ARVINS. QUISTAND WILLIAML. MARSHALL
684 of a variety of rules for the pseudo-critical temperature. The choice between the arithmetic and the geometric mean for the effective number of carbon atoms is not at all critical. I n almost all of the systems studied, the geometric mean leads to closer agreement with the measured values, but the difference between the two rules is generally less than the estimated error in the measurements. The principle of congruence is not nearly so effective for these mixtures as for the few systems discussed by Barker and Linton.lB They showed that the second virial coefficients for an equimolar mixture of methane and propane were within 0.5 cm3/mole of the values for pure ethane in the temperature range 377-510", and that there was good, if somewhat less spectacular, agreement between the second virial coefficients for an equimolar propanen-heptane mixture and those for n-pentane from 70 to 150". It is noteworthy, however, that in the case of the latter mixture the agreement is poorest at the lower temperatures, and, if one uses
Gunn's analysis12 of the experimental data from which the methane-propane virial coefficients are derived in place of the analysis used by Barker and Linton, there is a noticeable worsening at lower temperatures of the correspondence between the ethane virial coefficients and those for the methane-propane mixture. This effect is also to be seen in our data where the fit of the experimental points to the parabolas in Figure 5 is better at the higher temperatures. This effect is perhaps explained by considering the randomness of the molecular interactions. I n order for a system to adhere to the principle of congruence, it is necessary that there be a random interaction between the individual chain segments. I n the dilute gas a t low temperatures, although the molecular encounters are random, the angular dependence of the potential tends to favor some interactions between segments above others. As the temperature is raised, the orientation effects are of less importance and a more truly random situation is approached.
Electrical Conductances of Aqueous Sodium Chloride Solutions from
0 to 800"and at Pressures to 4000 Bars1#2 by Arvin S. Quid and William L. Marshall Reactor Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 97890 (Received August 21, 1967)
The electrical conductances of aqueous sodium chloride solutions (0.001-0.1 m) have been measured to temperatures of 800' and at pressures to 4000 bars. Limiting equivalent conductances for NaCl were calculated at integral temperatures and densities, and they were found to be a linear function of density (at constant temperature). Moreover, above 400" at constant density, Ao(NaC1) was essentially independent of temperature. Conventional ionization constants for the equilibrium NaCl Na+ C1- were obtained above 400" at solution densities below 0.8 g cm-a. Sodium chloride behaves as a weaker electrolyte as temperature increases (at constant solution density) and as solution density decreases (at constant temperature). From the conventional ionization constants (constant only a t constant density) the complete constants that include the concentration of water as a reactant were obtained. These complete constants (KO) are truly independent of solvent density or pressure, and depend only on temperature.
*
Introduction Measurements of properties of aqueous electrolyte solutions at high temperatures and pressures, particularly under conditions, have been the subject of several investigations in recent years. KnowlThe Journal of Physical Chemistry
+
edge of the properties of these solutions is important to individuals in many areas of study-for example, (1) Research sponsored by the U. S. Atomic Energy Commiaaion under contract with Union Carbide Corporation. (2) presented in part at the 15CJnd National Meeting of the American Chemical Society, New York, N. Y., Sept 1966.
ELECTRICAL CONDUCTANCES OF AQUEOUS NaCl
-
SOLUTIONS
to geochemists studying the mechanism of ore deposition under hydrothermal conditions, to engineers who design steam turbines that operate a t supercritical temperatures and pressures, and t o those interested in the development of economic methods to obtain potable water from sea water by distillation methods. Moreover, results obtained from the study of aqueous electrolyte solutions at elevated temperatures and pressures have particular usefulness in the development and testing of new theories of ionic solutions. For example, since the dielectric constant of water ranges from about 1 (supercritical temperatures, low pressures) to 102 (O", 4000 bars), the relationship between dielectric constant and other properties of electrolyte solutions can be studied without chauging the chemical composition of the solvent. This is an advantage over the ordinary studies of this type that are camed out a t 25". Usually, the dielectric constant of the solvent (water) is varied by adding another solvent such as dioxane that has a lower dielectric constant. However, the chemical composition of the solvent is also changed, and effects attributed to changes in dielectric constant may actually be due to changes in solvent compoiti ion.^,' Although very few studies have been carried out at supercritical temperatures and pressures, it does appear that these solutions exhibit simpler behavior than corresponding ones at room temperature. Probably the simplest and most direct method for obtaining information about the existence and behavior of ions in these solutions is the measurement of their electrical conductances. Although conductance measurements on aqueous electrolyte solutions were made at temperatures to 306" (at saturation vapor pressure) by Noyes and eo-workers early in this century? nearly 50 years elapsed before precise conductance measurements were extended into the supercritical region.n I n 1956, Franck reported some results of his research on conductance measurements of aqueous solutions to 750" and 2500 bars.' Since then, we have measured conductances of aqueous solutions of KPSOI, KHSOI, and H,SO, to 800" and 4000 bars! The present paper contains the results of an extensive investigation of NaCl solutions over the same conditions of temperature and pressure. Sodium chloride was selected not only because at room temperature it is a typical, strong, uni-univalent electrolyte but also because the results would be of interest in several other fields, for example, geochemistry, where hydrothermal brines containing high concentrations of NaCl have recently excited much interest.O From these studies on 0.001-0.1 m NaCl solutions, we have calculated limiting equivalent conductances over the complete range of temperature and pressure; thermodynamic equilibrium constants have also been calculated at conditions where NaCl h e haves as a weak electrolyte.
685
i -- OWLING JACKET
COOLING JACKET
Figure 1. Conductance cell for service to 800' and 4000 bars.
Experimental Section Apparatus. Some of the equipment and procedures have been described previously>'" but since several modifications have been made over the past several years, the Experimental Section of this paper will contain a nearly complete summary of the presently used equipment and procedures. Two different conductance cells were used for the measurements on sodium chloride solutions. One of these cells has been described previously.*,1o The other (new) conductance cell was designed to eliminate the need for pressure seals in the portion of the cell subjected to high temperatures. The essential features of this new cell are shown in Figures 1 and 2. Starting with a solid cylindrical bar of Udimet 700 (Special Metals, Inc., New Hartford, N. Y.) 1 in. in diameterand23.75 in. long, a0.250 0.001 in. diameter hole was bored its length by using equipment in the Oak Ridge National Laboratory Shops especially designed for precision work of this type. This hole was then enlarged to 0.45 in. diameter to a depth of 2.375 in. a t each end of the bar to accommodate the electrode holder
*
(3) W. L. Marshall and A. S. Quist, Proc. N d l . A d . Sci.
U.5..
58, 901 (1967). (4) A. 8. Quist and W.
L. Marshall, J . Phya. Chern.. in prees.
(5) A. A. Noyes. st al., "The Electrical Conductivity of Aqueous Solutions." Publioation No. 63, Carnegie Institution of Weshinbn. Washington. D. C.. 1907. (6) J. K. Fogo. 8. W. Beneon. and C. 22.212 (1954).
5. Copeland. J . Ckm. PAY&
(7) (a) E. U. Franck. Z. Phuaik. Chem. (Frankfurt). 8.92 (1956): (b) aid..8. 107. 192 (1956): (c) Anpeu.. Chem., 73, 309 (1961). (8) A. 8. Qui& et d.,(4J . Phus. Chem.. 67,2453 (1963): (b)
