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Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures
Chemical Engineering Science, 1964, Vol. 19, pp. 775-782. Pergamon Press Ltd., Oxford.
Printed in Great Britain.
Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures M. ORENTLICHERand J. M. PRAUSNITZ Cryogenic Engineering Laboratory, National Bureau of Standards, Boulder, Colorado and Department of Chemical Engineering, University of California, Berkeley, California 94720. (Received 26 February 1964) Abstract-Solubility data for hydrogen in liquids at low temperature and high pressure have been reduced by a thermodynamic relation similar to the Krichevsky-Kasamovsky equation but allowing for the variation of activity coefficient with hydrogen concentration. The parameters appearing in this relation have been partially correlated on the basis of a very simple solution model. The results show that under comparable conditions the solubility of hydrogen in simple inorganic solvents (argon, nitrogen and carbon monoxide) is considerably larger than that in light hydrocarbons (ethane, ethylene. propane and propylene), with methane falling in between these groups.
THE recent large increase in the use of liquid hydrogen for the space industry has focused attention on techniques for improving existing methods of liquid hydrogen production; the desire for such improvements has revived interest in the phase equilibria of hydrogen-containing systems at lowtemperatures. The solubility of a condensed component in compressed hydrogen gas can be calculated fairly well by using an appropriate equation of state for the gaseous phase [l-8] and the solubility of solids and of helium gas in liquid hydrogen has also received attention in the past few years [9-131. In this work we consider the solubility of hydrogen gas in cryogenic liquidst. The available experimental data have been reduced in a manner suggested by thermodynamic analysis and the reducing parameters obtained have been partly generalized in a manner suggested by using very simple concepts of the theory of solutions. The final correlation obtained should be useful for calculating the solubility of hydrogen in a variety of low-temperature solvents up to rather high pressures but not exceeding about 100 atm.
f'I=f4
(1)
f 1 is the fugacity of hydrogen in the vapour phase and fi is the fugacity of hydrogen in the liquid phase. The vapour phase fugacity is related to the mole fraction in the vapour phase y, by where
f 5 = &Y,P
(2)
Techniques for calculating the vapour-phase fugacity coefficient 4Z are given elsewhere [l, 2, 4-71. In many cases of practical interest, yZ N 1 and in that event the Lewis fugacity rule provides a very good approximation [2, 151. The liquid-phase fugacity is a function of temperature, pressure and composition. The effect of pressure is given by alnfi
( 1 8P
V,
T,x=RT
where CZis the partial molar volume of hydrogen in the liquid. The effect of composition at constant temperature and pressure is given by
fi=Y;&
THERMODYNAMIC ANALYSIS Let subscript 1 refer to the liquid solvent and let subscript 2 refer to hydrogen. At any temperature T and total pressure P the solubility of hydrogen t A correlation of hydrogen solubilities in hydrocarbons has been published by BENHAMet al. [14].
is determined by the equation of equilibrium
(4)
where H is Henry’s constant and yz is the activity coefficient of hydrogen normalized such that r:+l
as
x2+0
Henry’s constant is defined such that for a given hydrogen-solvent system it is a function of tem775
M. ORENTLICHER and
perature only
J. M.
In fJ = In H + 62" x2
H = limit& x2+0 x2
(5)
In y1 = &
(7)
If x2 is small and if the total pressure is not close to the critical of the solution, it is a good approximation to assume that b, is independent of pressure and composition. In that case, equations (l), (4) and (7) yield
f!i =InH+
I(% 1
(Sa)
Equation (8) contains three temperature-dependent parameters for any solvent of which H, Henry’s constant, is the most important. In order to obtain meaningful, unambiguous values of these parameters, data of very high accuracy are required, especially for very dilute solutions. However, data of this calibre are available only for argon [17] and therefore it is desirable to evaluate one of the parameters independently. The partial molar volume can be obtained from dilatometric measurements but unfortunately only a few of these have been made; nevertheless, with the help of an approximate theory it is possible to correlate and generalize these measurements enabling good estimates of partial molar volumes to be made. This generalization is achieved by noting that at temperatures well above the critical of hydrogen it is a good assumption to consider hydrogen to behave like a hard-sphere gas. Its equation of state is then given by
x$
(XT - 1)
(Hl&) - PS
DATA REDUCTION
where A is an empirical coefficient which, for a given hydrogen-solvent system, is a function only of temperature?. From the Gibbs-Duhem equation it then follows that In yz*= &
2A
Thus a semilogarithmic plot of the ratio f2/x2 at constant temperature against total pressure approaches a straight line for small values of x2.
For the solubility data under consideration here, x2 is always small, usually less than 0.1 and always less than 0.2. However, even for such small mole fractions, deviations from dilute solution behaviour are not negligible. For this small concentration range we make the very reasonable assumption that the activity coefficient of the solvent is given by the simple, one-parameter expression
In -
PRAUSNITZ
(8)
(v - b,) = y
x2
where Pf is the saturation (vapour) pressure of the solvent, and where i$ is the partial molar volume of hydrogen at infinite dilution. Equation (8) is similar to the Krichevsky-Kasarnovsky equation [19, 201 except that equation (8) takes into account deviations from Henry’s law due to the effect of composition in addition to the effect of total pressure. (An equation essentially identical to equation 8 was previously presented by KRICHEVSKY and ILINSKAYA in 1945 [21].) If A is set equal to zero, equation (8) becomes identical with the Krichevsky-Kasarnovsky equation. For small x2 (see Appendix I) equation (8) becomes t Equation (6) has been successfully used for liquid solutions of hydrogen by CCINNOLLY 1161,VOLK and HALSEY[17] and MAIMONI1181.
where b, is the van der Waals covolume (26.6 cm3/gmol). The internal pressure of the solvent is very nearly given by 6, 2, the square of the solubility parameter; as a reasonable approximation, therefore, the partial molar volume of dilute hydrogen in the solvent is given by RT 62” = b, + 8
(10)
In equation (10) b, is always much larger than RT/d12 except at temperatures close to the critical of the solvent when ~5,~is small. Under usual conditions, therefore, the partial molar volume of hydrogen is not very sensitive to temperature nor to the nature of the (non-polar) solvent. From limited experimental data [17, 22, 231, we
776
Thermodynamics
of hydrogen solubility in cryogenic solvents at high pressures
II
6-
STRAIGHT
CHAIN
(ETHANE
FIG. 1.
