THOMAS D. O'SULLIVAN AND NORMAN 0. SMITH
1460
The Solubility and Partial Molar Volume of Nitrogen and Methane in Water and in Aqueous Sodium Chloride from 50 to 125"and 100 to 600 Atm'
by Thomas D. O'Sullivan and Norman 0. Smith Department of Chemistru, Fordham University, New York, New York 10468 (Received March 11, 1969)
The solubility of nitrogen and of methane in water, 1 m NaCI, and 4 m NaCl at 51.5, 102.5, and 125.0" has been measured at pressures from 100 to 600 atm using a stirred autoclave and a direct sampling technique. The results for methane in the salt solutions differ from the only previous studies. At the lowest temperature, where the water vapor content of the gas phase can be ignored, In ( f / X ) for the dissolved gas is linear with total pressure, and the isobaric Henry's law applies up to the highest pressure for both gases. At the higher temperatures a curvature develops with rise in temperature, pressure, and, in general, salt concentration, but Henry's law may still apply. The data are interpreted in terms of the partial molar volume of dissolved gas and its variation with pressure, temperature, and salt concentration. Increase in NaCl concentration enhances the temperature coefficient of the partial molar volume of the dissolved gas. It also causes the latter to decrease at 51.5" but, in general, t o increase at 102.5 and 125.0°, except at the highest pressure and temperature. Salting-out coefficients are tabulated and found to be nearly the same for both gases, to be approximately independent of pressure, to pass generally through a minimum with rise in temperature, and to show a decrease with increase in salt concentration. At a pressure of 200 atm the solubility of methane in water, 1 m NaC1, and 4 m NaCl passes through a minimum at 79 f 2, 72 f 3, and 69 f 5", respectively.
The solubility of naturally occurring gases such as nitrogen and methane in sodium chloride solution, and its variation with pressure, temperature, and salt concentration is of interest not only to the physical chemist but to the geochemist, for both gases occur associated with brine in the earth's crust and are doubtless transported subterraneously in solution from high to low pressure regions. Very few studies of "permanent" gas in aqueous salt solution a t pressures of hundreds of atmospheres have been reported. The most extensive high-pressure solubility data for nitrogen in water are those of Wiebe, Gaddy, and Heins2 up to 100" and of Krase and c o - ~ o r k e r s ,but ~ ~ ~the only studies of its solubility in aqueous sodium chloride a t pressures other than atmospheric are from this laboratory: a preliminary one5 a t 30°, confined to pressures below 70 atm and involving a comparatively inaccurate technique , and an incomplete one6 confined to 1 na NaCl over a smaller temperature range. The most important measurements for pure methane in water are those of Culberson and A f ~ E l e t t a while ,~ its solubility in aqueous sodium chloride has been determined by Michels, Gerver, and BijP up to 220 atm and in this laboratorys at pressures not exceeding 65 atm. The measurements reported in the present paper have an accuracy much greater than that of the last two studies mentioned and extend to pressures of 600 atm. No partial molar volumes of gases dissolved in simple salt solutions appear to be available in the literature. The Journal of Physical Chemistry
Experimental Section The gases were obtained from The Matheson Co., Inc., their purity given as 99.996% for the Nz and 99.95% for the CH,. The solubility equilibria were obtained in a 1-gallon, 316 stainless steel stirred, packless autoclave, the temperature of which was controlled to f0.5" by a Minneapolis-Honeywcll Electr0-Pulse unit and Electronik 18 recorder, except for brief but unavoidable excursions of f 2 " . An ironconstantan thermocouple, calibrated against a certified thermometer, mas used to measure the autoclave temperature. The water used was distilled, passed through (1) Taken from the Ph.D. dissertation of T. D. 0. Portions of this paper were presented before the Division of Physical Chemistry at the 151st National Meeting of the American Chemical Society, Pittsburgh, Pa., March 1966, and before the Geochemical Society in San Francisco, Calif., Nov 1966. (2) R. Wiebe, V. L. Gaddy, and C. Heins, Jr., Ind. Eng. Chem., 24, 97 (1932); J. Amer. Chem. Soc., 55, 947 (1933). (3) J. B . Goodman and N. W. Krase, Ind. Eng. Chem., 23, 401 (1931). (4) A. W. Saddington and N. W. Krase, J . Amer. Chem. Soc., 56, 353 (1934). (5) N. 0. Smith, S. Keleman, and B. Nagy, Geochim. Cosmochim. Acta, 26, 921 (1962). (6) T . D. O'Sullivan, N. 0 . Smith, and B. Nagy, ibid., 30, 617 (1966). (7) 0. L. Culberson and J. J . McKetta, Trans. A m . Inst. Mech. Engr., 192, 223 (1951); J . PetroE. Technol., 2 , 319 (1950). (8) A. Michels, J. Gerver, and A . Bijl, Physica, 3, 797 (1936). (9) J. R. Duffy, N. 0. Smith, and B. Nagy, Ceochim. Cosmochim. Acta, 24, 23 (1961).
