J. Chem. Eng. Data 1983, 28, 339-340
339
Interactlon Second Virial Coefficients for Sodium-Inert Gas Mixtures Pablo A. Vlcharelll,t Robert C. Harshaw, and Carl B. Collins* Center for Quantum Electronics, The University of Texas at Dallas, Richardson, Texas 75080
Interactlon second vlrlal coefflclents for blnary mlxtures of sodlum vapor and the Inert gases are evaluated for the 200-2000 K temperature range. The calculatlons are based on the best experlmental lnteratomlc potentlal functlons available for NaHe, #aNe, NaAr, NaKr, and NaXe.
Introductlon Interest in the alkali-inert gas excimers has increased in recent years because of thelr potential utility in the development of new high-power visible lasers. Consequently, the Na-inert gas systems have been the object of numerous experlmental investigations, which include collisional line broadening ( 7 ), scattering (2-6), and laser excitation spectroscopy (7- 70). Several theoretical calculations have also been reported ( 7 7 - 75). I n addition, thermodynamic properties and second virial coefficients for pure alkali vapors (76, 77) and pure inert gases (76, 78) are available in the literature, but, to our knowledge, no alkali-inert gas interaction virial coefficients have been reported. The purpose of this paper is to present calculated values of interaction second virial coefficients for Nainert gas mixtures that can then be used to calculate the thermodynamic properties of such mixtures from knowledge of the properties of the pure component gases. Bask Equatlons
B ( T ) = x,2Bll(T)
+ ~ x ~ x ~ B ~+ ~X;B22(T) (T)
(4)
where the subscripts 1 and 2 are used to represent sodium and inert gas atoms, respectively. Potential Functions As can be seen from eq 3, potential energy data are needed for these calculations. Several investigators have reported experimental ( 7 - 70) and theoretical ( 7 7 - 75) ground-state potential energy functions for the Na-inert gas systems. For NaHe we adopt the potential function recently determined by Havey et ai. (70) using the temperature dependence of the red wing of the 3P Na resonance line perturbed by He. They concluded that the NaHe ground state can be described by a repulsive potential of the form V(R) = A exp(-BR)
(5)
where A = 61049.0 cm-l and B = 1.5104 A-'. The Morse function V(R) = De(exp[2a(R - Re)] - 2 exp[a(R -Re)]}
(6)
constructed from the spectroscopic data of Ahmad-Bitar et ai. (8) has been selected for the NaNe molecule. Here De = 8.1 cm-l, R e = 5.29 A, and a = 0.9311 A-l. The best ground-state potential function for NaAr reported to date is the one deduced by Tellinghuisen et ai. (9) from the dispersed fluorescence spectrum of this molecule. The form of this potential is that of a modified Morse curve
= D,(exp[2bo(R - Re)] - 2 exp[b0(R - Re)]} X (1 - 6 1 exP[(R - 6 2 ) / 6 3 I I (7) where De= 40.4 cm-l, R e = 4.994 A, 6 0 = 0.98693 A-l, 61 = 0.4988, 6 2 = 2.5981 A, and 63 = 1.2129 A. V(R)
I n the present work the vapor mixture is treated as a nonideal monoatomic assembly whose equation of state is given by PV/RT = 1
+ B(T)/V + C(T)/V2 + D(T)/V3 + ...
(1)
where B ( T ) ,C(T),and D(T) are second, third, and fourth virial Coefficients, respectively. We truncate this series at the B( T) term, which for a vapor mixture of n components takes the form (79) n
n
Finally, for NaKr and NaXe we choose a LennardJones (12-6) potential V(R) = DekRe/R)12 - 2(Re/RIel
(8)
with parameters reported by Duren et al. (3)from atomic beam scattering experiments. Here we have D e = 68.97 cm-l and R e = 4.73 A for NaKr, and D e = 100.2 cm-l and R e = 4.91 A for NaXe. Results
where X, is the mole fraction of the ith component and B&T) is given by B&T) = -2sNo~m(exp[-V,,(R)/k~]- 1}R2dR
(3)
Here V&R) denotes the potential between the ith and jth components, R is the Interatomic distance, k Is Boltzmann's constant, and N o Is Avogadro's number. For the special case of the binary mixture considered here, we write Present address: Jolnt Institute for Laboratory Astrophysics, University of Colorado and National Bureau of Standards, Boulder, CO 80309.
