186
Harvey S. Rosenberg and Webster B. Kay
The Solubility of Mercury in Polar Gases Harvey S. Rosenberg* and Webster
B. Kay
Battelle's Columbus Laboratories and The Ohio State University, Columbus, Ohio 43201
(Received June 20, 1973)
Publication costs assisted by Battelie's Columbus Laboratories
The concentration of mercury in the gas phase when liquid mercury is in equilibrium with methanol or acetone was measured a t pressures up to 30 atm from 220 to 300" using a radioisotope tracer technique. These concentrations were up to 21.6% greater than the concentrations in pure mercury vapor a t the same temperature. The data were used to determine the mixed second virial coefficients for mercury and the polar organic molecules. The experimental values for these coefficients were compared with theoretical values calculated from intermolecular potential functions. The solubility of mercury in methanol or acetone can cause an error of about 1 part in 500 in the pressure of gas isotherms measured in the presence of mercury at about 30 atm if the measured pressure is corrected by subtraction of the normal vapor pressure of mercury at the same temperature.
Introduction The phenomenon of solubility of solids and liquids in compressed gases is of great practical interest and is important wherever compressed gases or vapors are used. Of particular interest is the effect of mercury solubility on the accuracy of measurements of the volumetric behavior of compressed gases in those experiments in which mercury is used as the confining liquid. Previous work on the solubility of mercury in compressed gases is very limited. The expression for the solubility has been derived by Ewald, Jepson, and Rowlinsonl using the equilibrium condition that the chemical potential of the liquid mercury must equal the chemical potential of the mercury in the gas phase
The ratio c 2 / c 2 0 is a representation of the solubility and is the ratio of the concentration of mercury atoms in the presence of the added gas to the concentration of mercury atoms in pure saturated mercury vapor. Bl2 and Cl12 are the second and third virial coefficients for the interaction of one and two molecules of the added gas with one atom of mercury. Bll is the second virial coefficient of the added gas, u21 is the molar volume of liquid mercury, and u is the molar volume of the gas mixture. It is assumed in the derivation of eq 1 that (1) none of the added gas dissolves in the liquid mercury, ( 2 ) liquid mercury is incompressible, (3) the molar volume of saturated mercury vapor is much larger than the molar volume of the compressed gas mixture, and (4)the mole fraction of mercury in the mixture is very small. Experimental determinations have been made of the solubility of mercury in compressed argon by Stubley and Rowlinson,2 and in compressed propane and n-butane by Jepson, Richardson, and Rowlinson3 a t pressures up to 30 atm from 184 to 305". The concentrations of mercury in the compressed gases were up to 35% greater than the concentrations in pure mercury vapor at the same temperature, thus confirming previous calculations by Jepson and Rowlinson4 that this increase in the mercury concentration must affect adversely the accuracy of gas isotherms measured in the presence of mercury. No data The Journal of Physical Chemistry, Vol. 78, NO. 2, 1974
could be found in the literature on the solubility of mercury in the gases of polar compounds. The present study was undertaken to obtain more data on the accuracy of gas isotherms measured in the presence of mercury. The solubility of mercury was determined in compressed methanol and acetone gas, both of which are polar compounds.