REDUCED
I
TEMPERATURE,
0.9 T/Tc,
Solvent factor for partial molar volumes of hydrogen in two types of solvents. A, n-G [221; V, n-G 1231; n , A 1171.
find that equation (10) gives reasonably sults. If we define a solvent factor F by
good re-
FRT 62” = b2 + 6:
(11)
then we would expect F to be of the order of unity. In fact, at a solvent reduced temperature of 0.7, F is about l-2 in argon and about 2.2 in normal paraffins. Fig. 1 shows a plot of F vs. reduced temperature of the solvent with d1 evaluated at a reduced temperature of O-7. In subsequent calculations the lower line was used to calculate i& for the solvents argon, nitrogen, carbon monoxide and methane and the upper line was used for higher hydrocarbons. Table 1. Solvent
Argon Nitrogen Carbon monoxide Methane Ethane Ethylene Propane Propylene n-Hexane
-
LARGER]
0.8
0.7
0.6
HYXOCAREONS
I
I
0.34
AND
Temp. range (“W
87-140 90-95 68 79-86 68-90 90-127 116-173 144-200 144-172 228-277 172-228 378445
Using values of Vz calculated from equation (11) and Fig. 1 it was possible to compute the parameters H and A from the solubility data. The data which were used to obtain these parameters are those for the systems listed in Table 1. Hexane, of course, is not a cryogenic solvent but was included in this study in order to ascertain if there is a significant difference in the behaviour of hydrogen-containing solutions between low- and high-molecular weight solvents. The fugacity of hydrogen in the vapour phase was calculated from the known volumetric properties of hydrogen [14, 241; where necessary, small corrections for the effect of vapour-phase composition were made using a method based on van der
Hydrogen solubility data Pressure range Mm)
17-82 845 l-25 18-100 25-50 30-l 10 34-103 17-68 17-68 17-68 17-68 34-102
777
VOLK and HALSEY [17] MAIMONI [18] OMAR and DOKOUPIL [26] GONIKBERGet al. 127,281 DRAWERand FLYNN [29] FA~TOVSKYand GONIKBERG[30] BENHAM and KATZ [31] WILLIAMS and KATZ [32] WILLIAMSand KATZ [32] WILLIAM and KATZ [32] WILLIAMS and KATZ [32] NICHOLS et al. [23]
M. ORENTLICHER and J. M. PRAUSN~TZ
nine solvents under consideration and it is evident that the over-simplified theory does only a very approximate job in correlating the data. The top line correlates the data for the four small hydroTable 2.
0 FIG. 2.
\ 20
:
!
40 60 PRESSURE,
\ 80 ATM
I 100
830 660 500 385
5.0 + 0.5
30 31 35 44
co
68 73 78 83 88
640 550 470 440 400
7.0 f 0.7
31.2 31.8 32.6 33.6 34.4
NZ
68 79 86 90 95
540 450 390 370 340
7.0 + 0.7
30.4 31.5 32.0 33.0 344
90 110 116 127 144
1824 1036 970 838 630
15 f 3
29.7 31.0 31.6 32.6 36.0
144 158 172 200
3050 2400 2050 1400
19.5 * l-5
37.1 37.8 39.4 44.5
C2Hs
144 172 200 228
2600 2050 1650 1210
25 i 2
37.9 40.7 44.2 54.3
Cd-h
228 255 282
1670 1300 1030
25 f 2
50 51 63
C3Hs
172 200 228 268
3300 2600 1850 1320
25 i
39.6 41.7 48.8 55.6
n-CsHls
344 378 410 445
930 830 700 590
120
Fugacity of pure hydrogen gas at low temperatures.
CH4
Waals’ equation as discussed by HILDEBRAND and SCOTT [25]. The fugacity of pure hydrogen gas is shown in Fig. 2. Table 2 gives the parameters H, A and fir for hydrogen in nine solvents. The data are sufficiently detailed to give the temperature dependence of Henry’s constant but, over the temperature range under consideration, no significant variation of A with temperature could be detected. The accuracy of the A parameters is probably no better than lo-20 per cent; equation (8), however, is much more sensitive to H than it is to A. CORRELATION OF HENRY’S CONSTANTS
A reasonable technique for correlating Henry’s constants for hydrogen in non-polar solvents is suggested by a highly simplified solution theory which is outlined in Appendix II. This theory suggests that a plot of a reduced Henry’s constant (H divided by S:) vs. reduced temperature (T divided by T,,) should give a universal curve for all solvents. Such a plot is shown in Fig. 3 for the 778
for hydrogen
87 100 120 140
A
-0.31
Thermodynamic parameters solubility
CzH4
2
7.9 f 0.3
640 75.5 103.2 162
* v2mfrom volumetric data for solutions of hydrogen in argon and in hexane. For other solvents dam calculated from Fig. 1.
Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures and /iZL* = partial molar enthalpy of hydrogen in liquid solution at infinite dilution. = molar enthalpy of hydrogen in the hzv vapour phase. Values of the left-hand side of equation (12) are given in Table 3. Table 3.
Enthalpy function for dissolved hydrogen. dln H, a’Trl
Solvent
- 1.87
A, Nz, CO CH4 CzH4,Cs;Hs,C3Hs,C3Hs n-&H14 REDUCED
FIG. 3.
TEMPERATLiRE,
Reduced Henry’s constants H, = (H/S12)T,=O.7.
T/Tc,
SOLVENT MIXTURES
for hydrogen
carbons, ethane, ethylene, propane and propylene, and the bottom line correlates the results for the three small, essentially spherical molecules, argon, nitrogen and carbon monoxide. The data for the spherical hydrocarbon methane fall in between and those for hexane are a little below the top line for the other hydrocarbons. The deviation of the hexane line from that for the C, and C3 hydrocarbons is probably more due to the large difference in molecular size than to the large difference between solute temperatures. The significant difference between the top and bottom lines points out once again that the intermolecular forces between hydrogen and hydrocarbons are in some qualitative way different from the intermolecular forces between hydrogen and inorganic molecules as noted by ALDER [33] and HILDEBRAND and SCOTT [34].
