J . Phys. Chem. 1988, 92, 1988-1994
1988
Apparent Molar Volumes of Aqueous Argon, Ethylene, and Xenon from 300 to 716 K Daniel R. Biggerstafft and Robert H. Wood* Department of Chemistry, University of Delaware, Newark, Delaware 19716 (Received: June 23, 1987; In Final Form: October 14, 1987)
The difference in densities between water and aqueous solutions of argon, ethylene, and xenon were measured at temperatures from 298 to 720 K and pressures between 20 and 34 MPa by using a vibrating tube densimeter developed in our laboratory. The apparent molar volumes of these gases in water were calculated. For all three gases the volumes go through a maximum as temperature is increased at constant pressure. The compressibility of pure water goes through a maximum at very nearly the same temperature. The magnitude of the maximum increases and shifts to a lower temperature as the pressure decreases. The maximum in apparent molar volume of all three gases is approximately 1000 cm3 mol-' at 34 MPa and about 2500 cm3 mol-' at 26.7 MPa. These very high apparent molar volumes occur near the critical point of the solvent.
1
Introduction The measurement of the volumetric properties of aqueous solutions of the slightly soluble gases present formidable experimental difficulties. Because of these difficulties, previous measurements have been confined to temperatures near 298 K'-5 or to very high temperatures where the components are miscible.6 For xenon no data exist. Prior to this work, the remarkable volumetric behavior of these aqueous gases between 298 K and the supercritical region had not been observed although theoretical predictions had been made. Theoretical models predict that the partial molar volumes of the solutes are proportional to the compressibility of the solvent near the solvent's critical point.'-'' Thus, at pressures above but near the critical pressure of water, the partial molar volume of the gas is predicted to go throuth a very sharp maximum a t the same point that the compressibility of the water goes through a maximum. For solutes with strong attractive forces for the solvent the maximum becomes a minimum. These types of behavior have been found for other ~olvents.l*-'~ The magnitude of this maximum is not well predicted by theories, and experimental measurements of this maximum are important, both in testing and developing new theories and for an understanding of a variety of geochemical and industrial processes at high temperatures. A new vibrating tube densitometer developed in this laborat ~ r y ' ~allows , ' ~ the measurement of the apparent molar volume of slightly soluble gases at pressures up to 35 MPa and temperatures up to 720 K. This paper reports the first measurements of the apparent molar volumes for dilute aqueous argon, ethylene, and xenon solutions at temperatures from 300 to 720 K and pressures up to 34 MPa. The remarkable behavior predicted by the theories was observed. The maximum in the apparent molar volumes of all three solutes was about 2500 cm3 mol-' at 26.7 MPa.
Experimental Section The flow, vibrating-tube densimeter used for these measurements has been previously de~cribed.'~*'~ The densimeter measures the natural period of oscillation of a vibrating tube. The period squared is proportional to the density of the fluid inside the tube. A difference in density Ad between the density of a solution d and the density of water do is obtained by measuring the period of oscillation of a solution T and of water T~ and using Ad = d - do = k(? - 70') (1) where k is a calibration constant. The period of water, T ~ used , is an average of the before and after values for each solution measurement. This reduces uncertainties due to base-line drift. The apparent molar volume V, (cm3 mol-I) can be calculated from the molality m (mol kg-'), density of water, do, and solution, d (kg cm"), and the solute molecular mass M2 (kg mol-') by using
* Author to whom correspondence should be addressed. Present address: Reichhold Chemicals, Dover, DE 19901.
0022-3654/88/2092-1988$01.50/0
1
The apparent molar volume is the change in volume on adding solute divided by the moles of solute, so it is a partial molar volume calculated with finite differences. It is exactly equal to the partial molar volume only as m approaches zero. It is necessary to replace the vibrating tube before this work was begun. To start the tube vibrating, a voltage pulse was sent through the drive wire. The voltage was set so that at most 20 mW of power was dissipated across the drive wire. This ensured that the temperature rise in the tube due to the drive power was less than 0.05 K at the minimum flow rate of 0.3 mL mi&. The period of oscillation was found to be dependent on the drive voltage (0.005 I.IS mV-I), but the uncertainty introduced in the period due to fluctuations in the drive voltage ( N 1%) was small compared to the other sources of noise such as electrical noise from the heater and noise from the compressibility of water. The uncertainty in a measured Ad was 0.05 kg m-3 up to 475 K and 0.10 kg m-3 up to about 650 K. Above 650 K, the compressibility goes through a maximum which depends on the pressure. As the compressibility increases, density fluctuations in the tube increase due to small pressure fluctuations caused by the back-pressure regulator. These density fluctuations, along with greater electrical noise from the heaters, increase the uncertainty in the measured Ad near the maximum in compressibilityto as much as 2.0 kg m-3 at 26.7 MPa (1) Enns, T.; Sholander, P. F.; Bradstreet, E. D. J . Phys. Chem. 1965,69, 389. (2) Tiepel, E. W.; Gubbins, K. E. J . Phys. Chem. 1972, 76, 3044. (3) Moore, J. C.; Battino, R.; Rettich, T. R.; Handa, Y . P.; Wilhelm, E. J . Chem. Eng. Data 1982, 27, 22. (4) Biggerstaff, D. R.; White, D. E.; Wood, R. H. J . Phys. Chem. 1985, 89, 4378. ( 5 ) Bignell, N. J . Phys. Chem. 1984, 88, 5409. (6) Lenz, Von H.; Franck, E. U. Eer. Eunsenges. Phys. Chem. 1969, 73, 28. (7) Rosen, A. M. Rum. J . Phys. Chem. (Engl. Transl.) 1976, 50, 837. (8) Wheeler, J. C. Eer Eunsenges Phys. Chem. 1972, 76, 308. (9) Chang, R. F.; Morrison, G.;Levelt-Sengers, J. M. H. J . Phys. Chem. 1984,88, 3389. (10) Levelt Sengers, J. M. H.; Chang, R. F.; Morrison, G. In Equarions of State-Theories and Applications; Chao, K. C.; Robinson, R. L., Jr., Eds.; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986. (11) Levelt Sengers, J. M. H.; Everhart, C. M.; Morrison, G.; Pitzer, K. Chem. Eng. Commun. 1986, 47, 315. (12) Khazanova, N. E.; Sominskaya, E. E. Russ. J . Phys. Chem. (Engl. Transl.) 1971, 45, 1485. (13) Eckert, C. A,; Ziger, D. H.; Johnstone, K . P.; Ellison, T. K. Fluid Phase Equilib. 1983, 14, 167. (14) Fkkert, C. A.; Ziger, D. H.; Johnston, K. P.; Kim, S. J . Phys. Chem. 1986, 90, 2738. (15) Albert, H . J.; Wood, R. H. Rev. Sci. Instrum. 1984, 55, 589. (16) Albert, H. J. Ph.D. Dissertation, University of Delaware, June 1984.