SOLUBILITY AND PARTIAL MOLAR VOLUMEOF NITROGEN AND METHANE an ion-exchange column, and Nz or CH4 bubbled through it overnight. The salt, solutions were prepared in a similar manner using Baker Analyzed Reagent grade NaCl previously dried a t 115". They were made up by weight, but analyzed after a run by evaporation to dryness, as a check. The water, or solution, was transferred to the autoclave by suction, flushed with N2 or CH4 a t atmospheric pressure to remove any residual air, saturated with the gas at 50-100 atm, the pressure reduced, and the system again flushed. Gas was again admitted and the pressure and temperature brought to the desired values. High pressures were attained by means of a 1.5-hp compressor and compression cylinder. The pumping liquid was water, saturated with the gas being studied. Autoclave pressure was measured with a precision Heise-Bourdon gauge, 0 to 15,000 psi with an accuracy of &0.05%, calibrated frequently with a dead-weight tester and found to exhibit a hysteresis of about 0.1%. It is estimated that the maximum possible error in the pressures quoted in the tables is 0.5 atm below 100 atm and 1 atm at 000 atm. All connecting tubing (l/B in. i.d. except for the sampling tubes which were '/16 in.) and valves were of stainless steel. At least 8 hr was allowed for the attainment of equilibrium, and the same results were obtained when approached from higher and lower pressures. When equilibrium had been reached, 15-30 ml of saturated liquid sample was withdrawn at the rate of 0.5-1 ml/min into an evacuated, calibrated, water-jacketed buret system using mercury as leveling fluid and similar to that used elsewherel2 whereupon the gas flashed out of solution giving two phases in the burets. The first sample was always discarded. Results were found to be independent of the rate of sample withdrawal. During the sampling the equilibrium pressure in the autoclave was maintained by admitting more gas from the compression cylinder. By manipulation of the leveling bulbs mercury was cascaded through the liquid phase until no more gas bubbles were seen. Since at no time had the pressure in the burets exceeded 0.05 atm it was assumed that only a negligible amount of gas remained in solution. The pressure in the burets was now raised to atmospheric, arid the volumes of the liquid and gas phases and the temperature and atmospheric pressure recorded. After correcting for aqueous pressure'O and meniscus curvature, the number of moles of gas was calculated from the gas volume with the aid of tables of molar volume.ll Thenumber of moles of liquid was calculated from its volume, composition, and density.IO For each pressure three or more separate samples were withdrawn for analysis and the results averaged. Their average deviation was about 0.4%. The pressure was changed to a new value without replacing the liquid contents of the autoclave, the volume of which was never allowed to be less than 1500 cc. Measurements were made in this way for water, 1 rn NaCl, and
1461
4 m NaCl a t 51.5, 102.5, and 125.0". These isothermal runs were supplemented by isobaric ones; the solubility of methane (only) in the same three liquids was measured a t a number of temperatures under an estimated fixed partial pressure of methane of 200 atm in an effort to study quantitatively the effect of dissolved salt on the temperature of minimum solubility.
Results and Discussion The results of the isothermal work are given in Table
I, where P is total pressure (atm) and Xz is mole fracTable I: Solubility of Nz and CE-14 in HzO, 1.000 m NaCl, and 4.00 m NaCl (Mole Fraction of Dissolved Gas X lo4) -1
p, atm
m NaCIXNa XCHr
100.0 200.0 300.0 400.0 500.0 600.0
7.99 14.54 20.17 24.9 29.2 33.5
14.27 22.79 28.7 33.4 37.3 40.9
51.5' 5.93 10.76 14.97 18.60 22.16 25.3
10.76 16.95 21.38 25.0 27.9 30.7
101.0 201.0 302.0 403.0 503 0 604.0
7.77 14.47 20.05 25.2 29.8 33.7
13.55 22.05 28.7 33.3 38.5 41.9
102.5' 6.03 11.13 15.38 19.20 22.52 26.0
...
...
...
16.93 22.19 25.7 28.9 32.0
5.23 7.31 8.99 10.47 12.'05
8.26 10.79 12.11 13.19 14.33
103.0 204.0 305.0 405.0 507.0 608.0
8.08 14.92 20.47 25.7 30.6 35.1
14.34 23.21 29.6 34.3 39.6 43.0
125.0' 6.32 11.02 15.33 18.83 22.31 25.5
10.58 17.52 22.23 26.0 29.4 32.5
...