HEAT
- 2.80 - 3.18 - 2.21
Good experimental data on the solubility of hydrogen in mixed liquids are extremely rare. However, it is possible to make good estimates of this solubility with a minimum of assumptions by using information on the behaviour of all possible binary systems made up of the various components in the multicomponent solution. The details of such a calculation are presented elsewhere [35] but the results are summarized below for the case of a mixed solvent containing two components. As before, let subscript 2 stand for hydrogen and let subscripts 1 and 3 stand for the two solvents. All thermodynamic quantities are referred to P;, the vapour pressure of the reference solvent which in this case is arbitrarily chosen to be solvent 1. Henry’s constant for hydrogen in solvent 1 is designated by H,,,(P”) and that for hydrogen in solvent 3 by H&P;). These constants can be obtained from Fig. 3 and from the relation
OF SOLUTION
H&P3
The heat of solution of hydrogen at infinite dilution can be calculated from the slope of the data shown in Fig. 3. If the volatility of the solvent is neglected, the thermodynamic relation is
= H2,3(G) ev
s
p1scZ3 dP
PP
The activity coefficient solvent is defined by fi ” = xZHZ,JP;)
(12)
for hydrogen
exp
RT
in the mixed
p V, dP -
s P,’
c14j
RT
(15)
where EZ is the partial molar volume of hydrogen in the mixed solvent. This quantity must be estimated by interpolation from Fig. 1. It follows
where (13) 779
M.
ORENTLICHER
from the definition in equation (15) that yz + 1 only when both x2 and x3 approach zero. For the binary mixture (hydrogen-free) of the two solvents, assume that the excess free energy (symmetrical convention) is given by the one-parameter Margules equation 9= =
%3X1X3
- x1(1 - %)I +
these effects must be taken into account; the first, through the partial molar volume and the second, through a self-interaction coefficient. The equations and parameters presented in this work make it possible rapidly to calculate the solubility of hydrogen at low temperatures and high pressures in pure and mixed non-polar solvents.
(16)
where aI3 is a function of temperature. This parameter can be obtained from vapour-liquid equilibrium data or else can be estimated from an equation such as that of HILDEBRANDand SCOTT[37]. It can now be shown that in the ternary solution In y* = -alz[l
J. M. F’RAUSNITZ
and
%3X1X3
~23X3(1
-
+ x2>
Acknowledgment-The authors are grateful to the national science foundation for financial support.
APPENDIXI.
Equation (8) can be rewritten in a more convenient form which is valid for very small x2. First, rewrite the identity
(17)
The coefficient aI2 is identical to the coefficient (8) for hydrogen in solvent 1. The coefficient uZ3 can be found from
DERIVATIONOF EQUATION(Sa)
X;-l=(P-P;)(~)-l~~)
(AI.1)
A/RT in equation
H,
u23
=
a,, + In )
The limit of the last factor on the right-hand side is x; - 1 lim -= x2-+0 x2
3(C) (18)
H2,dP”)
p,fl+& 42
For small x2 p =fS(l -
CH2,,(P~)]“2CH2,3(P~)l”3 w? - ww3
(AI.3)
91
mixed sodPs) =
(AI.2)
To obtain the limit of the second factor, we have
For solutions which are very dilute in hydrogen the activity coefficient is found by setting x2 equal to zero in equation (17). It can then be shown that Henry’s constant for hydrogen in the mixed solvent is given by H 2,
-2
~2)
+
41
(1%
Hx2
(AI.4)
-Z
or
Equation (19) has the interesting property that even if the two solvents form an ideal solution (aI3 = 0), then Henry’s constant for hydrogen in the mixed solvent is not a linear but rather an exponential function of the solvent composition. (A1.6) Therefore
CONCLUSION Solubility data for hydrogen have been analysed and partly correlated with the help of a thermodynamic model. At advanced pressures deviations from Henry’s law occur because of two reasons: first, the effect of pressure on the thermodynamic properties of the condensed phase becomes appreciable and second, as the pressure rises the mole fraction of hydrogen in the liquid phase soon becomes sufficiently large to cause significant deviation from dilute solution behaviour. Both of
lim
(AI.7)
X2-+0
where the superscript s refers to the saturation pressure of component 1. Substituting equations (AI.2) and (AI.7) into equation (AI.l) we obtain -2(P - P”l) ~;~o(x’ - I) = [(H/e2)
_ Pg
(AI.8)
and therefore equation (8) in the text becomes
780
Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures
Equation (AII.5) then becomes
lim In fi’ X,+0
(1x2
2A @ - [(HI&)
- P;]
1
ln$= 1
An approximate value of Henry’s constant for hydrogen in a liquid at total pressure P can be calculated by an isothermal thermodynamic cycle consisting of (a) compression of pure hydrogen-gas from its partial pressure pz to the internal pressure of the solvent; (b) ideal mixing at the internal pressure; and (c) expansion back to the system pressure P. Using equation (9), the Gibbs free energy changes per mole of hydrogen for the three steps are
Ag, = Step
z =o*35 and similarly for ethane, ethylene, propane and propylene H
- - 0.65
s: -
Since H, for a given solvent, is only a function of temperature, it appears reasonable to correlate the experimental results by plotting H/St vs. T/T,, where T,, is the critical temperature of the solvent. Since Sf is itself a function of T/T,,, simplification is obtained by plotting H, vs. Tr, where
(AII.l)
@I
(AII.2)
Step (c) A& =
’ 62 dP = bz(P - Sf) + ‘$
s 612
H, s H/61
(P - 6:)
(AII.3)
T,, = T/T,,.
When the gas phase and the liquid phase are in equilibrium the total free energy change (steps a, b and c) must vanish and upon adding equations (AII.l), (AII.2) and (AII.3) and setting the sum equal to zero
,nGx2 -=
I _
b,(P
- P2)
RT
PZ
P2>
= 0
Cohesive energy densities (6:) of nine solvents are given in Table 4. These were evaluated from the known heats of vaporization and liquid densities of the solvents as described by HILDEBRAND and SCOTT [36].
(AII.4) Table 4.
(AII.5)
For all values of the total pressure P encountered in this work, the final term in equation (AII.5) is much less than unity and can be neglected. Ignoring vapour phase non-ideality at the pressure P, Henry’s constant is
H,pz
(with S: evaluated at T,, = 0.7)
and
1
St P-S? + bz(P-In x2 + In pz + 62 RT 1 Since S: & P, this becomes
(AII.8)
H
s P2
AgZ = RT In x2
H/6: = l/e = 0.37
Equation (AII.8) gives a good order of magnitude. For argon, nitrogen and carbon monoxide we find experimentally that at a reduced temperature of 0.7
APPENDIX II. SIMPLIFIEDSOLUTION MODEL
812 vdP = b,(6: - p?) + RT In 2
(AII.7)
and
which is equation @a).