0 1988 American Chemical Society
Apparent Molar Volumes of Ar, C2H4, and Xe and 665 f 10 K and 1.0 kg m-3 at 34 MPa and 690 f 5 K. The uncertainty in the experimental temperature varied from fO. 1 K at 300 K to f 1.O K at 720 K. The uncertainty in the pressure was k0.1 MPa. The water used as the reference and in making up the solutions was distilled, deionized water that was degassed by heating to 95 OC. The argon (99.9%), the ethylene (99.8%), and the xenon (99.995%) were purchased from Linde, Matheson, and Air Products, respectively. The aqueous gas solutions were prepared by filling a sample cylinder completely with degassed water and allowing the pressure of the gas to push 25% of the water out. The cylinder was placed in a thermostated water bath. The pressure of the gas in the sample cylinder was set to give approximately the desired concentration and was measured (3~0.5%) by using a Heise gauge. The times necessary to achieve suitable equilibration were determined by plotting the log of the pressure drop versus time for argon and the log of the solution density change versus time for xenon and ethylene. The times needed for 99% equilibration for the three solutions were determined to be 12, 48, and 48 h for argon, xenon, and ethylene, respectively, so the solutions were allowed to equilibrate a minimum of 24, 96, and 96 h, respectively. Experiments with longer equilibration times gave the same results. The sample loop was loaded under pressure by placing a metering valve at the exit of the loop and using the pressure in the sample cylinder to push solution into the loop which was initially filled with water. The pressure in the gas tank was used to maintain a constant pressure in the sample cylinder while solution was being transferred to the sample loop. An amount of solution equal to at least twice the volume of the sample loop was flushed through the loop before a sample was taken to ensure proper rinsing. Twice the volume of the sample loop was shown to be sufficient by using 3 times the volume and obtaining the same result. Two precautions were taken to prevent bubble formation in the sample solution while it was being loaded into the sample loop. First, the sample loop was loaded at a low flow rate to keep the pressure drop in the sample loop small. Second, the sample cylinder was kept in a thermostated water bath about 10 "C above the sample loop temperature as this lowers the vapor pressure of the solution when in the sample loop. With the sample cylinder 10 'C above the sample loop temperature, no bubbling was detected with loading flow rates from 0.3 to 1.5 mL min-' as determined by obtaining stable and reproducible sample plateaus with the densimeter. When the same sample loading technique was used to measure heat capacities, bubble formation was detected by erratic sample plateaus only when the sample cylinder temperature was dropped below the sample loop temperature with a loading flow rate of 0.5 mL min-I. A loading flow rate of approximately 0.75 mL min-' was used routinely in this work. The concentration of the aqueous gas solutions was calculated from the temperature of the bath T and the partial pressure of the gas P2,which was obtained by subtracting the vapor pressure of water from the total pressure PT. The error introduced in the concentration by not correcting for the change in the vapor pressure of water due to the pressure or the solute concentration is negligible. For ethylene, the solubility versus temperature and pressure data of Bradbury et was used. For argon and xenon, the Henry's law constant kH second virial coefficient B2, and the partial molar volume at infinite dilution, V2",were also used in calculating the concentration by usingI8
where x2and y 2 are the mole fraction of the solute in the liquid phase and gas phase, respectively, B,, is the second virial coefficient of water, and B12is the cross coefficient. This reduces with negligible error to ( 1 7) Bradbury, E. J.; McNulty, R.; Savage, R. L.; McSweeney, E. E. Ind. Eng. Chem. 1952, 44, 21 1 . (18) Potter, R. W.; Clynne, M. A. J . Solution Chem. 1978, 7 , 831.
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1989 (4) since (1 - y 2 ) 2is very small in this case. The Henry's law constant is corrected for pressure by using p2
V2"
1,
In k d p 2 , T ) = In kH(pI,T) i-
lliTd P
(5)
The Henry's law constants were determined from bat ti no'^'^^^^ smoothed solubility data for argon and xenon. Partial molar volumes of 32 and 46 cm3 mol-' were used for argon and xenon, respectively, andthe second virial coefficients (-13.87 and -121.04 cm3 mol-' for argon and xenon, respectively, at 308 K) were taken from Dymond and Smith.2' The estimated uncertainty in the concentrations is 1%. Reaction of ethylene with water at high temperatures was shown to be negligible in two ways. First, density measurements were performed at 680 K and a flow rates of 0.05 and 0.5 mL min-I. The two results agreed within experimental error. Second, a portion of the sample from the slow flow rate run was also collected and analyzed by gas chromatography. A 10-ppm ethanol standard was easily detected, and the sample showed no ethanol peak, so the extent of the reaction was negligible. Measurements with a vibrating tube may not be accurate when the pressure changes in the vibrating tube due to its acceleration are large enough to cause significant density changes. A rough calculation shows that the density changes in our most compressible solution are about 0.001%. Thus, this effect should cause no difficulty in all of the present measurements. Calibration. The instrument must be calibrated at each temperature. The calibration constant is obtained by measuring the period of the tube first with one fluid of known density and then another. Below 625 K, nitrogen and water were used. Two different techniques were used when calibrating with nitrogen and water, depending on the temperature. Up to 475 K, the vibrating tube was purged with nitrogen until no water remained and the period and temperature were recorded. The tube was then filled with water at a pressure that was about 3.5 MPa above saturation pressure and allowed to reequilibrate to the same temperature, and the period was recorded. From 475 to 600 K, the system pressure was set about 3.5 MPa above saturation pressure and nitrogen was injected into the system by filling the sample loop with nitrogen. This had the advantage of eliminating the large temperature perturbation on the block when going from system to atmospheric pressure due to either the heat of vaporization of water if water was in the tube or Joule-Thompson cooling if nitrogen was in the tube. The disadvantage of this technique was that as the critical temperature is approached, the vapor pressure of water begins to increase rapidly, the density of water begins to decrease rapidly, and the density of the nitrogen increases due to having higher system pressures. As a result, the difference in density begins to get small, thus decreasing the precision of the calibration constant, k. Above 625 K, the heat of vaporization of water gets small enough so that a large temperature perturbation did not occur when the system pressure was dropped to atmospheric pressure with water in the tube. This made it convenient to use water at two different pressures to calibrate the instrument above 625 K. The calibration constant, k, has been shown to decrease linearly with increasing temperature (-0.028%/K calculated from the elastic modulus of Hastelloy and -0.032%/K measured) and to be independent of pressure within experimental error.16 This can be used as a diagnostic test for proper construction of the vibrating tube. Figure 1 shows a plot of k versus temperature for all of the calibration constants, k, determined in this work. The first (19) Battino, R. Solubility Data Series; Clever, H. L., Ed.: Paragon Press: New York, 1980; Vol. 4, p 2. ( 2 0 ) Battino, R. Solubility Data Series; Clever, H. L., Ed.; Paragon Press: New York, 1980: Vol. 4, p 135. (21) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Gases; Clarendon Press: Oxford, 1969.