Apparatus The apparatus used in this work is a modification of that for the radioactive tracer technique developed by others3 to measure the concentration of mercury atoms in sealed glass tubes. The method avoids the obvious difficulties of trying to sample and analyze a compressed gas mixture in which one of the components is present in very small amounts. The concentration of mercury near the bottom of a vertical glass tube was determined first for a tube containing only mercury vapor and then for an identical tube containing the compressed gas saturated with mercury at the same temperature. Since the count rate is directly proportional to the number of mercury atoms, the ratio of the two observed count rates is a direct measurement of the solubility of the mercury vapor in the added gas. Each tube contained a small excess of liquid mercury in a cup at the top to ensure saturation a t all temperatures. Figure 1is a diagram of the apparatus. The glass sample tube was made of Pyrex precision-bore tubing with an internal diameter of 5.00 mm, an external diameter of about 9 mm, and a length of about 40 cm. It contained about 27 mg of radioactive mercury, and a closely fitting Mu metal (a highly magnetic iron-nickel alloy) stirrer, 30 mm long, sealed in a 4 mm 0.d. glass tube. The stirrer could be moved over the whole length of the tube up to the mercury cup by two C-shaped, 6-02 permanent magnets placed with opposing poles about 2.25 in. apart on the outside of a vapor bath. The magnets were moved up and down continuously by axial bearings and a chain-drive mechanism powered. by a simple 25-rpm gear motor. During actual counting, the stirrer was held stationary near the top of the tube by the magnets. For safety, the glass sample tube was placed in a nonmagnetic stainless steel tube, with a wall thickness of 'h6 in. and an outside diameter of 0.5 in., sealed on the bot-
187
The Solubility of Mercury in Polar Gases ; ; c -To r i% pressure +
regulation system
condenser
\]'in
Thermocouple well
dk
Thermocouple, cower/ Sand constantan
Expansion bellows
Glass positioning tube Supports and tu posit1oners Mercury metal ,tagged
Stainless steel tube
-g, e
000 00
with203 Hg Mu metal strip, glass
v
1
002
01
1
02
03
04
Density of Gas Mixture
1-
280
c
c x 3 OLeast O Csquares fit
a6 moles/1
05
(+),
07
4 08
Figure 2. The concentration of mercury in saturated gaseous mixtures with methanol.
0-Ring ,Viton Scintillation probe
Guides, for positioning tube
j
,-Mercury
seal
Rubber stopper Benzophenone
Figure 1. Diagram of apparatus.
tom by a welded plug and on the top by a 0.5-in. stainless steel Swagelok cap. The glass sample tube and the stainless steel case were maintained at constant temperature by total immersion in a benzophenone vapor bath. The vapor bath was surrounded by a vac.uum jacket and contained a glass tube to position the sample tube for counting. The bath temperature was adjusted and maintained at the desired value in the range 220-300" by close regulation of the pressure in the closed system. The temperature was measured accurately with a calibrated copper-constantan thermocouple junction located about 1 in. away from the mercury droplet in the sample tube. The mercury droplet was located in a cup near the top of the sample tube so as to prevent spurious condensations of mercury during start-up and operation of the vapor bath. The concentration of the mercury was measured, in arbitrary units, by a NaI scintillation probe which was completely surrounded by 4-in. lead-brick shielding (not shown in Figure 1). The counting face of the probe was shielded by 2 in. of lead but had a 1-in. square collimator so that it received almost all its radiation from the mercury in the gas phase and very little from the liquid mercury at top of the tube. The probe was maintained a t a constant 28" by a stream of water flowing through a copper coil wrapped around the probe.
The glass sample tubes were loaded upside down, first by pipetting 2 X 10-3 ml of liquid mercury, tagged with 203Hg(tIl2 = 46.59 days) at an initial specific activity of 7.5 mCi/g, and ensuring that the droplet fell through the cup hole and .into the tip at the bottom of the tube. Next the stirrer was added and the sample tube was attached to a vacuum manifold so that the polar vapor could be added by distillation in U ~ C U Ofrom ultra-high-purity methanol or acetone. The volume of vapor was measured at low pressure (3-10 cm) and 28.0" in a calibrated and thermostatted reservoir, and the mass was determined from the equation of state up to the second virial coefficient. Values of B11 for methanol and acetone at 28.0" were obtained from the literature.5 The filled sample tube was sealed off under vacuum with a gas-oxygen torch and turned right side up. A filled tube was inserted in the stainless steel case and placed in the vapor bath which was then brought up to the desired temperature. The sample was stirred continuously while the count rate was measured on a recording rate meter. After the count rate leveled off, which usually required 2 days, counts were taken on a scaler at intervals of about 4 hr until the agreement between successive count rates was less than the statistical error of 0.3% for an accumulated count of 100,000. The background was never more than 10% of the count rate. Tubes containing only the mercury vapor were counted twice, once during the methanol series and once during the acetone series. Each series consisted of five tubes loaded with mercury and organic compound at different densities, and one tube loaded with mercury alone. The mercury concentration was measured at five temperatures for each tube. At the conclusion of the experiments, the tips of the sample tubes were broken open to remove the mercury and organic compound, and to fill the tubes with distilled water. The volumes of the tubes were determined from the weight and density of water contained in them.
