0.5335 1.260

15.229 0.4127 1.425

20.009 0.3556 1.614

1 atm =0. 101325 MN/m

Pol

53
3 Table 8. Experimental Vapor Phase Compositions for the He -nD System

T P* y

2 y 2 P

K atm

( nDJ P i 2 ol

20.00 0.2906 1.00 1.00

5.217 0.0725 3 1.302

5.590 0.06942 1.335

8.441 0.0511 7 1.486

12.439 0.0402 5 1.723

15.637 0.0358 7 1.930

24.00 1.1058 1.00 1.00

3.634 0.3499 1.150

8.234 0.1798 1.339

12.340 0.1365 1.523

15.834 0.1154 1.653

28.00 2.9430 1.00 1.00

8.693 0.4187 1.237

12.242 0.3275 1.362

14.412 0.2922 1.431

30.00 4.4094 1.00 1.00

7.403 0.6741 1.132

9.904 0.5469 1.228

13.147 0.4458 1.329

16.937 0.3808 1.463

1 atm =0. 101325 MN/m

54
4

Table 9. Experimental Vapor Phase Compositions for the He -nH System

T P* y 2 y

x P

K atm

1 atm =0.101325 MN/m

(nH2> Pol

20.00 0.8948 1.00 1.00

6.151 0.1951 1.341

10.278 0.1370 1.574

14.865 0.1133 1.882

19.029 0.1047 2.227

24.00 2.5313 1.00 1.00

6.638 0.4699 1.232

10.710 0.3457 1.463

15.314 0.2839 1.718

19.938 0.2494 1.964

26.00 3.8820 1.00 1.00

8.621 0.5849 1.299

12.027 0.4665 1.445

16.076 0.4010 1.661

19.699 0.3782 1.919

28.00 5.6546 1.00 1.00

8.635 0.7741 1.182

11.775 0.6460 1.345

15.885 0.5626 1.580

20.077 0.5091 1.808

55
4 3 Table 10. He and He K-values for the nD Systems

T P*

atm

X

2 K

2 K

He4 He 3 He

4

He 3

9 2 0.00271 0.00258 329.5 346. 1 4 0.00475 0.00441 197.9 213.2

6 0.00606 0.00556 157.7 171.9

8 0.00688 0.00625 140.1 154.2

10 0.00740 0.00667 130.9 145.2

12 0.00767 0.00687 126.6 141.4

14 0.00789 0.00692 123.4 140.6

16 0.00802 0.00696 121.5 140.0

18 0.00824 118.4

20 0.00856 114.0

2 0.00285 0.00263 294.6 319.3

4 0.00520 0.00473 175.2 192.6

6 0.00675 0.00610 138.5 153.3

8 0.00778 0.00703 121.7 134.7

10 0.00855 0.00770 111.6 123.9

12 0.00903 0.00815 106.2 117.6

14 0.00943 0.00848 102.0 113.4

16 0.00975 0.00878 98.88 109.8

18 0.01002 96.37

20 0.01025 94.29

2 2 0.00280 0.00275 242. 1 246.5

4 0.00595 0.00555 138.4 148.4

6 0.00802 0.00728 108.7 119.8

8 0.00958 0.00838 93.58 107.0

10 0.01075 0.00905 84.75 100.7

12 0.01182 0.00952 77.91 96.73

14 0.01275 0.00985 72.78 94.21

16 0.01360 0.01015 68.62 91.94

18 0.01438 65.18

20 0.01518 61.94

4 2 0.00215 0.00202 197.4 210. 1 4 0.00622 0.00565 110.4 121.6

6 0.00955 0.00815 81.13 95.07

8 0.01195 0.00975 68.53 83.99

10 0.01375 0.01090 61.48 77.56

12 0.01525 0.01180 56.62 73. 17

14 0.01660 0.01248 52.78 70.21

16 0.01783 0.01300 49.68 68. 14

18 0.01898 47.06

20 0.02010 44.74

1 atm =0. 101325 MN/m

56
4 3 Table 10. He and He K-values for the nD Systems (continued)