1990 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
I
I
300
O
I
700
500 T/K
Figure 1. Plot of calibration constants versus temperature. This plot is a comparison of all of the calibration constants determined for the density measurements. The calibration constants have been divided into three sets chronologically which are described as follows: X, immediately after replacing the vibrating tube; 0, after remounting the drive and pickup wires on the vibrating tube and before the densimeter had been heated to 680 K for the first time and cooled back down to room temperature; 0 , after being heated to 6 8 0 K for the first time. This plot illustrates three things. First, the calibration constant decreases linearly with increasing temperature. Second, the characteristics of the tube changed after being heated to 680 K and then cooled to room temperature the first time. This caused the calibration constant to shift upward about 2% but the slope did not change. Third, the calibration constant was independent of the three different techniques used to calibrate the instrument. All three techniques used two fluids of known density. Up to 475 K, nitrogen at atmospheric pressure and water at pressures about 3.5 MPa above the vapor pressure of water were used. From 475 to 6 0 0 K, the water and nitrogen were at the same pressure, which was about 3.5 MPa above the vapor pressure of water. Above 625 K, water at two different pressures was used.
four calibration constants determined from 323 to 530 K had a spread of about 2% around a straight line and a much lower temperature coefficient. The drive and pickup wires were remounted. The calibration constants then fell on a straight line from 298 to 720 K with a spread of 0.5% (except one point with 1.2%) from 298 to 630 K and up to 2% from 650 to 720 K. This plot also shows that the value of k does not depend on the method of calibration. It is interesting to note that, after the first time the densimeter was heated to 680 K, the plot of k versus temperature shifted upward by about 2% but the slope (-0.032%/K) did not change. The major causes of the lower precision in determining k at the higher temperatures were an uncertainty in the temperature of 0.5 OC above 650 K and lower precision in measuring the period due to greater electrical noise. Due to the small differences in density between the solutions and water found in this study, these uncertainties in k introduce only a small error in Ad compared to the error introduced by the uncertainty in the period.
Results Table I gives the measured change in density from water, Ad, and the resulting apparent molar volume, V+,for aqueous argon, ethylene, and xenon. The uncertainties in Ad described earlier translate into approximately *I% in the volumes up to 625 K. Above 625 K where the volumes are changing rapidly, the volumes are known only to about *IO%. Prior to this work the only data available for argon were at temperatures from 276 to 298 K. Our previous results and the literature r e s ~ l t s ~ agree , ~ ~ +within * ~ experimental error and fit on a smooth curve with the present results. For aqueous xenon, no data are available for comparison with this study. The only data available for aqueous ethylene were measured by Moore et aL3 at 298 K and 0.1 MPa. Using a similar type of vibrating tube densimeter, they find V, = 51.3 f 1.8 cm3 mol-’ by measuring the change in density between degassed water and water saturated (22) Ennis, T.; Scholander. P. F.; Bradstreet, E. J. J . Phys. Chem. 1965, 69, 389. (23) Tiepil, R. W.; Gubbins, K. E. J . Phys. Chem. 1972. 76, 3044.
