Electrolyte solutions osmotic coefficients

Abstract A permeameter was developed for measurement of coupled flow phenomena in clayey materials. Results are presented on streaming potentials in a Na-bentonite induced by hydraulic flow of electrolyte solutions. Transport coefficients are derived from the experiments, assuming the theory of irreversible thermodynamics to be applicable. Hydraulic and electro-osmotic conductivities are consistent with data reported elsewhere. However the electrical conductivity of the clay is substantially lower. This is ascribed to the high compaction of the clay resulting in overlap of double layers... 

There are many measurement techniques for activity coefficients. These include measuring the colligative property (osmotic coefficients) relationship, the junction potentials, the freezing point depression, or deviations from ideal solution theory of only one electrolyte. The osmotic coefficient method presented here can be used to determine activity coefficients of a 1 1 electrolyte in water. A vapor pressure osmometer (i.e., dew point osmometer) measures vapor pressure depression. 

The solutions to this approximation are obtained numerically. Fast Fourier transfonn methods and a refomuilation of the FINC (and other integral equation approximations) in tenns of the screened Coulomb potential by Allnatt [M are especially useful in the numerical solution. Figure A2.3.12 compares the osmotic coefficient of a 1-1 RPM electrolyte at 25°C with each of the available Monte Carlo calculations of Card and Valleau [ ]. 

Figure A2.3.17 Theoretical (HNC) calculations of the osmotic coefficients for the square well model of an electrolyte compared with experimental data for aqueous solutions at 25°C. The parameters for this model are a = r (Pauling)+ r (Pauling), d = d = 0 and d as indicated in the figure.

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

Equation (7.45) is a limiting law expression for 7 , the activity coefficient of the solute. Debye-Htickel theory can also be used to obtain limiting-law expressions for the activity a of the solvent. This is usually done by expressing a in terms of the practical osmotic coefficient

electrolyte solute, it is defined in a general way as... 

The activity coefficient of the solvent remains close to unity up to quite high electrolyte concentrations e.g. the activity coefficient for water in an aqueous solution of 2 m KC1 at 25°C equals y0x = 1.004, while the value for potassium chloride in this solution is y tX = 0.614, indicating a quite large deviation from the ideal behaviour. Thus, the activity coefficient of the solvent is not a suitable characteristic of the real behaviour of solutions of electrolytes. If the deviation from ideal behaviour is to be expressed in terms of quantities connected with the solvent, then the osmotic coefficient is employed. The osmotic pressure of the system is denoted as jz and the hypothetical osmotic pressure of a solution with the same composition that would behave ideally as jt. The equations for the osmotic pressures jt and jt are obtained from the equilibrium condition of the pure solvent and of the solution. Under equilibrium conditions the chemical potential of the pure solvent, which is equal to the standard chemical potential at the pressure p, is equal to the chemical potential of the solvent in the solution under the osmotic pressure jt,... 

For a solution of a single electrolyte, the relationship between the mean activity coefficient and the osmotic coefficient is given by the equation... 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

The osmotic pressure of an electrolyte solution jt can be considered as the ideal osmotic pressure jt decreased by the pressure jrel resulting from electric cohesion between ions. The work connected with a change in the concentration of the solution is n dV = jt dV — jrel dV. The electric part of this work is then JteldV = dWcl, and thus jzc] = (dWei/dV)T,n. The osmotic coefficient 0 is given by the ratio jt/jt, from which it follows that... 

Thermodynamic methods also measure the activity coefficient of the solvent (it should be recalled that the activity coefficient of the solvent is directly related to the osmotic coefficient—Eq. 1.1.19). As the activities of the components of a solution are related by the Gibbs-Duhem equation, the measured activity coefficient of the solvent can readily be used to calculate the activity coefficient of a dissolved electrolyte. 

