PARTIAL MOLAL VOLUME OF CARBON DIOXIDE I N W A T E R SOLUTIONS W. J. P A R K I N S O N ' A N D NOEL DE NEVERS Department of Chemical Engineering, University of Utah, Salt Lake City, Utah The specific volumes of carbon dioxide-water solutions were measured in a visual cell, in the range of 0" to 40" C. and 15 to 500 p.s.i.0. From these measured volumes and published solubility data, the partial molal volumes of carbon dioxide in water were calculated. The experimental values were compared with the predictions of the Krichevsky-Kasarnovsky equation and the correlation of Lyckman, Eckert, and Prausnitz. The latter gave good agreement with the experimental data; the former, poor agreement.
H E R E are few data in the literature on the densities or Tpariial molal volumes of solutions of carbon dioxide in water (Angstrom, 1882; Lyckman et al., 1965). This information would be useful, not only in connection with secondary petroleum recovery projects which involve such solutions (de Severs, 1964, 1966), but also because it would allow a check on the predictions of these properties via the Krichevsky-Kasarnovsky equation (1935) and the correlation of Lyckman et al. (1965). The Krichevsky-Kasarnovsky equation for a gaseous solute in a nonvolatile solvent is
+
In ( f 2 / x Z h = W R T ) T P , In ( H T )
(1 )
The assumptions used in deriving this equation are: The vapor pressure of the solvent liquid is small compared to the total system pressure, the solute gas is only sparingly soluble in the solvent fluid, the partial molal volume is not a function of pressure, and the activity coefficient of the solute gas is not affected by changes in composition. The derivation is shown by Krichevsky and Kasarnovsky (1935), Wiebe and Gaddy (1939), and Dodge and Newton (1937). For a system which obeys Equation 1, isotherms on a plot of In (fi/z,) US. P , should be linear with slope & / R T . If the partial molal volume is dependent upon pressure or composition (at constant temperatures 5 %varies with pressure only), one would expect the isotherms on such a plot to be curved. Figure 1 is a plot for dilute solutions of carbon dioxide in water (z1 < 1 mole yo),made up from the solubility and fugacity compilation of I-Ioughten et al. (1957) for carbon dioxide-water solutions. Because of the assumptions of the Krichevsky-Kasarnovsky equation, one would not expect the equation to hold for large values of the mole fraction of the solute. Customarily it has been assumed here that large means zigreater than about 0.01. As shown on Figure 1, the isotherms appear straight. These data can be replotted with values of z1 significantly greater than 0.01 and the isotherms still appear straight over the range of temperature and pressure shown here. The partial molal volumes calculated from Figure 1 are shown in Figure 2 , as a function of temperature. The semiempirical partial molal volume correlation of Lyckman et al. (1965), given by them graphically, is approximately represented by
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This correlation is restricted to partial molal volumes a t infinite dilution. Its predictions are also shown on Figure 2. Experimental Method
The partial molal volume is defined as
TiPinz
Le., the slope of a plot of volume us. moles of solute a t constant pressure, temperature, and moles of solvent. One can, in principle, measure it directly by measuring the volumes of solutions of various known concentrations. An easier route experimentally is the one taken in this research, of measuring the volume of a saturated solution of carbon dioxide in water, as a function of pressure. It can be shown that V = T'(n1, n2, P , T ) , so that
Here
so
I n this research, [ d V / d P ] T . ~was * measured experimentally. [ d P / d n l ] ~ , nisz known from the measurements of the solubility of carbon dioxide in water, and [dV//lldP]nl,nz,~ was taken as the value for pure water (American Institute of Physics, 1957). The second term in Equations 4 and 6 contributed an average of 4.5% and a maximum of 8.65% to the partial molal volume. Experimental Apparatus and Materials
The experimental apparatus consisted of an equilibrium cell and rocking mechanism, a temperature-control system, a gas-supply manifold, and measuring devices. The equilibrium cell, which contained the carbon dioxidewater solution, was a single-window Jerguson gage, Catalog No. llR-5. The 304 stainless steel cell cavity was a n almostcylindrical hole, $ inch in diameter and about 12 inches long. Its maximum volume was about 6 cu. inches. VOL.
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8.0
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mercury, using the published density of mercury (Handbook of Chemistry and Physics, 1959). The solubility data of Houghton et al. (1957)were interpolated by fitting a fifthdegree polynomial in pressure and temperature to the data, and then reading values from this polynomial.
75%
Procedure 50%
The experimental procedure consisted of filling the equilibrium cell with distilled water, boiling off enough water to remove all air, setting and maintaining the temperature of the constant-temperature bath, pressurizing the cell with carbon dioxide, rocking the gas-liquid mixture to bring it to equilibrium, then measuring the meniscus level with a cathetometer. Equilibrium was reached when the solution stopped swelling. Results
The solution volume measured in the experiment was plotted against n1 (calculated from the interpolation routine) 7.0
6.5 PARTIAL PRESSURE CO?, atm.
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Figure 1. In (fi/x1) vs. pressure at constant temperature for carbon dioxide in water
E
73.500
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