Biggerstaff and Wood at 0.1 MPa with ethylene. We find V, = 45.7 f 0.5 cm3 mol-’ at pressures from 20 to 29 MPa. If both measurements are correct, it implies a pressure slope for V, of -0.22 f 0.07 cm3 MPa-] and for our measurements systematic errors of 1 cm3 mol-’ with opposite sign at 20 and 29 MPa. We believe the systematic errors in our measurements are much smaller than this. Our results yield a pressure slope of 0 f 0.04 cm3 MPa-’ at 298 K, -0.04 0.04 cm3 MPa-’ at 341 K, and -0.07 f 0.04 cm3 MPa-’ at 372 K. If Moore et al.’s actual experimental error were about twice their estimated error, their results would be consistent with ours. This is not bad agreement considering the experimental difficulties. Bigne1124has recently reported deviations from ideal behavior in volumes of mixtures of argon and hydrogen in water which are well beyond the random errors in his measurements. The results can be explained by (1) a change in the Henry’s law constant of about 3% in going from a binary to a ternary solution (saturated at 1 atm of pressure) or (2) a change in the apparent molar volume in the ternary solution of about 10%. In the present results and the earlier results for argon at 298.15 K, concentrations 100 times those of Bignell have been measured. The effect should be 100 times larger in these solutions. We have found no evidence of changes in apparent molar volume (is%),so an effect of this magnitude is not present in binary aqueous solutions of argon, xenon, or ethylene. It is unlikely that an effect of this magnitude is present in aqueous solutions of hydrogen or in hydrogen-argon mixtures. A change in Henry’s law constant of 3% is equally unlikely. This would imply a 3% change in the activity coefficient which implies pair interaction coefficients (gAB)that are about 100 times larger than any of the 72 observed interaction constants in a recent ~ o m p i l a t i o nand ~ ~ more than 100 times larger than the expected pair interaction coefficients for small nonpolar solutes.26 We conclude it is most likely that there are small (-3%) systematic errors in the results of Bignell. Lentz and Franck6 measured the volumes of mixtures of argon and water at high temperatures and pressures where the fluids are miscible. Their experimental pressures and concentrations of argon are higher than ours. Estimates of V, from their data fall on a smooth curve when plotted as a function of pressure at constant concentration at 673 and 713 K. With these results we can now compare kH at the saturation pressure from solubility measurements with the kH at 17.2 MPa calculated from heat capacities as a function of temperature, together with kH at 298 K and AH at 298 K. We use volumetric data to make pressure corrections to Henry’s law constants, kH, at a constant temperature using eq 5. The concentrations were low enough that we expect the apparent molar volume should be equal to the partial molar volume at infinite dilution below 600 K within experimental error. The partial molar volumes of aqueous argon up to 578 K can be used to make the above correction to the kH measurements of Crovetto et aL2’ in order to compare them with some previous work done in this l a b ~ r a t o r y . ~ The Henry’s law constants for aqueous argon at 17.2 MPa and high temperatures were calculated from the apparent molar heat capacities together with enthalpies and Gibbs energies of solution. Table I1 shows a comparison of the Henry’s law constants derived from the apparent molar heat capacity of Biggerstaff et al.4 and those derived from the solubility data of Crovetto et al.” corrected to 17.2 MPa by using the volumetric data in this work. The two agree within experimental error over the entire temperature range (fl-3% except at the highest temperature where it is 20%).
Discussion The apparent molar volumes, V,, of all three solutes exhibit spectacular behavior which is correlated with the density times the isothermal compressibility, P K ~ of , pure water. Figure 2 and Table I show that the behavior of V, of all three gases is very (24) Bignell, N. J . Phys. Chem. 1987, 91, 1687. (25) Spitzer, J. J.; Suri, S. K.; Wood, R. H.; Abel, E. G.; Thompson, P. T. J . Solution Chem. 1985, 14, 781. (26) Watanabe, K.; Anderson, H . C. J . Phys. Chem. 1986, 90, 795. (27) Crovetto, R.; Fernandez-Prini, R.; Japas. M. L. J . Chem. Phys. 1982, 76. 1077.
Apparent Molar Volumes of Ar, CzH4, and Xe
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1991
-
0.06
3000
Ym
-0.06
I n 2000
.
I I
’_
r
8 n
5
m
-
0.04
-
0.02
2c
>1000
similar. The volume increases slowly up to 600 K. The pressure dependence of V, is very small at 300 K and becomes easily measurable at approximately 475 K. Above 600 K the temperature and pressure dependence increase rapidly and the volumes go through a maximum that changes with pressure. The maximum at approximately 26.7 MPa for all three solutes occurs at 669 2 K, is greater than 2200 cm3 mol-’, and is sharper than the maximum at approximately 34 MPa which occurs at 690 2 K and is about 1000 cm3 mol-’. The very large magnitude of V, at the maximum can be appreciated if one calculates the “sociation” or “excess hydration” Ne”of water around an argon atom.’* This quantity is defined as the number of water molecules around an argon minus the number that would be there if the argon were not present. Thus,”
*
*
Ne” = x = ( g ~ \ ~1)4ar2 . dr/Vwo = -V2;”/VWo
(6)
where V’, is the molar volume of pure water, g A W is the solute-water pair correlation, and is the partial molar volume of the solute at infinite dilution. At 669 K and 26.7 MPa, V,. E V2’ for all three gases is approximately 3000 cm3 mol-’ which gives Ne” N 40 molecules. A single gas molecule excludes approximately 40 water molecules from its neighborhood, and g A W must be less than 1 at considerable distances from the argon. The above behavior is intuitively expected, based upon the type of solute-solvent interactions and the compressibility of water. The solute-solvent interactions are more repulsive than the solventsolvent interactions, so the solute will occupy a larger volume as the compressibility of water increases. At a constant pressure (above the critical pressure) the compressibility of water, K ~ increases and goes through a maximum which is dependent upon the pressure just like V,. Figure 2 shows comparisons of V, and P K T between 600 and 720 K for 26.7 and 34 MPa, respectively. At both pressures the volumes and compressibilities have a maximum within 4 f 2 K of each other. The difference in temperature of the two maxima may be because V, # V2’ at these molalities. Interactions between solvated argons at low concentrations are expected because (1) V, is very large and (2) aVzo/ax becomes infinite at the critical point. Eckert et al. find a good correlation between K~ and for solutes like naphthalene in carbon dioxide or ethylene. Their measurements extend to concentrations 10 times more dilute than the present measurements. The relationship between the partial molar volume at infinite dilution, V2’, and the compressibility of the pure solvent was predicted theoretically by Wheeler in 1972.’ Using a lattice gas model, he showed that for a solution where the solute-solvent interactions are more repulsive or only slightly attractive compared to the solventsolvent interactions, V2’ would go to positive infinity at the critical point of water proportional to the isothermal compressibility of pure water, K~ H e also showed that the opposite would occur when the solute-solvent interactions are much more attractive than the solvent-solvent interaction. In accord with this prediction very large and negative partial molar volumes have been found for aqueous electrolytes near the critical point of and for solutes like naphthalene and camphor in near-critical ethylene or carbon dioxide.”-14 Chang, Morrison, and Levelt Sengers’ give a theoretical relationship between the slope of the critical line and V2’ near the critical point. The reaction is
r2’
I
0 6 00 600
650
T/K
-0
700
.08
300C
.06 r
‘2 a
2000
n
r
1-
(I
E“
.04
5
m
+
P
>1000
.02
650
600
TIK
700
I
0.06 3001
XENON
0.06
-
ZOO(
I
a E
n
5 >*
rzo
1001
and [lim (aV,/ax),,] = x p o
600
650
700
T/K
Figure 2. Apparent molar volume, V,, plotted versus temperature for (a) ethylene, (b) argon, and (c) xenon: 0, experimental values at about 26.7 MPa; X, experimental values at about 34 MPa. For comparison the solid ~ these two pressures. For argon the dashed line gives lines give P K for the value of U20calculated from the slope of the critical line as a function of pressure and mole fraction.