Step (a)
-1
(AII.6)
x2
781
Cohesive energy densities of solvents at reduced temperature of 0.7 Solvent
812 (at4
Argon Nitrogen Carbon monoxide Methane Ethane Ethylene Propane Propylene n-Hexane
1720 1170 1170 1650 2000 2200 1940 2055 1750
M. ORENTLICHERand J. M. PRAUSNITZ REFERENCES [l] [2] [3] [4] [5] [6] [7] [8]
DOKOUPILZ., VAN SOEST,G. and SWENKER,M. D. P., Appl. Sci. Res. 1955 A5 182. PRAUSNITZJ. M., Amer. Inst. Chem. Engrs. J. 1959 3 5. PRAUSNITZJ. M. and BENSONP. R., Amer. Inst. Chem. Engrs. J. 1959 5 161. PRAUSNITZJ. M. and KEELERR. N., Amer. Inst. Chem. Engrs. J. 1961 7 399. PRAUSNITZJ. M. and Mvaas A. L., Amer. Inst. Chem. Engrs. J. 1963 9 5. REDLICHO., KISSER A. T. and TURNQUI~TC. E., Chem. Engng Progr. Symp. Ser. 48 No. 2 49 1952. REUSSJ. and BEENAKKERJ. J. M., Physica 1956 22 869. ROWL~NSON J. S. and RICHARDSONM. J., Aduances in Chemical Physics (Edited by PRIGOCINEI.) Vol. 2. Interscience, New York 1959. [9] BRAZINSKYI. and GOTTFRIEDB. S., NASA Tech. Note D-1403, August 1962. [lo] DoKoupr~ Z., Progress in Low-Temperature Physics (Edited by GORTER,C.) Vol. 3. Interscience, New York 1961. [ll] ECKERTC. A. and PRAUSNITZJ. M., J. Chem. Phys. 1963 39 246. [12] ROELLIGL. 0. and GIE~E C., J. Chem. Phys. 1962 37 114. [13] STREEIT, W. B., SONNTAG,R. E., VAN WYLEN, G. J., J. Chem. Phys. 1964,40, 1390 [14] BENHAMA. L., KATZ D. L. and WILLIAMSR. B., Amer. Inst. Chem. Engrs. J. 1957 3 236. [15] WALL F. T., Chemical Thermodynamics p. 307. Freeman, San Francisco 1958. [16] CONNOLLYJ. F., J. Chem. Phys. 1962 35 2892. 1171 VOLK H. and HALSEYG., J. Chem. Phys. 1960 33 1132. [18j MAIMONIA., Amer. Znst..Chem. Engrs: J. 1961 7 376. [I91 DODGE B. F. and NEWTON R. H., Zndustr. Engng. Chem. 1937 29 718. J. S., J. Amer. Chem. Sot. 1935 57 2168. PO1 KRICHEVSKYI. R. and KASARNOVSKY WI KRICHEVSKYI. R. and ILINSKAYAA. A., Z/I. fiz. khim, SSSR 1945 19 621. CONNOLLYJ. F. and KANDALICG. A., Chem. Engng Progr. Symp. Ser. 1963 59 No. 44, 8. ml t231 NICHOLSW., REAMERH. and SAGEB. H., Amer. Inst. Chem. Engrs. J. 1957 3 262. P41 American Znstitute ofphysics Handbook Section 4, p. 124. McGraw-Hill, New York 1957. P51 HILDEBRANDJ. H. and SCOTTR. L., Solubility of Nonelectrolytes p. 238. Reinhold, New York 1950. OMAR M. and DOKOUPILZ., Commun. Kamerlingh-Onnes Lab., University Leiden, No. 330, p. 1, 1963. WI ~71 DRAYERD. E. and FLYNN, T. M., Nat. Bur. Stand. Tech. Note No. 110, P.B. 161611, May 1961. GONIKBERGM., FASTOVSKY V. and GURVITSCHJ. G., Actu Physicochim. USSR 1939 11 865. ::; DRAYERD. E. and FLYNN T. M., Nat. Bur. Stand. Preprint R-244 1962; Tech. Note No. 108, P.B. 161609, May 1961. [301 FASTOVSKYV. and GONIKBERGM., Zh.fiz. khim. SSSR 1940 14 427. BENHAMA. L. and KATZ D. L.. Amer. Inst. Chem. Engrs. J. 1957 3 33. t::; WILLIAMSR. B. and KATZ D. L., Zndustr. Engng Chem. 1954 46 2512. [331 ALDER B., Ann. Rev. Phys. Chem. 1961 12 195. t341 HILDEBRANDJ. H. and Scorr R. L., Regular Solutions Chaps. 6 and 10. Prentice-Hall, Engelwood Cliffs, New Jersey 1962. t351 O’CONNELLJ. P. and PRAUSNITZJ. M., Zndustr. Engng. Chem. In press. I361 HILDEBRAN~J. H. and SCOTT R. L., Regular Solutions Appendix 5. Prentice-Hall, Englewood Cliffs, New Jersey 1962. 371 HILDEBRANDJ. H. and Scorr R. L., Regular Solutions Chap. 7. Prentice-Hall, Englewood Cliffs, New Jersey,1962.
R&m&-On a reduit les donnees de solubilite de l’hydrogene dans les liquides a basse temperature et haute pression a l’aide d’une relation thermodynamique analogue a l’equation de KruchevskyKasarnovsky mais permettant de tenir compte des variations du coefficient d’activite avec la concentration en hydrogene. Les parambtres de cette equation ont CtCcorreles en partie par un modele tres simple de la solution. 11en resulte que dans des conditions comparables la solubilite de l’hydrogene dans les solvants inorganiques (argon, azote et anhydride carbonique) est considbablement plus Clevee que dans les hydrocarbures legers (ethane, ethylene, propane et propylene). Le methane se situe entre ces deux groupes. Zusammenfassung-Loslichkeitsdaten fur Wasserstoff in Fltissigkeiten bei tiefen Temperaturen und hohen Drucken sind mittels einer thermodynamischen Beziehung reduziert worden, welche derjenigen von Krichevsky-Kasarnovsky Lhnlich ist, aber die Aenderung des Aktivitatskoeffizienten mit der Wasserstoffkonzentration beriicksichtigt. Die in dieser Beziehung vorkommenden Parameter konnten zum Teil durch eine Korrelation verkniipft werden, welche auf einem sehr einfachen Losungsmodell beruht. Die Ergebnisse zeigen, dass unter vergleichbaren Bedingungen die Loslichkeit des Wasserstoffes in einfachen anorganischen Losungsmitteln (Argon, Stickstoff, Kohlenmonoxid) bedeutend grosser ist als in leichten Kohlenwasserstoffen (Aethan, Aethylen, Propan, Propylen). Methan befindet sich zwischen diesen beiden Gruppen.
