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COMMUIVICATIONS TO THE EDITOR
On the Partial nnolal Volume of Helium in Water and Aqueous Sodium Chloride Solutions Publication costs assisted by the National Science Foundation
Sir. Recently Gardiner and Smith1 have reported some excellent new data for the solubility of helium in water and aqueous NaCl solutions. The experimental results compare favorably with the best values previously available2 due to an improved reduction of the raw data including a necessary meniscus correction. However, we would like to offer as a possibility an alternative thermodynamic analysis and interpretation of the experimental results. There are two expressions commonly used to evaluate the effects of pressure on gas ~ o l u b i l i t yand , ~ it is essential to recognize the assumptions involved. Basically, both stem from the expression of the fugacity of the ith component in the liquid phase f L in terms of its mole fraction x c , an activity coefficient y L and , a reference state fugacity f L O
f , = XIYlfiO (1) The Krichevsky-Kasarnovsky equation435 assumes for a binary mixture that the reference state is the infinitely dilute solute 2 in pure solvent 1, a t the temperature and total pressure oft he mixture, and that yz is unity.
where H2,l is the Henry's law constant for 2 in 1 defined at the saturation pressure PIS, and 32 is the partial molal volume a t infinite dilution. The last term in eq 2 corrects the reference state fugacity H z , from ~ pressure PIS to the reference pressure, chosen as P. Unless the solvent is expanded (Le., near its critical point) the usual assumption is that the compressibility of the solute is not unusually large;3 thus Dzm is relatively pressure independent, and the last term may be integrated
+ [UZm(P- P l " ) / R T l
(3) Equation 3 may be used to analyze data in the dilute range (low x2, where yz = 1) generally by plots of In ( f 2 / x 2 ) us. P to yield straight lines giving two unknown parameters, H Z J from the intercept and Dzi from the slope. At higher concentrations, it has frequently been noted that curvature O C C U ~ S ,and ~ this is presumed to be due to deviations from Henry's law (72 z 1). In the unsymmetric convention, the simplest possible nontrivial solution to the Gibbs-Dichem equations is a one-term Margules expression, which yields the Krichevsky-Ilinskaya equation6 In ( f 2 / x A = In
where even if Dzi is assumed constant, there are three parameters to be evaluated from the data, and quite extensive and accurate data are needed to evaluate so many parameters. Smith and his coworker^^^^ have chosen to interpret curvature in terms of variation of Dz= with pressure, assuming that the coefficient of isothermal compressibility p is a constant. This in effect introduces three parameters into eq 2 and certainly precludes any attempt to look at variations in 7 2 . Although the possibility of variation of 02- with concentration is discussed, this is clearly not possible, as the definition of the reference state defines the concentration at which D z m must be evaluated, that is at x2 = 0. By this analysis, some astounding values of p resulted, ranging from a negative compressibility of -30 X atm-I in pure water at 25" to +150 X a t m - l in water and one solution a t 100". For comparison p for pure water is just below 5 x atm-I over this range, while for most organics, not near their critical points, the range is 4-20 X 10-5 atm-1. Gardiner and Smith explain their negative values in terms of the effect of dissolved helium on the structure of the water. We wish to offer as an alternative possibility that although there does appear to be slight curvature in some of the data sets, the five or six points per set do not justify fitting three adjustable parameters, nor do they justify the decision of whether such curvature is due to compressibility of the solute rather than due to deviations from Henry's law. We find