(28) Guggenheim, E. A. Trans. Faraday SOC.1960, 56, 1159. (29) Quint, J. R.; Wood, R. H. J . Phys. Chem. 1985, 89, 380. (30) Benson, S . W.; Copeland, C. S.; Pearson, P. J. Chem. Phys. 1953,21, 2208. (31) Copeland, C. S . ; Silverman, J.; Benson, S. W. J . Chem. Phys. 1953, 21, 12.
(32) Berthold, J. T. Master’s Thesis, University of Delaware, August 1986.
,
1992 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
Biggerstaff and Wood
TABLE I: Density Difference and Apparent Molar Volume of Aqueous Argon, Ethylene, and Xenon" T/K pb/MPa m'lmol kg-' Add/kg m-3 Vme/cm3mol'' T/K pb/MPa m'/mol kg-' Addfkg m-3 Vde/cm3 mol-' A. Argon T/K(Bath) = 306.45; P/MPa(Bomb) = 9.306 663.21 26.72 0.0958 -18.04 1802.7 T/K(Bath) = 306.15; P/MPa(Bomb) = 9.478 26.72 0.0958 663.21 -17.47 1746.7 323.00 17.22 0.0977 0.92 30.6 323.00 323.00 323.00 323.00 323.00 323.00 323.00 323.00
17.22 17.22 17.22 29.77 29.77 29.77 29.77 29.77
0.0977 0.0977 0.0977 0.0977 0.0977 0.0977 0.0977 0.0977
0.92 0.91 0.91 0.98 0.94 0.93 0.93 0.89
30.6 30.7 30.7 29.9 30.3 30.4 30.4 30.8
664.60 664.60
T/K(Bath) = 306.45; P/MPa(Bomb) = 9.306 26.72 0.0958 -19.11 2307.1 0.0958 26.72 -18.88 2279.2
666.91
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.403 26.78 0.0770 -13.97 2686.6
667.31 667.31
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.403 34.20 0.0770 -5.43 34.20 0.0770 -5.40
672.13 672.13
T/K(Bath) = 308.35; P/MPa(Bomb) = 8.947 26.58 0.0905 -8.72 243 1.1 26.58 0.0905 -9.15 2546.6
677.06 677.06 677.06 677.06
T/K(Bath) = 308.35; P/MPa(Bomb) = 8.444 26.58 0.0862 -5.98 2246.8 0.0862 -6.74 2513.5 26.58 34.57 0.0862 -6.84 503.8 34.57 0.0862 -6.96 511.0
687.09 687.09 687.09 687.09
T/K(Bath) = 306.45; P/MPa(Bomb) = 8.465 26.72 0.0885 -1.49 26.72 0.0885 -1.66 0.0885 33.28 -7.78 33.28 0.0885 -1.65
889.6 964.8 973.3 958.7
696.93 696.93 696.93 696.93
T/K(Bath) = 306.45; P/MPa(Bomb) = 8.092 26.72 0.00 0.0852 26.72 0.0852 0.00 33.96 0.0852 -4.46 33.96 0.0852 -4.52
273.2 273.2 855.0 865.5
716.49 716.49 716.49 7 16.49
T/K(Bath) = 306.25; P/MPa(Bomb) = 7.410 26.99 0.0791 0.00 26.99 0.0791 0.12 34.27 0.0791 -1.24 34.27 0.0791 -1.24
310.9 215.7 561.8 561.8
366.7 365.2
367.53 367.53 367.53 367.53
T/K(Bath) = 306.65; P/MPa(Bomb) = 9.520 0.0974 0.81 20.64 20.64 0.0974 0.83 29.60 0.0974 0.80 0.0974 0.84 29.60
428.60 428.60 428.60 428.60 428.60 428.60 428.60 428.60 428.60 428.60 428.60
T/K(Bath) = 306.65; P/MPa(Bomb) = 8.375 20.71 0.0875 0.35 20.71 0.0875 0.43 20.71 0.0875 0.32 21.32 0.0875 0.39 21.32 0.0875 0.40 21.32 0.0875 0.34 28.57 0.0875 0.34 28.57 0.0875 0.35 28.57 0.0875 0.35 28.57 0.0875 0.36 28.57 0.0875 0.35
38.6 37.5 39.0 38.1 37.9 38.7 38.5 38.4 38.5 38.3 38.4
477.20 477.20 477.20 477.20 480.08 480.08
T/K(Bath) = 306.35; P/MPa(Bomb) = 8.802 20.78 0.0916 -0.08 0.0916 -0.09 20.78 29.43 0.0916 0.00 29.43 0.0916 0.00 20.7 1 0.0916 -0.08 0.09 16 -0. I O 20.7 1
46.9 47.0 45.4 45.4 47.0 47.3
530.13 530.13 530.13 530.13 530.13 530.13 530.13 530.1 3
T/K(Bath) = 306.15; P/MPa(Bomb) = 8.678 20.85 0.0907 -0.66 20.85 0.0907 -0.70 20.85 0.0907 -0.65 20.85 0.0907 -0.66 20.85 0.0907 -0.68 29.53 0.0907 -0.55 29.53 0.0907 -0.57 29.53 0.0907 -0.52
60.8 61.4 60.6 60.7 61.0 58.1 58.5 57.5
298.22 298.22 298.22 298.22 298.22 298.22
T/K(Bath) = 306.65; P/MPa(Bomb) = 7.265 21.66 0.1707 -3.12 21.66 0.1707 -3.02 21.66 0.1707 -3.02 21.66 0.1707 -3.00 21.66 0.1707 -3.06 21.66 0.1707 -2.99
46.0 45.4 45.4 45.3 45.7 45.3
579.1 1 579.1 1 579.1 1 579.1 1 579.1 1 579.00 579.00
T/K(Bath) = 306.15; P/MPa(Bomb) = 8.285 20.78 0.0872 -1.75 0.0872 -1.68 20.78 20.78 0.0872 -1.63 20.78 0.0872 -1.63 20.78 0.0872 -1.57 0.0872 -1.43 28.92 28.92 0.0872 -1.46
93.5 91.9 90.8 90.8 89.6 84.3 84.9
298.65 298.65 298.65 298.65 298.65 298.65 298.65
T/K(Bath) = 305.65; P/MPa(Bomb) = 2.942 19.95 0.0952 -1.74 19.95 0.0952 -1.71 19.95 0.0952 -1.75 19.95 0.0952 -1.74 19.95 0.0952 -1.72 28.91 0.0952 -1.75 28.91 0.0952 -1.72
46.0 45.7 46.1 46.0 45.8 45.9 45.5
602.42 602.42 602.42 602.42