782
Printed in Great Britain.
Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures M. ORENTLICHERand J. M. PRAUSNITZ Cryogenic Engineering Laboratory, National Bureau of Standards, Boulder, Colorado and Department of Chemical Engineering, University of California, Berkeley, California 94720. (Received 26 February 1964) Abstract-Solubility data for hydrogen in liquids at low temperature and high pressure have been reduced by a thermodynamic relation similar to the Krichevsky-Kasamovsky equation but allowing for the variation of activity coefficient with hydrogen concentration. The parameters appearing in this relation have been partially correlated on the basis of a very simple solution model. The results show that under comparable conditions the solubility of hydrogen in simple inorganic solvents (argon, nitrogen and carbon monoxide) is considerably larger than that in light hydrocarbons (ethane, ethylene. propane and propylene), with methane falling in between these groups.
THE recent large increase in the use of liquid hydrogen for the space industry has focused attention on techniques for improving existing methods of liquid hydrogen production; the desire for such improvements has revived interest in the phase equilibria of hydrogen-containing systems at lowtemperatures. The solubility of a condensed component in compressed hydrogen gas can be calculated fairly well by using an appropriate equation of state for the gaseous phase [l-8] and the solubility of solids and of helium gas in liquid hydrogen has also received attention in the past few years [9-131. In this work we consider the solubility of hydrogen gas in cryogenic liquidst. The available experimental data have been reduced in a manner suggested by thermodynamic analysis and the reducing parameters obtained have been partly generalized in a manner suggested by using very simple concepts of the theory of solutions. The final correlation obtained should be useful for calculating the solubility of hydrogen in a variety of low-temperature solvents up to rather high pressures but not exceeding about 100 atm.
f'I=f4
(1)
f 1 is the fugacity of hydrogen in the vapour phase and fi is the fugacity of hydrogen in the liquid phase. The vapour phase fugacity is related to the mole fraction in the vapour phase y, by where
f 5 = &Y,P
(2)
Techniques for calculating the vapour-phase fugacity coefficient 4Z are given elsewhere [l, 2, 4-71. In many cases of practical interest, yZ N 1 and in that event the Lewis fugacity rule provides a very good approximation [2, 151. The liquid-phase fugacity is a function of temperature, pressure and composition. The effect of pressure is given by alnfi
( 1 8P
V,
T,x=RT
where CZis the partial molar volume of hydrogen in the liquid. The effect of composition at constant temperature and pressure is given by
fi=Y;&
THERMODYNAMIC ANALYSIS Let subscript 1 refer to the liquid solvent and let subscript 2 refer to hydrogen. At any temperature T and total pressure P the solubility of hydrogen t A correlation of hydrogen solubilities in hydrocarbons has been published by BENHAMet al. [14].
is determined by the equation of equilibrium
(4)
where H is Henry’s constant and yz is the activity coefficient of hydrogen normalized such that r:+l
as
x2+0
Henry’s constant is defined such that for a given hydrogen-solvent system it is a function of tem775
M. ORENTLICHER and
perature only
J. M.
In fJ = In H + 62" x2
H = limit& x2+0 x2
(5)
In y1 = &
(7)
If x2 is small and if the total pressure is not close to the critical of the solution, it is a good approximation to assume that b, is independent of pressure and composition. In that case, equations (l), (4) and (7) yield
f!i =InH+
I(% 1
(Sa)
Equation (8) contains three temperature-dependent parameters for any solvent of which H, Henry’s constant, is the most important. In order to obtain meaningful, unambiguous values of these parameters, data of very high accuracy are required, especially for very dilute solutions. However, data of this calibre are available only for argon [17] and therefore it is desirable to evaluate one of the parameters independently. The partial molar volume can be obtained from dilatometric measurements but unfortunately only a few of these have been made; nevertheless, with the help of an approximate theory it is possible to correlate and generalize these measurements enabling good estimates of partial molar volumes to be made. This generalization is achieved by noting that at temperatures well above the critical of hydrogen it is a good assumption to consider hydrogen to behave like a hard-sphere gas. Its equation of state is then given by
x$
(XT - 1)
(Hl&) - PS
DATA REDUCTION
where A is an empirical coefficient which, for a given hydrogen-solvent system, is a function only of temperature?. From the Gibbs-Duhem equation it then follows that In yz*= &
2A
Thus a semilogarithmic plot of the ratio f2/x2 at constant temperature against total pressure approaches a straight line for small values of x2.
For the solubility data under consideration here, x2 is always small, usually less than 0.1 and always less than 0.2. However, even for such small mole fractions, deviations from dilute solution behaviour are not negligible. For this small concentration range we make the very reasonable assumption that the activity coefficient of the solvent is given by the simple, one-parameter expression
In -
PRAUSNITZ
(8)
(v - b,) = y
x2
where Pf is the saturation (vapour) pressure of the solvent, and where i$ is the partial molar volume of hydrogen at infinite dilution. Equation (8) is similar to the Krichevsky-Kasarnovsky equation [19, 201 except that equation (8) takes into account deviations from Henry’s law due to the effect of composition in addition to the effect of total pressure. (An equation essentially identical to equation 8 was previously presented by KRICHEVSKY and ILINSKAYA in 1945 [21].) If A is set equal to zero, equation (8) becomes identical with the Krichevsky-Kasarnovsky equation. For small x2 (see Appendix I) equation (8) becomes t Equation (6) has been successfully used for liquid solutions of hydrogen by CCINNOLLY 1161,VOLK and HALSEY[17] and MAIMONI1181.
where b, is the van der Waals covolume (26.6 cm3/gmol). The internal pressure of the solvent is very nearly given by 6, 2, the square of the solubility parameter; as a reasonable approximation, therefore, the partial molar volume of dilute hydrogen in the solvent is given by RT 62” = b, + 8
(10)
In equation (10) b, is always much larger than RT/d12 except at temperatures close to the critical of the solvent when ~5,~is small. Under usual conditions, therefore, the partial molar volume of hydrogen is not very sensitive to temperature nor to the nature of the (non-polar) solvent. From limited experimental data [17, 22, 231, we
776
Thermodynamics
of hydrogen solubility in cryogenic solvents at high pressures
II
6-
STRAIGHT
CHAIN
(ETHANE
FIG. 1.