that the two-parameter eq 3 represents the actual (not smoothed) experimental data to a t least the degree of its precision, and gives superior values of H Z J and D z m . Rather than the smoothed data presented in ref 1, we fit the actual experimental points8 and found that at 25 and 50" the precision of the fit of eq 3, with constant > 2 m , was virtually as good as the three-parameter fit, and within probable experimental error. Moreover, the values of the Henry's law constants thus determined (see Table I) appear to be in a t least as good agreement with literature data as those reported in ref l. At 100" we found that even a three-constant fit of the In ( f 2 / ~ )data gave standard deviations of 3-570. Thus although compressibility of the solute would be greatest at the highest temperature, the data do not appear to justify evaluation of three parameters. The only value of 02- 'for which comparison can be made is that for helium in pure water a t 50". Using eq 3 The Journal of Physical Chemistry, Vol. 77,No. 16, 1973
Communications to the Editor
2020
TABLE I: Henry's Law Constants and Pa~tialMolal Volumes for Helium in Water and Aqueous NaCl Solutions
Eq 3 Temp, "C 25
50
Solvent 1.003 m 4.067 m
H2 0 1.003 m 4.067 m
100
NaCl NaCl NaCl NaCl
Hz0 1.003 m 4.067 m
NaCl NaCl
Pzm , cc/mol
15.6 14.7 15.3 14.4 17.9 21.1 23.1 20.8
we find 15.3 cc/mol from the data in ref 1, and exactly the same value from those in ref 2a. Using their three-parameter fit, Gardiner and Smith' reported a value of 26.9 cc/ mol from their data and 20.0 cc/mol from the data of ref 2a. Since there are such large discrepancies between the values of 0 2 - calculated from eq 3 and those reported by Gardiner and Smith, we suggest that a feasible approach for choosing between these alternative interpretations could be the experimental determination of OZ=- from dilatometric data at modest pressures. However, the experimental determination of p for helium would be most difficult, requiring high-pressure dilatometry. In conclusion, we feel that the unusual values of /3 found for helium may not be real, but rather the results of smoothing and round-off in the data reduction. A great many extraordinarily precise data would be required for the evaluation of three adjustable parameters to verify such possible compression of a dissolved gas, and for the data reported, the Krichevsky-Kasarnovsky equation gives an adequate representation.
Acknowledgment. The authors are grateful to the National Science Foundation for financial support, and they
The Journalof Physical Chemistry, Vol. 77, No. 16, 1973
~ 2 . 1 atm ,
x 10-5
H z , ~atm , X (ref 1)
H 2 , , ,atm x 10-5 (ref 9)
1.790 3.041 1.337 1.698 2.91 7 1.197 1.390 2.495
1.78 3.31 1.42 1.7% 3.06 1.32 1.57 2.64
1.80 3.36 1.43, 1.44
1.04, 1.10
wish to express their appreciation to Professor Smith for supplying the original experimental data.
References and Notes G. E. Gardiner and N. 0. Smith, J. Phys. Chem., 76, 1195 (1972). (a) R. Wiebe and V. L. Gaddy, J. Amer. Chem. Soc., 57, 847 (1935); (b) H. A. Pray, C. E. Schweikert, and B. H. Minnich, lnd. Eng. Chem., 44, 1146 (1952). J. M. Prausnitz, "Molecular Thermodynamics of Fluid-Phase Equilibria," Prentice-Hall, Englewood Cliffs, N. J . , 1969, Chapter 8. I. R. Krichevsky and J. S. Kasarnovskv. J. Amer. Chem. Soc.. 57. 2168 (1935). B. F. Dodge and R . H. Newton, Ind. Eng. Chem., 29, 718 (1937). I. R. Krichevsky and A. A. Ilinskaya, Zh. Fiz. Khim. USSR, 19, 621 (19451. ?. D.-O'Sullivan and N. 0. Smith, J. Phys. Chem., 74, 1460 (1970). N. 0. Smith, personal communication, 1972. (a) T. J. Morrison and N. N. B. Johnstone, J. Chem. SOC., 3441 (1954); (b) T. J. Morrison and N. N. B. Johnstone, ibid., 3655 (1955); (c) S. K. Shorr, R. D. Walker, Jr., and K. E. Gubbins, J. Phys. Chem., 73, 312 (1969).
Department of Chemical Engineering School of Chemical Sciences University of Illinois, Urbana 67807 Received March 2, 1973
C. K. Hsieh C. A. Eckert"