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.341 21.42 0.0764 -2.28 21.42 0.0764 -2.28 0.0764 -1.81 29.10 0.0764 -1.77 29.10
125.6 125.6 107.4 106.2
341.13 341.13 341.13 341.13
T/K(Bath) = 306.65; P/MPa(Bomb) = 7.141 21.54 0.1697 -3.24 21.54 0.1697 -3.22 21.54 0.1697 -3.26 21.54 0.1697 -3.20
48.1 48.0 48.2 47.9
627.35 627.35 627.35 627.35
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.610 23.7 1 0.0788 -4.10 23.71 0.0788 -4.05 33.72 0.0788 -2.55 33.72 0.0788 -2.45
209.5 207.6 140.4 137.3
656.79 656.79
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.568 26.31 0.0785 -9.08 26.31 0.0785 -9.26
691 .O 702.7
T/K(Bath) = 306.65; P/MPa(Bomb) = 2.963 20.98 0.0942 -1.58 20.98 0.0942 -1.79 20.88 0.0942 -1.88 0.0942 -1.84 20.88 20.88 0.0942 -1.83 20.88 0.0942 -1.84 28.70 0.0942 -1.81 28.70 0.0942 -1.83
45.7 48.0 49.0 48.5 48.4 48.5 41.9 48.2
656.79 656.79
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.293 34.20 0.0760 -4.19 34.20 0.0760 -4.13
341.42 341.42 341.42 341.42 341.42 341.42 341.42 341.42
256.5 253.9
662.20 662.20
T/K(Bath) = 307.65; P/MPa(Bomb) = 8.740 26.44 0.0896 -13.18 1401.3 0.0896 26.44 -15.87 1676.6
372.22 372.22 372.22 372.22 372.22 372.22 372.22
T/K(Bath) = 306.65; P/MPa(Bomb) = 6.927 0.1667 -3.38 21.66 0.1667 -3.45 21.66 -3.38 21.66 0.1667 0.1667 -3.40 29.07 0.1667 -3.38 29.07 0.1667 -3.37 29.07 -3.35 29.07 0.1667
50.7 51.2 50.7 50.6 50.5 50.4 50.3
32.2 32.0 32.3 31.9
B. Ethylene
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1993
Apparent Molar Volumes of Ar, CzH4, and Xe
TABLE I (Continued) ~
~~
T/K
mc/mol kg-' Add/kg n i 3 V$/cm3 mol-' T/K(Bath) = 306.65: P/MPa(Bomb) = 2.935 pb/MPa
I
376.19 376.19 376.19 376.19 376.19 376.19
'22:14 22.14 22.14 28.84 28.64 28.84
'
0.0942 0.0942 0.0942 0.0942 0.0942 0.0942
T/K
,
'
-1.97 -2.00 -1.97 -1.96 -1.98 -1.95
51.5 51.9 51.6 51.2 51.4 51.0
677.09 677.09 677.09 677.09
mc/mol kg-' Add/kg m-) V4d/cm3mol-' T/K(Bath) = 308.35:. P/MPa(Bomb) = 7.803 , pb/MPa '26.72 26.72 34.64 34.64
0.1697 0.1697 0.1697 0.1697
'
'-11.14 -10.94 -16.12 -13.97
2063.2 2027.1 567.1 497.8
696.95 696.95 696.95 696.95
T/K(Bath) = 306.45; P/MPa(Bomb) = 7.548 26.78 0.1717 -2.81 795.1 -2.57 741.7 26.78 0.1717 33.38 0.1717 -14.05 879.9 33.38 0.1717 -14.18 887.9 T/K(Bath) = 306.45; P/MPa(Bomb) = 7.444 26.72 0.1717 -0.79 409.7 -0.76 401.9 26.72 0.1717 33.96 0.1717 -8.97 824.6 -8.93 821.4 33.96 0.1717
716.52 716.52 716.52 716.52
T/K(Bath) = 306.25; P/MPa(Bomb) = 7.348 0.1717 -0.32 336.1 26.88 -0.31 332.7 26.88 0.1717 459.7 0.1717 -2.34 34.27 34.27 0.1717 -2.40 468.8
74.1 74.2 75.0
298.90 298.90
T/K(Bath) = 306.65; P/MPa(Bomb) = 2.149 0.0681 6.07 33.41 33.41 0.068 1 6.05
42.5 42.8
576.80 576.80 576.80 576.80 576.80 576.80
T/K(Bath) = 308.15; P/MPa(Bomb) = 7.479 111.7 0.1687 -6.47 20.43 -6.47 111.7 20.43 0.1687 105.5 0.1687 -6.14 26.58 -6.06 104.6 26.58 0.1687 -5.88 102.3 27.47 0.1687 101.8 0.1687 -5.84 27.47
376.15 376.15
T/K(Bath) = 305.95; P/MPa(Bomb) = 2.218 27.94 0.0720 5.23 0.0720 5.26 27.94
57.9 57.4
T/K(Bath) = 306.15; P/MPa(Bomb) = 2.032 20.91 0.0661 1.75 135.5 20.91 0.066 1 1.49 143.9 0.0661 1.79 132.3 28.25 28.25 0.0661 1.80 131.9
602.42 602.42 602.42 602.42
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.306 0.1677 -7.97 148.3 21.42 -7.84 146.5 21.42 0.1677 -6.90 127.6 29.10 0.1677 -6.94 128.1 29.10 0.1677
599.09 599.09 599.09 599.09
T/K(Bath) = 306.35; P/MPa(Bomb) = 2.135 0.0685 0.65 187.7 26.75 26.75 0.0685 0.71 185.3 33.61 0.0685 1.50 151.0 0.0685 1.48 151.7 33.61
627.25 627.25 627.25 627.25
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.265 227.7 0.1677 -10.90 23.71 -10.34 218.4 23.71 0.1677 -7.58 153.8 33.79 0.1677 0.1677 -7.61 154.3 33.79
628.01 628.01 628.01 628.01
656.82 656.82 656.82 656.82
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.844 656.3 0.1697 -19.17 26.41 0.1697 -19.05 652.3 26.41 264.3 0.1697 -10.74 34.30 0.1697 -10.65 262.6 34.30
657.16 657.16 657.16 657.16 657.16