REDUCED
I
TEMPERATURE,
0.9 T/Tc,
Solvent factor for partial molar volumes of hydrogen in two types of solvents. A, n-G [221; V, n-G 1231; n , A 1171.
find that equation (10) gives reasonably sults. If we define a solvent factor F by
good re-
FRT 62” = b2 + 6:
(11)
then we would expect F to be of the order of unity. In fact, at a solvent reduced temperature of 0.7, F is about l-2 in argon and about 2.2 in normal paraffins. Fig. 1 shows a plot of F vs. reduced temperature of the solvent with d1 evaluated at a reduced temperature of O-7. In subsequent calculations the lower line was used to calculate i& for the solvents argon, nitrogen, carbon monoxide and methane and the upper line was used for higher hydrocarbons. Table 1. Solvent
Argon Nitrogen Carbon monoxide Methane Ethane Ethylene Propane Propylene n-Hexane
-
LARGER]
0.8
0.7
0.6
HYXOCAREONS
I
I
0.34
AND
Temp. range (“W
87-140 90-95 68 79-86 68-90 90-127 116-173 144-200 144-172 228-277 172-228 378445
Using values of Vz calculated from equation (11) and Fig. 1 it was possible to compute the parameters H and A from the solubility data. The data which were used to obtain these parameters are those for the systems listed in Table 1. Hexane, of course, is not a cryogenic solvent but was included in this study in order to ascertain if there is a significant difference in the behaviour of hydrogen-containing solutions between low- and high-molecular weight solvents. The fugacity of hydrogen in the vapour phase was calculated from the known volumetric properties of hydrogen [14, 241; where necessary, small corrections for the effect of vapour-phase composition were made using a method based on van der
Hydrogen solubility data Pressure range Mm)
17-82 845 l-25 18-100 25-50 30-l 10 34-103 17-68 17-68 17-68 17-68 34-102
777
VOLK and HALSEY [17] MAIMONI [18] OMAR and DOKOUPIL [26] GONIKBERGet al. 127,281 DRAWERand FLYNN [29] FA~TOVSKYand GONIKBERG[30] BENHAM and KATZ [31] WILLIAMS and KATZ [32] WILLIAMSand KATZ [32] WILLIAM and KATZ [32] WILLIAMS and KATZ [32] NICHOLS et al. [23]
M. ORENTLICHER and J. M. PRAUSN~TZ
nine solvents under consideration and it is evident that the over-simplified theory does only a very approximate job in correlating the data. The top line correlates the data for the four small hydroTable 2.
0 FIG. 2.
\ 20
:
!
40 60 PRESSURE,
\ 80 ATM
I 100
830 660 500 385
5.0 + 0.5
30 31 35 44
co
68 73 78 83 88
640 550 470 440 400
7.0 f 0.7
31.2 31.8 32.6 33.6 34.4
NZ
68 79 86 90 95
540 450 390 370 340
7.0 + 0.7
30.4 31.5 32.0 33.0 344
90 110 116 127 144
1824 1036 970 838 630
15 f 3
29.7 31.0 31.6 32.6 36.0
144 158 172 200
3050 2400 2050 1400
19.5 * l-5
37.1 37.8 39.4 44.5
C2Hs
144 172 200 228
2600 2050 1650 1210
25 i 2
37.9 40.7 44.2 54.3
Cd-h
228 255 282
1670 1300 1030
25 f 2
50 51 63
C3Hs
172 200 228 268
3300 2600 1850 1320
25 i
39.6 41.7 48.8 55.6
n-CsHls
344 378 410 445
930 830 700 590
120
Fugacity of pure hydrogen gas at low temperatures.
CH4
Waals’ equation as discussed by HILDEBRAND and SCOTT [25]. The fugacity of pure hydrogen gas is shown in Fig. 2. Table 2 gives the parameters H, A and fir for hydrogen in nine solvents. The data are sufficiently detailed to give the temperature dependence of Henry’s constant but, over the temperature range under consideration, no significant variation of A with temperature could be detected. The accuracy of the A parameters is probably no better than lo-20 per cent; equation (8), however, is much more sensitive to H than it is to A. CORRELATION OF HENRY’S CONSTANTS
A reasonable technique for correlating Henry’s constants for hydrogen in non-polar solvents is suggested by a highly simplified solution theory which is outlined in Appendix II. This theory suggests that a plot of a reduced Henry’s constant (H divided by S:) vs. reduced temperature (T divided by T,,) should give a universal curve for all solvents. Such a plot is shown in Fig. 3 for the 778
for hydrogen
87 100 120 140
A
-0.31
Thermodynamic parameters solubility
CzH4
2
7.9 f 0.3
640 75.5 103.2 162
* v2mfrom volumetric data for solutions of hydrogen in argon and in hexane. For other solvents dam calculated from Fig. 1.
Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures and /iZL* = partial molar enthalpy of hydrogen in liquid solution at infinite dilution. = molar enthalpy of hydrogen in the hzv vapour phase. Values of the left-hand side of equation (12) are given in Table 3. Table 3.
Enthalpy function for dissolved hydrogen. dln H, a’Trl
Solvent
- 1.87
A, Nz, CO CH4 CzH4,Cs;Hs,C3Hs,C3Hs n-&H14 REDUCED
FIG. 3.
TEMPERATLiRE,
Reduced Henry’s constants H, = (H/S12)T,=O.7.
T/Tc,
SOLVENT MIXTURES
for hydrogen
carbons, ethane, ethylene, propane and propylene, and the bottom line correlates the results for the three small, essentially spherical molecules, argon, nitrogen and carbon monoxide. The data for the spherical hydrocarbon methane fall in between and those for hexane are a little below the top line for the other hydrocarbons. The deviation of the hexane line from that for the C, and C3 hydrocarbons is probably more due to the large difference in molecular size than to the large difference between solute temperatures. The significant difference between the top and bottom lines points out once again that the intermolecular forces between hydrogen and hydrocarbons are in some qualitative way different from the intermolecular forces between hydrogen and inorganic molecules as noted by ALDER [33] and HILDEBRAND and SCOTT [34].