Results The solubilities were tabulated as the ratio c ~ / c ~ O The . ~ pressures listed in this tabulation were determined from the equation of state up to the second virial coefficient using literature values for B11.7.S The ratio cz/c20 inThe Journal of Physical Chemistry, Vol. 78, No. ,?, 1974
188
Harvey S. Rosenberg and Webster B. Kay
Density of Gas Mixture
(t),m o l e s / l
Figure 3. The concentration of mercury in saturated gaseous mixtures with acetone. BlOnkS ond%OuMIll
r -260-
$
I
I
IC'I
41
Exporlmmlal dolo
TABLE I: Second Virial Coefficients of Interaction for Mercury-Methanol and Mercury-Acetone Systems B I Zcma/mol , Temp.
Mercury-methanol
O C
220.0 240 .O 260 .O 280 .O 300 .O
-'M200
220
2io
2 L
$0
A
320
Temperature, C
Figure 4. Second virial coefficients of interaction for mercurymethanol system.
-126 - 120 - 112 - 114 - 110
Discussion The experimental values of Blz may be compared with those calculated by various methods. The force constants The Journal 01 Physical Chemistry, Vol. 78,No. 2, 1974
- 156
' '
-154
- 146
- 136 - 123
describing the potential of interaction between a nonpolar atom or molecule (subscript n) and a polar molecule (subscript p) may be obtained from the following empirical combining laws given by Hirschfelder, Curtbs, and Bird10 bnp= %((Tn tnp
creases with increasing gas density at constant temperature and decreases with increasing temperature a t constant density. Figures 2 and 3 show In (c2/cz0) as a function of the density of the gas. According to eq 1, the mixed second virial coefficient B12 may be calculated from the initial slopes of the curves in these figures. The solubility data were subjected to a regression analysis which indicated that a second-order polynomial gave the most statistically significant fit to the data. Therefore, the experiments were not sufficiently accurate for a reliable measurement of the third virial coefficient Cllz. However, there is no doubt that C1lz must be positive as would be expected from the discussion of Rowlinson, Sumner, and Sutton.9 Values of B12 were calculated from the first coefficient of the second-order polynomials and are listed in Table I as functions of temperature. The values of B I Zare precise to within 5% and estimated to be accurate to within 10%.
Mercury-acetone
+ ap)(l + (r"6 cntp(1
4 [)'
(2) (3) (4)
a n is the polarizability of the nonpolar molecule and pLpis the dipole moment of the polar moIecule. The effective total energy of interaction between a nonpolar and a polar molecule has the same form as that between two nonpolar molecules so that B12 may be estimated from the tabulations of the Lennard-Jones potential. Values of B I Zcalculated from these interaction force constants (refer to Table 11) are shown as curve b in Figures 4 and 5 . The agreement between experimental and calculated values is very good for the mercury-methanol system, but poor for the mercury-acetone system. Also shown as curve a in these figures are values of B12 calculated for ideal binary mixtures by the method of Prausnitz and Gunn,ll using literature values for E11 and B 2 2 ; 7 , 8 J 2 not surprisingly, there is a complete lack of agreement with the experimental data. A method has been presented by Blanks and Prausnit213 for estimating B I Z for nonpolar-polar binary mixtures which corrects for the displacement of the dipole
The Solubility of Mercury in Polar Gases
189
TABLE 11: Molecular Force Constantsa ~
Mercury (Lennard-Jones)
Item (potential function)
e l k , OK u, A" a n t A" / ~ p ,D uo cm3/mol a
610 2.85 5.39
Methanol (Stockmayer)
Acetone (Stockmayer)
634 2.40
479 3.68
1.66 118
2.74 211
~~
Ethane (Lennard-Jones)
243
Propane (Lennard-Jones)
242
References 7, 8, 10, and 12.