...
5.67 7.40 9.21 10.41 12.27
8.25 10.05 11.64 13.22 14.38
I
...
...
5.00 7.00 8.78 10.34 11.79
8.05 9.97 11.54 13.03 14.44
tion of dissolved gas. X:! was calculated for the salt solutions as if the salt were undissociated. The solubilities for nitrogen in water agree with those of Wiebe, et aLJ2within about 1.5% at 51.5" and 1.8% at 102.5". The values for methane in water differ from those interpolated from the work of Culberson and McKetta7 by about 1% at 51.5", 1.5% at 102.5", and 8% at 125.0". The results for methane in both water and salt solution differ seriously from those of Michels, et aLlgobtained by an inaccurate pressure decline technique. In determining the extent to which Henry's law applies for each of the systems a t each temperature it may be noted that P / X , increases with P even a t 51.5" where the partial pressure of water, p ~ ~ contributes 0 , negligibly to P. At larger pressures the condition of (IO) "International Critical Tables," Vol. 3, McGraw-Hill Publications, New York, N. Y., 1928. (11) F. Din, "Thermodynamic Functions of Cases," Vol. 3, Butterworth and Co. Ltd., London, 1961. Volume 74, Number 7 April 9, 1970
1462
THOMAS D. O'SULLIVANAND NORMAN 0. SMITH
constant total pressure, which is inherent in Henry's law, becomes important. I n addition, fugacity should be used in place of partial pressure of permanent gas. Krichevsky and Kasarnovsky, l2 and later Kobayashi and Katz,la showed that by combining Henry's law fz =
kXz(T, P constant)
(1)
(where fz is the fugacity of the solute gas and X z its mole fraction) with other thermodynamic relations, and assuming VZ,the partial molar volume of dissolved gas, to be independent of P In (fz/Xz) = In k*
+ (PVz/RT)
(2) where k* is the limiting value of f z / X zas P is reduced indefinitely, or the Henry's law constant. Although this result is correct, both pairs of investigators derived it by arguments involving the mutual cancellation of errors. In ref 12 an essential part of the derivation is the use of the approximation dpz = RT d In Xz (where P Z is chemical potential), which implies the absence of any dependence of pz on P. It is this very dependence that forms the basis for the article. In ref 13 dp2 = VzdP, valid only for fixed composition, is equated to dpz = RT d In fz and integrated, and then the concentration is permitted to vary. These difficulties can be avoided as follows. Since pz = pz(T, P, Xz), dpzP= ( ~ , u z / ~ ~ z ) dXz T , P VZdPT. At any one temperature, however, dpz = RT d In fz so (bpz/bXz)T,p= RT(b In fZ/bxZ)T,p* Moreover, by eq 1, valid only for d T = d P = 0, (a In fz/bXz)T,P = ~ / X Z or ( d p ~ / b X z ) T , p= RT/XZ. It follows that for isothermal changes RT d VZd P = RT d In X Z Vz d P In fz = (RT/Xz)dXz or
+
+
+
(3) Integration between P = P*, a very small pressure (where X Z = XZ*, fz = fz*) and P = P (where X z = Xz,fz = fz), assuming Vz independent of P, yields eq 2. is Thus when the isobaric Henry's law holds and independent of P a plot of In ( f z / X z )vs. P is linear with a slope of Vz/RTand an intercept of In k*. It is to be noted also that if the isobaric Henry's law holds, V2 must be independent of Xzat constant total pressure and equal to the value at infinite dilution, VZ". Experimentally, however, it is virtually impossible to separate the effects of the variables Xz and P on Vz. At 51.5' the gas phase is essentially pure nitrogen (or methane) so the gas partial pressure is given by P , from which . f and ~ ~f C H r can be determined by reference t a b l e ~ . l ' ~Figure ~ ~ 1 is a plot of In (fz/Xz) os. P. The lines are straight within experimental error. The evidence is strong, therefore, that at this temperature Henry's law holds for all three solvents up to 600 atm for both gases and that Vz is independent of P. At the higher temperatures, however, it is possible only to estimate the fugacities. The gas phase now has a water vapor content that cannot be ignored,
vz
The Journal of Physical Chemistry
IO-'^, atrn.