HEAT
- 2.80 - 3.18 - 2.21
Good experimental data on the solubility of hydrogen in mixed liquids are extremely rare. However, it is possible to make good estimates of this solubility with a minimum of assumptions by using information on the behaviour of all possible binary systems made up of the various components in the multicomponent solution. The details of such a calculation are presented elsewhere [35] but the results are summarized below for the case of a mixed solvent containing two components. As before, let subscript 2 stand for hydrogen and let subscripts 1 and 3 stand for the two solvents. All thermodynamic quantities are referred to P;, the vapour pressure of the reference solvent which in this case is arbitrarily chosen to be solvent 1. Henry’s constant for hydrogen in solvent 1 is designated by H,,,(P”) and that for hydrogen in solvent 3 by H&P;). These constants can be obtained from Fig. 3 and from the relation
OF SOLUTION
H&P3
The heat of solution of hydrogen at infinite dilution can be calculated from the slope of the data shown in Fig. 3. If the volatility of the solvent is neglected, the thermodynamic relation is
= H2,3(G) ev
s
p1scZ3 dP
PP
The activity coefficient solvent is defined by fi ” = xZHZ,JP;)
(12)
for hydrogen
exp
RT
in the mixed
p V, dP -
s P,’
c14j
RT
(15)
where EZ is the partial molar volume of hydrogen in the mixed solvent. This quantity must be estimated by interpolation from Fig. 1. It follows
where (13) 779
M.
ORENTLICHER
from the definition in equation (15) that yz + 1 only when both x2 and x3 approach zero. For the binary mixture (hydrogen-free) of the two solvents, assume that the excess free energy (symmetrical convention) is given by the one-parameter Margules equation 9= =
%3X1X3
- x1(1 - %)I +
these effects must be taken into account; the first, through the partial molar volume and the second, through a self-interaction coefficient. The equations and parameters presented in this work make it possible rapidly to calculate the solubility of hydrogen at low temperatures and high pressures in pure and mixed non-polar solvents.
(16)
where aI3 is a function of temperature. This parameter can be obtained from vapour-liquid equilibrium data or else can be estimated from an equation such as that of HILDEBRANDand SCOTT[37]. It can now be shown that in the ternary solution In y* = -alz[l
J. M. F’RAUSNITZ
and
%3X1X3
~23X3(1
-
+ x2>
Acknowledgment-The authors are grateful to the national science foundation for financial support.
APPENDIXI.
Equation (8) can be rewritten in a more convenient form which is valid for very small x2. First, rewrite the identity
(17)
The coefficient aI2 is identical to the coefficient (8) for hydrogen in solvent 1. The coefficient uZ3 can be found from
DERIVATIONOF EQUATION(Sa)
X;-l=(P-P;)(~)-l~~)
(AI.1)
A/RT in equation
H,
u23
=
a,, + In )
The limit of the last factor on the right-hand side is x; - 1 lim -= x2-+0 x2
3(C) (18)
H2,dP”)
p,fl+& 42
For small x2 p =fS(l -
CH2,,(P~)]“2CH2,3(P~)l”3 w? - ww3
(AI.3)
91
mixed sodPs) =
(AI.2)
To obtain the limit of the second factor, we have
For solutions which are very dilute in hydrogen the activity coefficient is found by setting x2 equal to zero in equation (17). It can then be shown that Henry’s constant for hydrogen in the mixed solvent is given by H 2,
-2
~2)
+
41
(1%
Hx2
(AI.4)
-Z
or
Equation (19) has the interesting property that even if the two solvents form an ideal solution (aI3 = 0), then Henry’s constant for hydrogen in the mixed solvent is not a linear but rather an exponential function of the solvent composition. (A1.6) Therefore
CONCLUSION Solubility data for hydrogen have been analysed and partly correlated with the help of a thermodynamic model. At advanced pressures deviations from Henry’s law occur because of two reasons: first, the effect of pressure on the thermodynamic properties of the condensed phase becomes appreciable and second, as the pressure rises the mole fraction of hydrogen in the liquid phase soon becomes sufficiently large to cause significant deviation from dilute solution behaviour. Both of
lim
(AI.7)
X2-+0
where the superscript s refers to the saturation pressure of component 1. Substituting equations (AI.2) and (AI.7) into equation (AI.l) we obtain -2(P - P”l) ~;~o(x’ - I) = [(H/e2)
_ Pg
(AI.8)
and therefore equation (8) in the text becomes
780
Thermodynamics of hydrogen solubility in cryogenic solvents at high pressures
Equation (AII.5) then becomes
lim In fi’ X,+0
(1x2
2A @ - [(HI&)
- P;]
1
ln$= 1
An approximate value of Henry’s constant for hydrogen in a liquid at total pressure P can be calculated by an isothermal thermodynamic cycle consisting of (a) compression of pure hydrogen-gas from its partial pressure pz to the internal pressure of the solvent; (b) ideal mixing at the internal pressure; and (c) expansion back to the system pressure P. Using equation (9), the Gibbs free energy changes per mole of hydrogen for the three steps are
Ag, = Step
z =o*35 and similarly for ethane, ethylene, propane and propylene H
- - 0.65
s: -
Since H, for a given solvent, is only a function of temperature, it appears reasonable to correlate the experimental results by plotting H/St vs. T/T,, where T,, is the critical temperature of the solvent. Since Sf is itself a function of T/T,,, simplification is obtained by plotting H, vs. Tr, where
(AII.l)
@I
(AII.2)
Step (c) A& =
’ 62 dP = bz(P - Sf) + ‘$
s 612
H, s H/61
(P - 6:)
(AII.3)
T,, = T/T,,.
When the gas phase and the liquid phase are in equilibrium the total free energy change (steps a, b and c) must vanish and upon adding equations (AII.l), (AII.2) and (AII.3) and setting the sum equal to zero
,nGx2 -=
I _
b,(P
- P2)
RT
PZ
P2>
= 0
Cohesive energy densities (6:) of nine solvents are given in Table 4. These were evaluated from the known heats of vaporization and liquid densities of the solvents as described by HILDEBRAND and SCOTT [36].
(AII.4) Table 4.
(AII.5)
For all values of the total pressure P encountered in this work, the final term in equation (AII.5) is much less than unity and can be neglected. Ignoring vapour phase non-ideality at the pressure P, Henry’s constant is
H,pz
(with S: evaluated at T,, = 0.7)
and
1
St P-S? + bz(P-In x2 + In pz + 62 RT 1 Since S: & P, this becomes
(AII.8)
H
s P2
AgZ = RT In x2
H/6: = l/e = 0.37
Equation (AII.8) gives a good order of magnitude. For argon, nitrogen and carbon monoxide we find experimentally that at a reduced temperature of 0.7
APPENDIX II. SIMPLIFIEDSOLUTION MODEL
812 vdP = b,(6: - p?) + RT In 2
(AII.7)
and
which is equation @a).
