uids and vapors, respectively. Similar data for use of the Johnson-Grayson method are given for liquids and vapors in Tables 4 and 5, respectively. As shown, the pseudocompound method gave marked improvement over the Johnson-Grayson method for predicting the enthalpy of petroleum fractions. Further work has also shown its superiority in predicting the heat capacity of petroleum fraction vapors. This leads to the potential conclusion that the pseudocompound approach can be extended to correlate other thermodyfiamic properties of petroleum fractions, such as heat capacity, entropy and fugacit.y, and may also be applicable to prediction of the transport properties-viscosity and thermal conductivity. Literature Cited API Division of Refining, "Technical Data Book-Petroleum Refining," Chapter 7 , 2 n d ed, New York. N. Y . , 1970. API Research Project 44, "Selected Values of Properties of Hydrocarbons and Related Compounds," Tables of Physical and Thermodynamic Properties of Hydrocarbons, A and M Press, College Station, Tex., 1972.
Chao, K. C., Greenkorn. R. A., Proceedings 50th Annual Convention, NGPA. pp 42-46, Tulsa, Okla.. 1971. Cur!, R. F., Jr.. Pitzer. K. S., lnd. €ng. Chem., 50, 265 (1958). Huang, P. K., M. S. Thesis, T h e Pennsylvania State University, University Park, Pa., 1973. Huang, P. K.. Daubert, 1. E., lnd. Eng. Chem., Process Des. Develop., 13, 193 (1974). Johnson, R. L., Grayson, H. G., Petrol. Rehner. 40 ( 2 ) , 123 (1961). Lenoir, J . M., Hipkin, H . G..J. Chem. Eng. Data, 18, 195 (1973). Passut, C. A,, Danner, R. P., Ind. Eng Chem.. Process Des. Develop., 11. 543 (1972).
Receiuedfor review December 31, 1973 Accepted April 22,1974 Supplementary Material Available. A sample calculation using the pseudocompound method will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplementary material from this paper only or microfiche (105 X 148 mm, 24X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 16th St., N.W., Washington, D. C. 20036. Remit check or money order for $3.00 for photocopy or $2.00 for microfiche, referring to code number PROC-74-359.
Activity Coefficients at High Concentrations in the Hydrochloric Acid-Sodium Chloride-Water System Edward W. Funk' Universidad
Tecnica del Estado, Santiago. Chile
Semiempirical equations are proposed to describe the activity coefficients at high concentrations in the HCI-NaCI-H20 system; these equations complement the Bronsted-Guggenheim treatment of dilute solutions. The proposed equations for the activity coefficients of the electrolytes contain two parameters determined using activity coefficient data for the ternary system. One parameter is independent of the total molality and the other decreases systematically with molality; both are only weak functions of temperature. The activity coefficient of water in the ternary system is well described using only data for the binary subsystems. The activity coefficients have been defined similarly to those of nonelectrolytes; however, they are easily related to the familiar mean ionic activity coefficients often used for electrolyte solutions. An important advantage of these new activity coefficients is that they allow a simple description of phase equilibria involving electrolytes
Introduction Activity coefficients in concentrated aqueous electrolyte solutions are necessary for a great variety of chemical, metallurgical, and geological problems. Although there is a large number of experimental data (Harned and Owen, 1958; Robinson and Stokes, 1970; Seidell, 1965) for ternary aqueous electrolyte systems, few equations are available to correlate the activity coefficients of these systems in the concentrated region. The most successful present methods are those discussed by Meissner and coworkers (Meissner and Kusik, 1972, 1973; Meissner and Tester, 1972; Meissner, et al., 1972) and Bromley (1973). For the development of a thermodynamic framework especially suited to concentrated systems, there are complete and precise thermodynamic data for the HC1-NaC1HzO system and its constituent binaries from very low molality u p to highly concentrated solutions. Figure 1 shows the mean ionic activity coefficients of HC1 and NaCl (Robinson and Stokes, 1970) as functions of the mo-
' Corporate
Research Laboratory, Exxon Research and Engineering,
Linden, N. J. 07036 362
Ind. Eng. Chern., Process
Des. Develop., Vol. 13, No. 4 , 1974
lality a t 25°C in their respective binary solutions, and also the activity coefficient of each electrolyte a t infinite dilution in the ternary solution. In dilute solutions, the activity coefficients of the electrolytes change only slightly with composition at constant total molality; however, this change becomes large in concentrated solutions. For numerous applications, it is important to describe the composition dependence of these activity coefficients using a minimum of data for the ternary system. I t is very difficult to describe accurately the activity coefficients in the above system from low concentrations up to highly concentrated or saturated solutions. Fortunately, the region below total molalities of 0.2 is already well described by the Bronsted-Guggenheim theory. Harned's rule is usually used for the concentrated region although, unfortunately, the ternary parameters in Harned's rule depend on both temperature and total molality; often it is difficult to extrapolate the parameters to new conditions. The proposed equations for the activity coefficients of the electrolytes contain ternary parameters that are easily extrapolated to unstudied conditions of temperature and
tion, the Debye-Huckel limiting law. However, the second part of the excess Gibbs energy is very similar to the Wohl expansion used for nonelectrolyte solutions (Prausnitz, 1969). Considering a ternary aqueous solution of ions j , k , and a common ion i, the excess Gibbs energy (gE) is
2
2Aijxixj i2Aikxixk
= $(Debye-HCckel)
(1)
/-
of 0.5L
0.0
1
1.0
2.0
3.0
where ion j belongs to electrolyte 2 and k to electrolyte 3. x L is the ionic mole fraction of ion i, and the parameters A,,, A I k characterize the interactions between pairs of ions. As suggested by the Bronsted rule, no terms appear for the interaction between ions of like sign. Equation 1 is differentiated to calculate the ionic activity coefficients using the same technique as for nonelectrolytes. Combining these ionic activity coefficients to form the mean ionic activity coefficients, y I , we obtain the Bronsted-Guggenheim equations for two 1-1 electrolytes with a common ion
I
4.0
M 0L A L I T Y
Figure 1. Mean ionic activity coefficients for the HCl-NaCl-H20 system at 25'C.