0021-958818311728-0339$01.50/0
Using the integral above, we have numerically evaluated interaction B 12( T) coefficients for the 200-2000 K temperature range using Newton-Cotes integration formulas. Contributions due to excited molecular states (20)were found to be negligible and thus were not included In our resutts, which are summarized in Table I. The uncertainties are estlmated to be less than 3%. Experimental values for the primary second virial coefficients Bll(T) have been published by Ewlng et ai. (77)and calculated values have been given by Sannigrahi and Mohammad (27). For a list of B22(T)values for the various inert gases we refer the reader to the recent compilation by Dymond and Smith (78). With these pure component data and the 6 12( T) coefficients 0 1983 American Chemical Society
J. Chem. Eng. Data 1983, 28, 340-343
340
Table I. Interaction Second Virial Coefficients (cm3/mol) Gas Atom Pairs
for Sodium-Inert
Literature CHed
listed in Table I it is now a straightforwardtask to evaluate B( r ) coefficients for any particular mixture of Na vapor and inert gases using eq 4. Subsequently, PVT properties for such mixtures can be easily derhred by uslng a real gas as the model.
(1) York. 0.; Scheps, R.; Qallagher. A. J . Chem. Phys. 1975, 6 3 , 1052-64. (2) Buck, U.; Pauly, H. 2.Fhys. 1988, 208, 390-417. (3) DGren. R.; Raabe. G. P.; Schller, Ch. 2. h y s . 1988, 274, 410-21. W. Chem. phys. Lett. 1988, 56. 67-70. (4) DGren, R.; QW, (5) Malerich, C. J.; Cross, R. J., Jr. J . Chem. phys. 1970, 52. 386-92. (6) Carter, G. M.; plltcherd, D. E.; Kaplan, M.; Ducas. T. W. Fhys. Rev. Lett. 1075. 35. 1144-7. (7) S-&#ey, R. E.; Auerbach, D. A.; Flch. P. S.H.; Levy, D. H.; Wharton, L. J . Chem. phvs. 1077. 66. 3778-85. (8) Ahmad-Bttar, R.fLapatovich, W.P.; Prkhard, D. E.; Renhorn. I. Fhys. Rev. Lett. 1977. 39, 1657-60. (9) Telllnghulsen, J.; Ragone. A.; Kim, M. S.; Auerbach, D. J.; Smalley. R. E.; Wharton, L.; Levy, D. H. J . chem. phys. 1979, 77, 1283-91. (10) Havey. M. D.; Froklng, S. E.; Wright, J. J. Fhys. Rev. Lett. 1980, 45, 1783-6. (11) BayliS, W. E. J . C M . F h p . 1989, 51, 2665-79. (12) Pascale, J.; Vandsplanque, J. J . Chem. Fhys. 1974, 60, 2278-89. (13) Saxon, R. P.; Olson, R. E.; Liu. B. J . Chem. F h p . 1977, 6 7 , 2692-702. (14) Czuchaj, E.; Slenklewicz, J. 2. Netvforsch. A 1979, 34. 694-701. (15) Diren. R.; Mor&, 0. J . Chem. Fhys. 1980, 73, 5155-9. (16) Stull, D. R.; Prophet, H. I n “JANAF Thermochemical Tables”, 2nd ed.; U.S.@ v e “ e n t Rlntlng OWlce: Washington, DC. 1971; NaH. St8nd. Ref. oata Ser. (US., Natl. BW. std.),NO. 37. (17) Ewlng, C. T.; Stone, J. P.; Spann, J. R.; Miller, R . R. J . Chem. Eng. Deb 1988, 7 1 , 468-73. (18) Dymond, J. H.; Smlth, E. B. In “The Vlrlal Coefflclents of Pure Gases and Mixtures”; Clarendon Press: Oxford, 1980. Curtlss. C. F.; Bird, R. B. In (19) See. for example: Hlrschfelder, J. 0.; “Molecular Theory of Gases and Liquids”; W y : New York. 1954. F’ltzer, K. J . Chem. F h p . 1919, 37,960-7. (20) Slnanoglu, 0.; (21) Sannlgrah, A. B.; Mohammed, S. N. Mol. Fhys. 1978, 37, 963-70.