T/K(Bath) = 306.15; P/MPa(Bomb) = 2.073 26.85 0.0673 -5.09 658.5 665.0 0.0673 -5.18 26.85 34.74 0.0673 -0.28 25 1.5 0.0673 -0.28 251.3 34.74 34.74 0.0673 -0.26 250.1 T/K(Bath) = 306.15; P/MPa(Bomb) = 2.053 26.72 0.0667 -8.90 2126.0 26.72 0.0667 -9.25 2193.2 33.38 0.0667 -1.71 367.4
662.26 662.26
T/K(Bath) = 306.45; P/MPa(Bomb) = 7.623 -25.35 1299.4 26.65 0.1727 -25.48 1305.8 26.65 0.1727
665.83 665.83 665.83
T/K(Bath) = 306.65; P/MPa(Bomb) = 2.032 -4.37 2089.3 26.58 0.0648 -4.50 2134.5 26.58 0.0648
664.58 664.58
T/K(Bath) = 306.45; P/MPa(Bomb) = 7.623 -28.64 2033.3 26.65 0.1727 -28.25 2003.8 26.65 0.1727
67 1.48 67 1.48
667.23 667.23 667.23 667.23
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.782 3232.4 0.1697 -3 1.64 26.65 26.65 0.1697 -26.12 2626.7 -12.48 357.8 34.30 0.1697 -12.26 352.3 34.30 0.1697
690.17 690.17 690.17 690.17
T/K(Bath) = 308.75; P/MPa(Bomb) = 2.032 27.05 0.0599 0.00 813.1 27.05 0.0599 0.00 813.1 34.41 0.0599 -2.33 751.8 34.41 0.0599 -2.51 779.9
672.13 672.13
T/K(Bath) = 308.35; P/MPa(Bomb) = 7.810 -17.26 2724.9 26.44 0.1697 26.44 0.1697 -18.72 2966.4
717.59 717.62 717.62
T/K(Bath) = 308.35; P/MPa(Bomb) = 2.025 0.0606 0.85 164.4 26.99 0.0606 0.44 439.0 35.77 35.77 0.0606 0.18 523.7
423.16 423.16 423.16 423.16 423.16 423.16
T/K(Bath) = 306.85; P/MPa(Bomb) = 6.982 0.1677 -3.80 21.80 -3.88 21.80 0.1677 0.1677 -3.84 21.80 28.15 0.1677 -3.80 -3.87 28.15 0.1677 0.1677 -3.79 28.15
56.7 57.3 57.0 56.4 56.9 56.4
513.07 5 13.07
T/K(Bath) = 306.65; P/MPa(Bomb) = 7.058 -4.69 28.42 0.1687 0.1687 -4.71 28.42
73.6 73.8
513.12 513.12 513.12
T/K(Bath) = 305.85; P/MPa(Bomb) = 7.706 -4.84 29.65 0.1717 0.1717 -4.84 29.65 0.1717 -4.90 29.65
74.0 74.0 74.5
5 15.20 515.20 515.20
T/K(Bath) = 307.75; P/MPa(Bomb) = 7.306 -4.60 20.56 0.1687 0.1687 -4.61 20.56 -4.71 20.56 0.1687
687.11 687.1 1 687.1 1 687.11
C. Xenon
For each experimental run a header line gives the equilibration temperature of the sample bath, T/K(Bath), and the total pressure of the sample bomb at equilibrium, P/MPa(Bomb). bThis is the experimental pressure of the density experiment. CThemolality was calculated from the temperature of the bath and the partial pressure of the gas in the bomb. dThe difference in density between the solution, d, and water, do, was calculated from4 Ad = d - do = k ( -~ T ~~ ~where ) , k is a calibration constant and T and r 0are the periods of oscillation of the vibrating tube containing solution and water, respectively. eThe apparent molar volume, V,, was calculated by V, = [ ( l / d - l/do)/m] M2/d, where d and do are the densities of solution and water, respectively, in kg ~ m - M~ ,is the molality, and M2 is the solute molecular mass in kg mol-'.
+
where K~ is the isothermal compressibility of the solvent, d P / dx(gRLand dT/dxIsRL refer to the initial slope of the critial line, and dP/d7lC,,, denotes the critical slope of the solvent's vapor
pressure curve. We have estimated the slopes of the critical curve (with a n accuracy of &SO%) from graphs of the results of Lentz and Franck for argon.6 The calculated values of p2' are plotted
J . Phys. Chem. 1988, 92, 1994-2000
1994
found for measurements closer to infinite dilution and closer to the critical point. The theoretical and experimental findings that V20 is proportional to K~ shows that any theory or correlation must include this factor in order to work well near the critical point. The corresponding-states treatment of Brelvi and O ' C ~ n n e includes l~~ this factor. The scaled particle theory of gas solubility3' and the perturbation theory of Neff and M c Q ~ a r r i egive ~ ~ reasonable results only if the experimental value of the solvent density and its temperature derivative are used in the calculation since this builds in the experimental value of K~ for water. Marshall and co-workers have correlated chemical equilibria as simple functions of the density of the solvent and the t e m p e r a t ~ r e . ~ This ~.~~ procedure gives terms proportional to K~ for AV, and these equations can fit data near the critical point.