molality. These parameters were determined using activity coefficient data for the above ternary system. The activity coefficient of water in the ternary system is estimated using only data for the binary systems. The proposed equations allow the calculation of activity coefficients for the HC1-NaCl-HZO system in the molality range of 0.2 to approximately 10 and for temperatures of 0 to 50°C. The activity coefficient used in the proposed equations is defined analogously to that of a nonelectrolyte; however, it is easily related to the mean ionic activity coefficient. This new activity coefficient is useful for the description of activity coefficients in concentrated solutions, but would be of little value for dilute solutions or transport phenomena. A particular advantage of this new activity coefficient is that it leads to simple, useful expressions for solid-liquid and vapor-liquid equilibria. The proposed equations for the activity coefficients are presently limited to concentrations above 0.2 m in the HC1-NaCl-HZO system. Further study is required before they can be applied to other systems or to systems containing more than two electrolytes. Nevertheless, they show particular promise for the treatment of solid-liquid equilibria in multicomponent aqueous salt systems.
Thermodynamics of Dilute Solutions The activity coefficients in dilute aqueous solutions (molalities less than 0.2) can be described using the Bronsted-Guggenheim theory (Harned and Robinson, 1968). The equations for the activity coefficients are derived by first defining the excess Gibbs energy a s the difference between the Gibbs energy of the solution and that when each ion is in its standard state of infinite dilution. For convenience, this expression is divided into two parts; the first leads to the Debye-Huckel limiting law, and the second is the correction to the Debye-Huckel theory. The first part of the excess Gibbs energy is not written explicitly, since it is not possible to form a simple, intuitive expression that gives, after appropriate differentia-
where c is the Debye-Huckel constant, m2 and m 3 are the molalities of the electrolytes, and I is the ionic strength. The interaction parameters of eq 2 and 3 can be readily calculated using only data for the binary solutions. However, without further interaction terms, the BronstedGuggenheim equations are limited to molalities below 0.2.
Harned's Rule Activity coefficients in concentrated solutions are often described using Harned's rule (Harned and Owen, 1958). This rule states that for a ternary solution a t constant total molality the logarithm of the activity coefficient of each electrolyte is proportional to the molality of the other electrolyte. The expressions for the activity coefficients are written
log
i.2
= log i / 2 ( 0 ) -
log
;3
= log
;3(n)
@~?J71?
- ~321712
(4) (5)
where subscript 2 refers to HC1 and 3 to NaC1. The activit y coefficient yzCo, is calculated a t the total molality of the solution and assuming the absence of 3; there is a similar definition for y 3 , o ) . The parameters 0 2 3 and CY32 characterize the interactions occurring between electrolytes 2 and 3. Harned's rule correlates the experimental activity coefficients for most ternary aqueous electrolyte solutions. For dilute solutions, eq 4 and 5 reduce to the Bronsted-Guggenheim equations, and the parameters Cy23 and CY32 can be expressed in terms of the interaction parameters of the Bronsted-Guggenheim theory. For concentrated solutions, Harned's rule is a simple empirical extension of the Bronsted-Guggenheim theory. Thus, it is surprising how well the rule describes activity coefficients in highly concentrated solutions. Figure 2 presents the parameters of eq 4 and 5 as functions of temperature and total molality. The experimental data compiled and discussed by Harned and Owen (1958) were used to calculate the experimental parameters shown in Figure 2 . The parameter 0 2 3 changes significantly with temperature and molality; howeuer, it becomes independent of molality a t high molalities. On the other hand, Cy32 Ind. Eng. Chem., Process Des. Develop., Vol. 13, No. 4 , 1974
363
-0.0'
I
I
t
Ex P e n I H e N T A L 0
POI N T 6
10.C
-0.M
Au*-59.56 + 0.179 t
- 09!
** t