Ne, 7440-01-9; Ar,
Recelved for revlew September 28, 1981. Revised manuscript received
T,K 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
NaHe 121.14 101.83 89.50 80.69 73.96 68.58 64.16 60.42 57.22 54.42 51.96 49.76 47.79 46.01 44.38 42.89 41.52 40.25 39.08
NaNe
NaAr
NaKr
NaXe
45.61 44.94 43.18 41.33 39.60 38.02 36.59 35.29 34.12 33.04 32.06 31.15 30.31 29.53 28.80 28.12 27.48 26.88 26.31
- 12.31
-57.15 - 9.58 11.82 23.68 31.05 35.97 39.42 41.93 43.80 45.22 46.32 47.17 41.84 48.36 48.77 49.10 49.35 49.54 49.69
-- 146.18
11.83 21.74 26.58 29.15 30.54 31.26 31.59 31.68 31.61 31.44 31.21 30.93 30.63 30.31 29.98 29.65 29.31 28.98
Registry No. Ne, 7440-23-5; He, 7440-59-7; 7440-37-1; Kr, 7439-90-9; Xe, 7440-63-3.
-58.51 - 19.67 1.89 15.43 24.60 31.15 36.01 39.73 42.63 44.94 46.80 48.33 49.58 50.62 51.49 52.23 52.84 53.37
- - - .- - .
February 22. 1982. Accepted March 7, 1983.
Sechenov Salt-Effect Parametert H. Lawrence Clever Solubilky Research and InformationProject, Department of Chemlstty, Emory Unhersky, Atlanta, Georgia 30322
The unHs used to express the electrolyte and nonelectrolyteconcentrations affect the numerical valw of the sah-offect parameter. Converrlon factors among the diffwlmt modes of exproWon of the saH4ect parameter are derived and m e typical n m w k a l values are pre8ented. The effects of random errors In the nonelectrolyte concentrations In water and t b squeous eledrdyte solution are dlswmod. A set of evaluated saH4ect parameters are pr0sent.d for up to 12 gases dissolved In aqueous rodkm chiorlde and potarslum hydroxide 80Mlons at 298.15 K. Introduction The effect of an electrotyte on the soiubliity of a nonelectrolyte has been systematically studied since the pioneering work of I. M. Sechenov (J. Setschenow) ( 7 ) on the solubility of carbon dioxlde in blood and in various aqueous electrolyte solutions between 1874 and 1892. A nonelectrolyte wll have a different solubility in water and in an aqueous electrolyte solution mainly because of the effect of the electrolyte on the nonelectrolyte actMty coefkht. The electrolyte may increase the nonelectrolyte activity coefficient (decrease the noneiectplesented h part at the symposlwn on the ~hennodynamk~ e h a v l ~ofr Electrolytes In Mlxed Solvents, 183rd Amerlcan Chemical Soclety Meetlng, Las Vegas, NV, March 1982.
002 1-95681831 1728-034080 1.5010
trolyte solubility, saltout)or it may decrease the nonelectrolyte activity coefficient (increase the nonelectrolyte activity coefficient, salt-in). There are many reviews of the salt-effect experimental data and theories (2- 70). The usual experimental measure of the salt effect is the Sechenov salt-effect parameter. Sechenov ( 7 7 , 72) proposed the empirical equation a = ao exp(-klx) where a’ and a are the Bunsen coefficients of the nonelectrolytegas solubility in water and aqueous salt soiutlon, x is the dilution, and k is the salteffect parameter. Sechenov tested the equation by measuringthe sdubiitty of carbon dioxide in a concentrated (sometlmes saturated) electrolyte solution, a number of ditutions of the solution, and pure water. He used the solubility in the most concentrated solution and water to establish the constant. He then calculated the solubility in the various solutions to compare with the experimental value. The agreement between equation and experiment was usually satisfactory. Many of Sechenov’s origlnal Bunsen coefficients for carbon dioxide in water and aqueous electrolyte solution agree within a few percent of modern values. Rothmund (73)was apparently the first to put Sechenov’s equation in the form commonly used today. In the notation of this paper that is
k,/(dm3 mol-‘) = /(c,/(moi dm4))1 log kc:/(moi
dm-3))/(c,/(moi dm-3N) (1)
0 1983 American Chemical Society