TABLE 11: Comparison of Henry's Law Constants for Argon, kH, Calculated from Solubilities and Heat Capacities
T IK 298.15' 308.15' 318.15' 328.15e 338.15e 348.15' 309.9' 335.9' 365.3' 368.3' 397.3' 424.7f 453.7f 568.d
k,lMPa solubilitya solubilityb heat capacity' P,,, 17.2 MPa 17.2 MPa 4023 4671 5264 5777 6190 6495 4748 6093 6409 6601 6144 53 36 4354 1774
4927 5691 6384 6985 7462 7813 5788 7351 7689 7915 7358 6384 5216 1774
AkH/MPad 17.2 MPa
1846 5724 6417 6996 7443 7752 5631 7355 1967 7966 7492 6520 5283 1438
81 -33 -3 3 -1 I 19 61 157 -4 -278 -5 1 - 1 34 -1 36 -67 336
Acknowledgment. This work was supported by the National Science Foundation under G r a n t s CHE8009672 arid CHE8412592. W e also thank Dorothy E. White, William E. Davis, and Patricia S. Bunville for their help.
"Henry's law constants, kH.at saturation pressure derived from solubility data. * k Hcalculated from solubility and corrected to 17.2 MPa by using In kH(P2.T)= In kH(P,,T)+ 13 ( V 2 ; " / R TdP, ) where is the partial molar volume at infinite dilution of the solute. kH calculated from heat capacity data in ref 3. d A k H = k , at 17.2 MPa derived from solubility data - kHat 17.2 MPa derived from heat capacity data. 'Solubility data from ref 19. fSolubility data from ref 27.
Registry No. H 2 0 , 7732-18-5; Ar, 7440-37-1; Xe. 7440-63-3; C2H4. 74-85-1. (33) Brelvi, S. W.; O'Connel, J. P. AIChE J. 1972, 18, 1239. (34) Pierotti, R.A. Chem. Reu. 1976, 76, 717. (35) Neff, R. 0.;McQuarrie, D. A. J. Phys. Chem. 1973, 77, 413. (36) Marshall, W . L.; Franck, E. U. J . Phys. Chem. ReJ Data 1981, IO, 295. (37) Frantz, J. D.; Marshall, W. L. Am. J. Sci. 1984, 284. 651 (38) Marshall, W. L. Rec. Chem. Prog. 1969, 30. 61.
in Figure 2. There is qualitative agreement between the results. The maximum is in the correct place, but the calculated values are too low a t temperatures below the maximum and too high above the maximum. Presumably, better agreement would be
Apparent Molar Heat Capacities of Aqueous Argon, Ethylene, and Xenon at Temperatures up to 720 K and Pressures to 33 MPa Daniel R. Biggerstafft and Robert H. Wood* Department of Chemistry, University of Delaware, Newark, Delaware 19716 (Received: June 23, 1987; In Final Form: October 1 4 , 1987)
The apparent molar heat capacities, Cp,m, of aqueous solutions of argon, ethylene, and xenon were measured at temperatures decreases from 300 to 720 K with a flow, heat capacity calorimeter developed in our laboratory. For all three gases CP,* as temperature is increased, goes through a shallow minimum at about 420 K, then rises to a maximum -5000 J mol-l K-' at about 665 K, and decreases to a minimum -5000 J mol-' K-' at 685 K for pressures near 33 MPa. This remarkable behavior at high temperatures is due to the proximity of the critical point of water. The behavior is qualitatively similar to ( d 2 p / d P ) , where p is the density of water.
-
Introduction A previous paper from this laboratory reported the first experimental measurements of the heat capacity of an aqueous solution of a slightly soluble gas. The measurements were on aqueous argon solutions from 300 to 600 K.' These results showed a remarkable behavior. The apparent molar heat capacity of aqueous argon increased to a very large and positive value at 600 K. Theoretical models predict that, at pressures above but near the critical pressure of pure water, the apparent molar heat capacity of slightly soluble gases will get very large and positive as the temperature increases, then suddenly decrease to a large and negative value, and finally, gradually increase again.*" Corresponding behavior for the enthalpies of gases in other solvents has been found?+ and similar behavior has been found at liquid-liquid critical points." This paper reports experimental measurements * A u t h o r to whom correspondence should be addressed ' Present addre>, Reishhold Chemicals, Dot er. DE I9901
0022-3654/88/2092-1994$01.50/0
of the heat capacity of dilute aqueous argon, ethylene, and xenon a t temperatures up to 720 K. The qualitative predictions of the ( 1 ) Biggerstaff, D. R.; White, D. E.; Wood. R. H. J . Phys. Chem. 1985, 89, 4378. (2) Wheeler, J. C. Ber. Bunsenges. Phys. Chem. 1972, 76, 308. (3) Chang, R. F.; Morrison, G.; Levelt, Sengers, J. M. H. J . Phys. Chem. 1984, 88, 3389. (4) Levelt Sengers, J. M. H.; Chang, R. F.; Morrison, G. Equation of State-Theories and Applications; Chao, K . C.; Robinson, R. L., Jr., Eds.; ACS Symposium Series 300; American Chemical Society: Washington, DC, 1986. ( 5 ) Levelt Sengers, J. M. H.; Everhart, C. M.; Morrison, G.; Pitzer, K. S. Chem. Eng. Commun. 1986, 47, 315. ( 6 ) Chang, R. F.; Levelt Sengers, J. M. H. J. Phys. Chem. 1986,90,5921. (7) Morrison, G.; Levelt Sengers, J . M. H.; Chang, R. F.; Christiansen, J . J . Supercritical Fluid Technology; Penninger, J . M. L.; Radosz, M.; McHugh, M. A,; Krukonis, V. J., Eds.; Elsevier: Amsterdam, 1985; p 2 5 . (8) Christianson, J. J.; Walker, T. A. C.; Schofield, R.S.; Faux, P. W.: Harding, P. R.; Izatt, R. M. J. Chem. Thermodyn. 1984, 16, 445 and references cited therein.
0 1988 American Chemical Society