Figure 1. Solubility of Na and of CH, in HgO, 1 m NaCl, and 4 m NaCl at 51.5': 0, Nz; 0, CHI.
but the analyses of previous investigators do not always and agree, as comparisons of the data for nitrogen4*l6~l6 methanel6V17 show. The Gibbs-Poynting equation, (b In p ~ , o / b P )=~ Vz/RT, cannot be relied upon to give a quantitative answer because of the nonideality of the gas-water vapor mixture. l8 Even when the gasphase composition is known, there is still the problem of finding the fugacity of the permanent gas. The Lewis and R,andall rulelg can be used but is not reliable, again because of gas mixture nonideality. Nevertheless the fugacities at 102.5 and 125.0' were estimated by finding them for the pure gas at the same pressure and temperat~re'~sl4 and multiplying these by the mole fraction of water as given in the l i t e r a t ~ r e . ~ ~This ' ~ ~ 'mole ~ fraction is greatest for the highest temperatures and the lowest pressures, being 0.030 for methane at 125.0' and 103.0 atm. The fugacity of pure methane under (12) I. R.Krichevsky and J. S. Kasarnovsky, J . Amer. Chem. 80% 57, 2168 (1935). (13) R.Kobayashi and D. L. Katz, I d . Eng. Chem., 45, 440 (1953). (14) W.E. Deming and L. E. Shupe, Phgs. Rev., 37, 638 (1931). (15) E.P.Bartlett, J . Amer. Chem. Soc., 49, 65 (1927). (16) M. Rigby and J. M. Prausnitz, J . Phys. Chem., 72, 330 (1968). (17) R.H. Olds, B. H. Sage, and W. N. Lacey, Ind. Eng. Chem., 34, 1223 (1942). (18) N.0 . Smith, J. Chem. Educ.,40, 317 (1963). (19) G. N. Lewis and M. Randall, "Thermodynamics," rev. by K. 5. Pitzer and L. Brewer, McGraw-Hill Publications, New York, N. Y., 1961,p 295.
SOLUBILITY AND PARTIAL h/IOLAR VOLUME OF
NITROGEN AND METHANE
?o-'P, otm.
1463
IO-'P, otm.
Figure 2. Solubility of NZand cf CHd in HzO, 1 m NaCl, and 4 m NaCl a t 102.5': 0 , Nz; 0, CH4.
Figure 3. Solubility of Nz and of CHI in H20, 1 m NaCl, and 4 m NaCL a t 125.0': 0 , Nz; 0, CH,.
these conditions is 99.1 atm, S O ~ C His~estimated to be ~) 0.970(99.1) = 96.1 atm, and In ( ~ c H ~ / X C=H 11.11. The resulting graphs are shown in Figures 2 and 3 for 102.5- and 125.0", respectively. It is evident that at these temperatures there is more scatter in the data, the increased difficulty of controlling the temperature of the large mass of the autoclave and the greater sensitivity of pressure to temperature being largely responsible. For this reason the location of the lines is uncertain, but it is clear that a curvature develops with rise in pressure, temperature, and, generally, salt concentration. This is the first time such curvature has been pointed out, although the data of Culberson and McKetta' for methane in water at 102.5' (interpolated), for example, suggest it. It was apparently not considered by Kobayashi and Katz13 in their treatment of the same data. Curvature could conceivably be caused by one or more of the following: (1) inapplicability of Henry's law, (2) erroneous estimation of fugacities from faulty gas composition data and/or failure of the Lewis and Randall rule, (3) variation of V2with P. Since, however, Henry's law is valid at 51.5' and would be expected to become more, rather than less, valid with rise in temperature, it seems reasonable to suppose that the curvature does not lie in (1). Validity of Henry's law means that V2is independent of X2 a t fixed P. It is likewise possible to eliminate (2) since the lines are curved in the same direction even when no correction is
made to the fugacities for the presence of water vapor, and the corrections, even if known accurately, would reduce the uncorrected values of In ( f 2 / X 2 more ) at the lower pre8sures than a t the higher ones, thus making the curvature greater. It appears, therefore, that the curvature must be attributed to decrease of V2 with increase in P. Such a decrease in V2 is entirely to be expected. Furthermore, the increased curvature with rise in T requires that [a(V2/RT)/bP],= ( l / R T ) . (bV2/aP).become more negative with increase in T . This, in turn, requires that (bV2/bP)Tbecome more negative-a reasonable possibility since (bV/bP), does so for pure liquids. Thus the observed curvature can be accounted for qualitatively