Step (a)
-1
(AII.6)
x2
781
Cohesive energy densities of solvents at reduced temperature of 0.7 Solvent
812 (at4
Argon Nitrogen Carbon monoxide Methane Ethane Ethylene Propane Propylene n-Hexane
1720 1170 1170 1650 2000 2200 1940 2055 1750
M. ORENTLICHERand J. M. PRAUSNITZ REFERENCES [l] [2] [3] [4] [5] [6] [7] [8]
DOKOUPILZ., VAN SOEST,G. and SWENKER,M. D. P., Appl. Sci. Res. 1955 A5 182. PRAUSNITZJ. M., Amer. Inst. Chem. Engrs. J. 1959 3 5. PRAUSNITZJ. M. and BENSONP. R., Amer. Inst. Chem. Engrs. J. 1959 5 161. PRAUSNITZJ. M. and KEELERR. N., Amer. Inst. Chem. Engrs. J. 1961 7 399. PRAUSNITZJ. M. and Mvaas A. L., Amer. Inst. Chem. Engrs. J. 1963 9 5. REDLICHO., KISSER A. T. and TURNQUI~TC. E., Chem. Engng Progr. Symp. Ser. 48 No. 2 49 1952. REUSSJ. and BEENAKKERJ. J. M., Physica 1956 22 869. ROWL~NSON J. S. and RICHARDSONM. J., Aduances in Chemical Physics (Edited by PRIGOCINEI.) Vol. 2. Interscience, New York 1959. [9] BRAZINSKYI. and GOTTFRIEDB. S., NASA Tech. Note D-1403, August 1962. [lo] DoKoupr~ Z., Progress in Low-Temperature Physics (Edited by GORTER,C.) Vol. 3. Interscience, New York 1961. [ll] ECKERTC. A. and PRAUSNITZJ. M., J. Chem. Phys. 1963 39 246. [12] ROELLIGL. 0. and GIE~E C., J. Chem. Phys. 1962 37 114. [13] STREEIT, W. B., SONNTAG,R. E., VAN WYLEN, G. J., J. Chem. Phys. 1964,40, 1390 [14] BENHAMA. L., KATZ D. L. and WILLIAMSR. B., Amer. Inst. Chem. Engrs. J. 1957 3 236. [15] WALL F. T., Chemical Thermodynamics p. 307. Freeman, San Francisco 1958. [16] CONNOLLYJ. F., J. Chem. Phys. 1962 35 2892. 1171 VOLK H. and HALSEYG., J. Chem. Phys. 1960 33 1132. [18j MAIMONIA., Amer. Znst..Chem. Engrs: J. 1961 7 376. [I91 DODGE B. F. and NEWTON R. H., Zndustr. Engng. Chem. 1937 29 718. J. S., J. Amer. Chem. Sot. 1935 57 2168. PO1 KRICHEVSKYI. R. and KASARNOVSKY WI KRICHEVSKYI. R. and ILINSKAYAA. A., Z/I. fiz. khim, SSSR 1945 19 621. CONNOLLYJ. F. and KANDALICG. A., Chem. Engng Progr. Symp. Ser. 1963 59 No. 44, 8. ml t231 NICHOLSW., REAMERH. and SAGEB. H., Amer. Inst. Chem. Engrs. J. 1957 3 262. P41 American Znstitute ofphysics Handbook Section 4, p. 124. McGraw-Hill, New York 1957. P51 HILDEBRANDJ. H. and SCOTTR. L., Solubility of Nonelectrolytes p. 238. Reinhold, New York 1950. OMAR M. and DOKOUPILZ., Commun. Kamerlingh-Onnes Lab., University Leiden, No. 330, p. 1, 1963. WI ~71 DRAYERD. E. and FLYNN, T. M., Nat. Bur. Stand. Tech. Note No. 110, P.B. 161611, May 1961. GONIKBERGM., FASTOVSKY V. and GURVITSCHJ. G., Actu Physicochim. USSR 1939 11 865. ::; DRAYERD. E. and FLYNN T. M., Nat. Bur. Stand. Preprint R-244 1962; Tech. Note No. 108, P.B. 161609, May 1961. [301 FASTOVSKYV. and GONIKBERGM., Zh.fiz. khim. SSSR 1940 14 427. BENHAMA. L. and KATZ D. L.. Amer. Inst. Chem. Engrs. J. 1957 3 33. t::; WILLIAMSR. B. and KATZ D. L., Zndustr. Engng Chem. 1954 46 2512. [331 ALDER B., Ann. Rev. Phys. Chem. 1961 12 195. t341 HILDEBRANDJ. H. and Scorr R. L., Regular Solutions Chaps. 6 and 10. Prentice-Hall, Engelwood Cliffs, New Jersey 1962. t351 O’CONNELLJ. P. and PRAUSNITZJ. M., Zndustr. Engng. Chem. In press. I361 HILDEBRAN~J. H. and SCOTT R. L., Regular Solutions Appendix 5. Prentice-Hall, Englewood Cliffs, New Jersey 1962. 371 HILDEBRANDJ. H. and Scorr R. L., Regular Solutions Chap. 7. Prentice-Hall, Englewood Cliffs, New Jersey,1962.
R&m&-On a reduit les donnees de solubilite de l’hydrogene dans les liquides a basse temperature et haute pression a l’aide d’une relation thermodynamique analogue a l’equation de KruchevskyKasarnovsky mais permettant de tenir compte des variations du coefficient d’activite avec la concentration en hydrogene. Les parambtres de cette equation ont CtCcorreles en partie par un modele tres simple de la solution. 11en resulte que dans des conditions comparables la solubilite de l’hydrogene dans les solvants inorganiques (argon, azote et anhydride carbonique) est considbablement plus Clevee que dans les hydrocarbures legers (ethane, ethylene, propane et propylene). Le methane se situe entre ces deux groupes. Zusammenfassung-Loslichkeitsdaten fur Wasserstoff in Fltissigkeiten bei tiefen Temperaturen und hohen Drucken sind mittels einer thermodynamischen Beziehung reduziert worden, welche derjenigen von Krichevsky-Kasarnovsky Lhnlich ist, aber die Aenderung des Aktivitatskoeffizienten mit der Wasserstoffkonzentration beriicksichtigt. Die in dieser Beziehung vorkommenden Parameter konnten zum Teil durch eine Korrelation verkniipft werden, welche auf einem sehr einfachen Losungsmodell beruht. Die Ergebnisse zeigen, dass unter vergleichbaren Bedingungen die Loslichkeit des Wasserstoffes in einfachen anorganischen Losungsmitteln (Argon, Stickstoff, Kohlenmonoxid) bedeutend grosser ist als in leichten Kohlenwasserstoffen (Aethan, Aethylen, Propan, Propylen). Methan befindet sich zwischen diesen beiden Gruppen.
782