T P*

atm

s: 2 K

2 K

He

4 He3 He4

He

3

6 2 0.00040 0.00032 153.0 191.3

4 0.00550 0.00525 89. 11 93.35

6 0.00982 0.00902 64.55 70.28

8 0.01322 0.01158 53.46 61.04

10 0.01585 0.01335 47.34 56.20

12 0.01812 0.01485 43.02 52.49

14 0.02005 0.01605 39.93 49.88

16 0.02190 0.01715 37.28 47.61

18 0.02362 35. 10

20 0.02528 33. 18

8 4 0.00320 0.00312 71.78 73.62

6 0.00853 0.00805 52.19 55.30

8 0.01278 0.01142 43.39 48. 56

10 0.01612 0.01395 38.52 44. 51 12 0.01910 0.01603 34.83 41.50

14 0.02185 0.01795 31.92 38.86

16 0.02443 0.01965 29.54 36.73

18 0.02692 0.02128 27.51 34.81

20 0.02942 25.69

6 0.00538 0.00525 39.72 40.70

8 0.01118 0.01065 32.55 34. 17 10 0.01618 0.01458 28.20 31. 30

12 0.02062 0.01780 25. 17 29. 16 14 0.02475 0.02070 22.79 27.25

16 0.02862 0.02340 20.92 25. 59 18 0.03235 0.02600 19.34 24.07

20 0.03588 18.05

2 8 0.00640 0.00617 23.48 24. 36

10 0.01357 0.01251 19.63 21,29

12 0.02009 0.01787 17.27 19.42

14 0.02616 0.02248 15.50 18.03

16 0.03179 0.02670 14. 16 16.85

18 0.03727 0.03054 13. 11 16. 00

20 0.04257 12.05

1 atm =0. 101325 MN/m

57
4 3 Table 11. He and He K-values for the nH Systems

T P*

atm

X

2 K

2 K

He

4 He 3 He4

He 3

2 0.00250 0.00238 208.9 219.4

4 0.00650 0.00559 112.9 131.3

6 0.00980 0.00798 82. 10 100.8

8 0.01265 0.00985 66.37 85.24

10 0.01515 0.01141 56.79 75.41

12 0.01745 0.01290 50.09 67.76

14 0.01950 0.01432 45.30 61.69

16 0.02130 41.77

18 0.02295 38.95

20 0.02450 36.58

2 2 0.00130 0.00120 153. 5 166.3

4 0.00690 0.00575 80.42 96.50

6 0.01165 0.00915 57.79 73.58

8 0.01585 0.01200 46.20 61.02

10 0.01955 0.01470 39.25 52.20

12 0.02285 0.01750 34.60 45. 18

14 0.02580 0.02040 31.29 39.57

16 0.02860 0.02335 28.65 35.09

18 0.03125 26.51

20 0.03375 24.75

4 4 0.00530 0.00440 59.38 71.52

6 0.01145 0.00935 43.30 53.03

8 0.01675 0.01355 34.99 43.25

10 0.02145 0.01755 29.86 36.50

12 0.02580 0.02155 26.23 31.41

14 0.02995 0.02595 23.47 27.08

16 0.03390 0.03050 21.31 23.68

18 0.03770 19.56

20 0.04140 18. 10

6 6 0.00825 0.00715 33.45 38.60

8 0.01485 0.01240 27. 14 32.51

10 0.02095 0.01760 22.86 27.22

12 0.02660 0.02340 19.92 22.65

14 0.03205 0.02960 17.66 19. 12 16 0.03735 0.03625 15.88 16.36

18 0.04255 14.44

20 0.04760 13.26

1 atm =0. 101325 MN/m
4 3 Table 11. He and He K-values for the nH Systems (continued)