on the basis of the behavior of Fs. I n order to apply eq 3 to the results it would have been helpful to have low-pressure data to reduce the uncertainty of extrapolation to zero pressure. However, because of the paucity of such data a t all temperatures and the inherent difficulty of fugacity measurements a t higher temperatures, where the gas phase has an appreciable water content, only the data of the present study were used. The data for 51.5" were fitted to In ( f 2 / X 2 )= a bP and those for 102.5 and 125.0' to In ( f 2 / X 2 )= a' b'P c'P2 (with the two exceptions indicated), giving the parameters shown in Table 11. They generally reproduce the experimental values of In ( f 2 / X 2 within ) 0.05, 0.06, and 0.07% a t the three temperatures, respectively. Table I11 gives the
+ +
+
Volume 74,Number 7 April 8 , lOYO
THOMAS D. O'SULLIVAN AND NORMAN 0. SMITH
1464 Table 11: Parameters in Ln ( f i / X ~ = ) a Temp, Gas
HzO-----
r -
51.5 51.5
CHd
NZ CH4 a
1 m NaCI--
r -
lO*b
a
10ab
11.615 10,905
1.278 1 393
11.923 11.195
1.230 1.394
12.688 11.964
1.221 1.374
I
HzO-------------. 10'b' 107~'
11.662" 11.001 11.604 10.943
1.222" 1.647 1.450 1,905
c -
a'
11.899 11.286 11.826 11,224
-3.94 -3.25 -5,99
Table 111: Henry's Law Constants and Partial Molar Volumes of Dissolved Gas at 51.5' r-HtO--
lo%*, atm
Fa, cm'mol-1
-1 CH4
Nz
m NaClCHI
7 - 4 m NaCINs CH4
1.108 0.544 1.507 0.728 3.238 1.570 34.05 37.10 32.76 37.12 32.52 36.61
Table IV : Partial Molar Volumes of Dissolved Gas (cm* mol-') P, atm
r--Hz0--~ N8 CH4
200 400 600
37.7 37.7 37.7
45.9 41.1 36.2
200 400 600
43.1 38.9 34.6
54.4 46.6 38.7
P-1 Nz
m NaCI--. CH4
102,5O 40.3 37.9 33.5 125,O" 50.5 41.9 33.2
r - 4 m NaCI--, Nz CHI
44.3 42.1 40.0
41.2 39.6 38.0
49.3 49.3 49.3
64.7 46.8 38.8
62.7 46.7 30.8
66.1 51.3 36.5
limiting Henry's law constants and partial molar volumes (pressure and composition independent) at 515" determined from the parameters. At the higher temperatures, where extrapolation was deemed too uncertain, and where curvature indicated a pressure dependence of V2, only the latter was calculated, and this for rounded pressures, not infinite dilution (Table IV). The Henry's law constant of Table I11 for nitrogen in water at 51.5" may be compared with the following obtained by interpolation of the results of low-pressure solubility measurements: 1.109 (ref 20) and 1.117 X 105 atm (ref lo), and that in 1 rn NaCl with 1.441 X IO5 (ref 20). Those for methane in water may, similarly, be compared with 0.580 (ref 20), 0.585 (ref lo), and 0.581 X 105 (ref 2 l ) , and in 17n NaCl with 0.763 X lo5 (ref 20). The high-pressure data of Wiebe, et UZ.,~ for nitrogen yieId 1.103 X IO5 and those of Culberson and McKetta7 for methane 0.541 X l o 6 (both in water) a t this temperature-in support of the present values The Journal of Physical Chemistry
1 m NaC1-10'b'
107~'
1.384 1.507 1.807 1.919
-1.93 -1.75 -6.58 -6.09
P-----
a'
12,644 11.973" 12.409 11.888
4 m NaC1-----7 10'b'
1.389 l.59ga 2.405 2.473
1070'
-1.32 -12.2 -11.3
+ b'P.
Parameters for In (fi/Xz) = a'
Nz
m NaCl
------4
a
a'
102.5 102.5 125.0 125.0
+ b'P' + c'P2
a'
lOab
7 -
Nz CH4
=
a
OC
N%
+ bP and Ln ( f i / X , )
rather than of some of the data of low-pressure studies. One wonders whether lower temperature Henry's law constants, determined by linear extrapolation of good high-pressure data, are not actually the more reliable. Similar doubt of the validity of certain commonly used techniques for determining gas solubilities at low preswres has been expressed by HoriutiZ2 It is possible to estimate, from the data of Table I, that 1 ft3of sedimentary rock, of 20% porosity, saturated with brine (50,000ppm NaCl), can accommodate about 1 mol of methane in solution when in equilibrium with that gas at the pressure and temperature existing at a depth of 10,000ft. Nearly all of the previously published partial molar volumes at temperatures of 50" and higher have been obtained by extrapolation of high-pressure data. The values in Table I11 are in excellent agreement with those obtained by other^'^^'^ using the same method. Direct experimental measurements of Vzo at these temperatures have been attempted by Krichevski and II'nsl
