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M. RIGBYAND J. M. PRAUSNITZ
lattice modes of the platinum and molecular modes of the adsorbed carbon monoxide. Grimleyll has treated the general problem of the vibrations of adsorbed molecules by a method which includes the interactions between lattice modes and molecular modes. In applying his treatment to the data obtained by Eischens' group218 he estimated, also neglecting intraniolecular interactions, that v1 was shifted about 30 cm-l upward by platinum lattice modes at 156 cm-l, Le., Grimley's
calculation suggests that the unperturbed value of v1 lies at about 446 cm-l. When our value of v1 is corrected by the same amount, the values 17.01, 3.01, and 1.09 mdynes/A are obtained for FCO, FCM,and f, respectively. These values tend toward those obtained by Joneslgbut they still suggest a strong interaction between the platinum crystallites and the adsorbed carbon monoxide. (11) T. B. Grimley, Proc. Phys. SOC.(London), 79, 1203 (1962).
Solubility of Water in Compressed Nitrogen, Argon, and Methane by M. Rigby and J. M. Prausnitz Department of Chemical Engineering, University of California, Berkeley, California 94720 (Receiwed August 8, 1967)
The vapor-phase solubility of water was measured in compressed nitrogen, argon, and methane at 25, 50, 75, and 100" and at various pressures between 20 and 100 atm. The volumetric properties of the vapor mixtures were described by the virial equation of state, and second virial cross coefficients were obtained from the solubility data. The solubility of a liquid in a gas at low pressures may be calculated from the vapor pressure of the liquid. Raoult's law yields an expression for the mole fraction, yl, of the liquid component in the gaseous phase y1
=
(1
- XZ)PS P
where x2 is the mole fraction of the gaseous component dissolved in the liquid, Pais the vapor pressure of the (pure) liquid, and P is the total pressure. At low pressures, x2 is negligibly small and the solubility is given directly by the ratio of the vapor pressure of the liquid to the total pressure. At high pressures, approaching the critical pressure of the mixture, the nonideality of the liquid phase becomes important in determining the vapor-phase solubility. However, in the intermediate pressure range with which this work is concerned, the critical factor determining the solubility is the nonideality of the vapor phase. The equilibrium of a binary system consisting of a heavy (liquid) component 1 and a light (gaseous) component 2 is governed by the equation ftL
the experimental quantities pressure, P, temperature, T,and the liquid and vapor compositions x and y to give
= ffV
where i = 1,2,f f is the fugacity of component i, and the superscripts L and V refer, respectively, to the liquid and vapor phases. The fugacities may be related to The JoUTnal of Physical Chemistry
where & is the vapor-phase fugacity coefficient, yr(P3 is the liquid-phase activity coefficient, ffocpr) is the reference fugacity of component i at T and at the reference pressure P', and :?z is the liquid partial molar volume. In the temperature range 25-lOO", the solubility in water of argon, nitrogen, and methane is very small, and to a good approximation we may take yl('I) = 1 and OIL = 2rlL (pure). I n the pressure range under consideration here, liquid water is essentially incompressible. The mole fraction of water in the gas may therefore be written
Since x2 is very small compared to unity, the vaporphase solubility is determined primarily by the fugacity coefficient (bl. This may be calculated from the virial equation of state.
SOLUBILITY OF WATER IN COMPRESSED
NITROGEN, ARGON,AND
33 1
METHANE
HEISE GAUGES
(5) 'MANIFOLD
where v is the vapor molar volume, Bll is the second virial Coefficient of water, and Blz is the second virial cross coefficient. Under the conditions used in this study, yl