K, T P'

atm

J"2 '2 K

He

4 He 3 He4

He

3

8 6 0.00190 0.00160 20.37 24. 19

8 0.01175 0.01005 16.95 19.82

10 0.02020 0.01745 14.65 16.96

12 0.02795 0.02435 12.88 14.79

14 0.03535 0.03190 11.50 12.75

16 0.04280 0.04000 10.29 11.01

18 0.05020 9.313

20 0.05770 8.463

9 8 0.00720 0.00636 13.57 15.36

10 0.01762 0.01545 11.77 13.42

12 0.02725 0.02402 9.963 11.30

14 0.03667 0.03270 8.759 9.823

16 0.04562 0.04152 7.867 8.644

18 0.05533 7.002

20 0.06314 6.530

1 atm =0. 101325 MN/m

59
T

K

19-20

20-22

22-24

24-26

P'" atm

24

6

8101214

16

18

20

24

6810

1214

16

18

20

24

6

8 10

1214

16

18

20

24

6

8 10

1214

16

18

20

Table 12 Heats of Solution

AH J/mol

s 4 He -nD.

354

385

410

445

504

555

602

651

650

600

359

431

443

481

503

567

617

668

715

769

448

496

642

684

705

701

705

709

715

714

661

556

593

644

678

713

724

745

761

775

He -nD.

L 255

321

362

42 7 501

582

680

768

473

477

451

421

379

357

339

325

351

437

508

532

573

613

645

658

243

686

784

828

836

862

887

930

4 He -nH He -nH.

564

621

642

663

676

677

677

690

704

715

666

634

610

600

608

631

650

667

687

670

659

693

714

738

763

787

807

507

563

576

611

673

741

812

658

719

756

785

798

833

863

824

741

761

848

903

959

1 atm =0. 101325 MN/m

60
Table 12 Heats of Solution (continued)

T

K atm 4 He -nD.

AH J/mol

s He -nD.

4

He -nH. He -nH.

26-28

28-29

28-30

30-32

4

6810

1214

16

18

20

810

12

14

16

18

20

6810

1214

16

18

20

810

1214

16

18

20

655

643

632

624

639

678

704

737

774

953

1004

1089

1134

1176

1205

1230

1233

1304

1446

1503

1538

1558

1552

1613

719

726

692

706

711

756

785

1070

1227

1230

1232

1239

1262

1288

1351

1538

1622

1648

1668

1630

1501

142 5 1347

1320

1298

1313

1327

1359

1502

1478

1736

1837

1810

1927

1751

1414

1498

1432

1290

1226

1199

1721

1581

1817

1761

1633

1 atm =0. 101325 MN/m

61

FORM '.3S-114A (1-71) 2. Gov't Accession No.

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. Technical Note 621

3. Recipient's Accession No.

4. TITLE AND SUBTITLE Liquid -Vapor Equilibrium in the Binary

Systems of He and He with nD and nH

5. Publication Date July 1972

6. Performing Organization Code

7. AUTHOR(S) M. J. Hiza 8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. Project/Task/Work Unit No. NATIONAL BUREAU OF STANDARDS, Boulder Labs,

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

11. Contract/Grant No. SANL 807-004

12. Sponsoring Organization Name and Address U. S. Atomic Energy Commission

San Francisco Operations Office

2111 Bancroft Way

Berkeley, California 94704

13. Type of Report & Period Covered Tech> Note #621

Jan 71 thru Mar 72

14. Sponsoring Agency Code

IS. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) Experimental data are reported for the equilibrium liquid and vapor phase com4 3 4

positions of the He - nD and He -nD systems from 20 to 30 K and the He -nH

3

and He -nH. systems from 20 to 28 K. The maximum experimental pressures were

2 4 3 20 and 16 atm (2.0 and 1.6 MN/m ) for the He and He systems, respectively. In

addition, vapor pressures were measured from 20 to 34 K for nD and from 20 to 30 K for nH . 2

Values of Henry's constants, enhancement factors, K-values, and heats of solution

were derived from the experimental data for each system. The derived properties

4 4 are compared with those derived from previous data for the He -nH , He -pH , and

3 2 2

He -nH„ systems.

17. KEY WORDS (Alphabetical order, separated by semicolons) Binary systems; gas solubility; He 4 -nD? ; He -nD ; He -nH^jHe -riirL^; liquid-vapor equilibrium; nD vapor pressure;

nH\ ? vapor r>rmKur&, 7 vapr

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