The ideality of the solvent in aqueous electrolyte solutions is commonly tabulated in terms of the osmotic coefficient 0 (e.g., Pitzer and Brewer, 1961, p. 321 Denbigh, 1971, p. 288), which assumes a value of unity in an ideal dilute solution under standard conditions. By analogy to a solution of a single salt, the water activity can be determined from the osmotic coefficient and the stoichiometric ionic strength Is according to,... 

In addition to the activity and osmotic coefficients at room temperature, the first temperature derivatives and the related enthalpy of dilution data were considered for over 100 electrolytes (26, 29). The data for electrolytes at higher temperatures become progressively more sparse. Quite a few solutes have been measured up to about 50°C (and down to 0°C). Also, over this range, the equations using just first temperature derivatives have some validity for rough estimates in other cases. But the effects of the second derivative (or the heat capacity) on activity coefficients at higher temperatures is very substantial. 

Arbuckle, R. "A Bibliography of Sources of Experimental Data Leading to Activity or Osmotic Coefficients for Polyvalent Electrolytes in Aqueous Solution" Nat. Bur. Stand. Special Publ. No. 485, July 1979. 

Most determinations of activity and osmotic coefficients of an electrolyte solution are based on these experimental techniques ... 

Activity and osmotic coefficient data derived from ten experimental methods have been critically evaluated and correlating equations have been formulated for more than 100 aqueous polyvalent electrolyte systems at 298 K. Evaluations for the major reference solutions KC1 and NaCl (Hamer and Wu, 1972), and CaCl (Staples and Nuttall, 1977) have been published that for (Staples,... 

The techniques used in the critical evaluation and correlation of thermodynamic properties of aqueous polyvalent electrolytes are described. The Electrolyte Data Center is engaged in the correlation of activity and osmotic coefficients, enthalpies of dilution and solution, heat capacities, and ionic equilibrium constants for aqueous salt solutions. 

Goldberg, R. N., (1980a). "Evaluated Activity and Osmotic Coefficients for Aqueous Electrolyte Solutions Thirty-Seven Unibivalent Systems," manuscript in preparation. 

Goldberg, R. N., B. R. Staples, R. L. Nuttall and R. Arbuckle, (1977). "A Bibliography of Sources of Experimental Data Leading to Activity or Osmotic Coefficients for Polyvalent Electrolytes in Aqueous Solution", Nat. Bur. Stand. (U.S.) Spec. Publication 485, U.S. Gov t. Printing Office, Washington, D.C. 

Wu, Y. C. and W. J. Hamer, (1969). "Osmotic Coefficients and Mean Activity Coefficients of a Series of Uni-Bivalent and Bi-Univalent Electrolytes in Aqueous Solutions at 25°C," National Bureau of Standards Report (NBSIR) 10052, Part XIV, 83 p. 

The osmotic coefficients calculated from Eq. (9) can be brought into good agreement with solution data up to about 1M for aqueous solutions of alkali (26) and alkaline earth halides, (30) tetraalkyl ammonium halides, T3l) mixed electrolytes, where the Harned coefficients are measured, (32) and electrolyte-non electrolyte mixtures, where Setchenow coefficients are measured. 

The activity of water is related formally to the molality of the electrolyte by means of the osmotic coefficient, (p, of the solution ... 

This expression is analogous to Eiq. (2.3), in that (1 — (p) expresses the contribution of the solvent and In y+ that of the electrolyte to the excess Gibbs energy of the solution. The calculation of the mean ionic activity coefficient of an electrolyte in solution is required for its activity and the effects of the latter in solvent extraction systems to be estimated. The osmotic coefficient or the activity of the water is also an important quantity related to the ability of the solution to dissolve other electrolytes and nonelectrolytes. 

Electrostatic and statistical mechanics theories were used by Debye and Hiickel to deduce an expression for the mean ionic activity (and osmotic) coefficient of a dilute electrolyte solution. Empirical extensions have subsequently been applied to the Debye-Huckel approximation so that the expression remains approximately valid up to molal concentrations of 0.5 m (actually, to ionic strengths of about 0.5 mol L ). The expression that is often used for a solution of a single aqueous 1 1, 2 1, or 1 2 electrolyte is... 