from the center of the polar molecule and which emphasizes many of the nonpolar characteristics of the polar material. The interaction force constants are still obtained from eq 2, 3, and 4, but up, cp, and [ are replaced by up', t p f , and 5'. cp'is defined as 0;
= 0.&2Vcl~3
(5)
where uc is the critical molar volume of the polar molecule. Since polar forces do not seriously affect the molar volume at the critical point, eq 5 is an approximate method for estimating the collision diameter due to nonpolar forces only. tp' is defined as the Lennard-Jones energy parameter of the hydrocarbon homomorph of the polar molecule. The homomorph of a polar molecule is a nonpolar molecule having very nearly the same size and shape, i.e., ethane and propane are the hydrocarbon homomorphs of methanol and acetone, respectively. t f is defined as
E'
=
Kd
(6)
where KP is an empirical, temperature-independent correction factor which reflects the displacement of the polar dipole from the center of the molecule. K P is equal to unity when the dipole is at the molecular center and larger than unity for all other cases, but is independent of the properties of the nonpolar molecule. Values of Blz estimated from the modified interaction force constants (refer to Table 11) with KP equal to unity are shown as curve c in Figures 4 and 5. In both cases, calculated absolute values of Blz are considerably less than experimental absolute values, possibly because the dipole is not located at the center of the polar molecule. A trial-and-error calculational procedure was used to determine which value of KP for methanol and acetone gavc the best fit to the experimental data. The results yielded a value of 1.8 for methanol and 1.4 for acetone and the appropriate calculated values for Bl2 are shown as curve d in Figures 4 and 5. However, in view of the very limited data available, not much confidence can as yet be placed on the reliability of values for Kp. The effect of mercury on the observed gas pressure may be calculated by comparing the virial expansions for the pressure, p l , of nl moles of gas in a volume, V , in the absence of mercury with the pressure, p , of nl moles of gas and n2 moles of mercury in the same volume, V, at the same temperature, T. The result can be mathematically approximated as4
Values of x2, the mole fraction of mercury in the gas mixture, may be calculated from eq 1 since, for small values of n2, x2/xza is about equal to cZ/c2O. Equation 7 was used to calculate Ap/p for methanol and acetone in the presence of mercury at 260" up to a gas density of 1 M . These corrections were compared with the usual procedure of subtracting the normal vapor pressure of mercury from the observed pressure and it was found that at about 30 atm, an error of up to 0.2% can be introduced into the pressure measurement. At higher pressures, the error would be expected to increase. However, estimates of this error at higher pressures are difficult to make because of the lack of accurate data for third virial coefficients.
Supplementary Material Available. A tabulation of mercury solubility in compressed methanol and acetone as a funotion of gas density and temperature will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 x 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number JPC-74-186. References and Notes A. H. Ewald, W. B. Jepson, and J. S. Rowlinson, Discuss. Faraday SOC., 15, 238 (1953). D. Stubley and J. S. Rowlinson, Trans. Faraday Soc., 57, 1275 (1961). W. B. Jepson, M. J. Richardson, and J. S. Rowlinson, Trans. FaradaySoc., 53,1586 (1957). W. B. Jepson and J. S. Rowlinson, J. Chem. f h y s . , 23, 1599 (1955). J. D. Lambert, G. A. H. Roberts, J. S. Rowlinson, and V. J. Wilkinson, froc. RoyalSoc., Ser. A, 196,113 (1949). See paragraph at end of paper regarding supplementary material. J. S. Rowlinson, Trans. Faraday Soc., 45,974 (1949). I. Brown and F. Smith, Aust. J. Chem., 13,30 (1960). J. S. Rowlinson, F. H. Sumner. and J. R. Sutton, Trans. Faraday SOC., 50, 1 (1954). J. 0.Hirschfelder, C. F. 'Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," Wiley, New York, N. Y., 1954, p 223. J. M. Prausnitzand R . D.Gunn, AlChEJ., 4,430 (1958). J. B. Douglas A. F. Ball, and D. C. Giddings, J. Res. Nat. Bur. Stand.. 46.334 (1951). R. F. Blanks and J. M: Prausnitz, AlChEJ., 8,430 (1962).
The Journal of Physical Chemistry, Vol. 78, No. 2, 1974