The activity of water is obtained by inserting Eq. (6.12) into Eq. (6.11). It should be mentioned that in mixed electrolytes with several components at high concentrations, it is necessary to use Pitzer s equation to calculate the activity of water. On the other hand, uhjO is near constant (and = 1) in most experimental studies of equilibria in dilute aqueous solutions, where an ionic medium is used in large excess with respect to the reactants. The ionic medium electrolyte thus determines the osmotic coefficient of the solvent. 

In more complex solutions of high ionic strengths with more than one electrolyte at significant concentrations, e.g., (Na, Mg, Ca " ) (Cl, SOl ), Pitzer s equation may be used to estimate the osmotic coefficient the necessary interaction coefficients are known for most systems of geochemical interest. 

K. S. Pitzer, Ion interaction approach. In Activity Coefficients in Electrolyte Solutions (R. M. Pytkowicz, Ed.), pp. 157-208. CRC Press, Boca Raton, Florida, 1979 K. S. Pitzer and J. J. Kim, Thermodynamics of electrolytes. IV. Activity and osmotic coefficients for mixed electrolytes. J. Am. Chem. Soc. 96, 5701-5707 (1974) and earlier articles cited. 

The papers in the second section deal primarily with the liquid phase itself rather than with its equilibrium vapor. They cover effects of electrolytes on mixed solvents with respect to solubilities, solvation and liquid structure, distribution coefficients, chemical potentials, activity coefficients, work functions, heat capacities, heats of solution, volumes of transfer, free energies of transfer, electrical potentials, conductances, ionization constants, electrostatic theory, osmotic coefficients, acidity functions, viscosities, and related properties and behavior. 

The osmotic coefficients of the binary electrolyte solutions, 02 and 0ref were calculated by means of the Lietzke-Stoughton relation (11) enlarging the Debye-Hiickel equation with empirical terms ... 

Solutions are usually classified as nonelectrolyte or electrolyte depending upon whether one or more of the components dissociates in the mixture. The two types of solutions are often treated differently. In electrolyte solutions properties like the activity coefficients and the osmotic coefficients are emphasized, with the dilute solution standard state chosen for the solute.c With nonelectrolyte solutions we often choose a Raoult s law standard state for both components, and we are more interested in the changes in the thermodynamic properties with mixing, AmjxZ. In this chapter, we will restrict our discussion to nonelectrolyte mixtures and use the change AmjxZ to help us understand the nature of the interactions that are occurring in the mixture. In the next chapter, we will describe the properties of electrolyte solutions. 

PI8.2 Given that the osmotic coefficient for an electrolyte solution has the form... 

Osmotic coefficients for KC1 and CaCh were obtained from Appendix 4 of G. N. Lewis, M. Randall, K. S. Pitzer, and L. Brewer, Thermodynamics, Second Edition, McGraw-Hill Book Company, New York, 1961. Values for LaCl3 were obtained from F. H. Spedding, H. O. Weber, V. W. Saeger, H. H. Petheram, J. A. Rard, and A. Habenschuss, Isopiestic Determination of the Activity Coefficients of Some Aqueous Rare Earth Electrolyte Solutions at 25 °C 1. The Rare Earth Chlorides , J. Chem. Eng. Data, 21, 341-360 (1976). 

Activity coefficients of H4[SiWi204o] obtained in 0.0004 to 0.04 M concentrations in queous solutions have also been reported11S. The results obtained agree with the Debye-Huckel theory for 1—4 electrolytes. Osmotic coefficients of 12-tungsto-silicic acid have also been reported116. ... 

M. Manciu, E. Ruckenstein Comments on the Osmotic Coefficients and Surface Tensions of Aqueous Electrolyte Solutions Role of the Dispersion Forces JOURNAL OF PHYSICAL CHEMISTRY B 108(2004)20479-20481. 

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