Activity and Osmotic Coefficients

Pitzer, K. S. and Guillermo Mayorga, "Thermodynamics of Electrolytes. II. Activity and Osmotic Coefficients for Strong Electrolytes with One or Both Ions Univalent," J. Phys. Chem., 1973, 77, 2300. 

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. 

Goldberg, R. N. Nuttall, R. L. "Evaluated Activity and Osmotic Coefficients for Aqueous Solutions The Alkaline Earth Metal Halides" J. Phys. Chem. Ref. Data, 1978, 7,... 

Staples, B. R. "Activity and Osmotic Coefficients of Aqueous Sulfuric Acid" J. Phys. Chan. Ref. Data, in press. 

Staples, B. R. Nuttall, R. L. "Computer Programs for the Evaluation of Activity and Osmotic Coefficients" Nat. 

Critical evaluations of activity and osmotic coefficient data were undertaken early in the 1930-1940 period by Harned and Owen (1958) and by Robinson and Stokes, (1965). Wu and Hamer (1968) evaluated activity and osmotic coefficient data for a series of electrolytes but their work on polyvalent electrolytes was not completed. Their work on the 1 1 electrolytes was published in 1972. The evaluation of polyvalent electrolyte data has been continuing in the Electrolyte Data Center at the National Bureau of Standards, and this paper will summarize the methods used in evaluating data for over 100 aqueous polyvalent electrolytes. 

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,... 

In addition, the critical evaluation of enthalpies of dilution and solution, as well as evaluations of heat capacities have been initiated. These evaluations will allow calculations and correlations of activity and osmotic coefficients as a function of temperature and composition. 

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. 

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... 

Clegg, S. L, and P. Brinibleconibe, Equilibrium Partial Pressures and Mean Activity and Osmotic Coefficients of 0-100% Nitric Acid as a Function of Temperature, J. Phys. Chem., 94, 5369-5380 (1990), and references therein. 

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. 

In this paper the authors propose to make a general derivation for the work function of a particle having the characteristics of an ion-dipole. Further, it is planned to apply this result to obtain equations for the activity coefficient and osmotic coefficient for an ion-dipole particle. The theory will be checked by applying it to published data on the activity and osmotic coefficients for ions, dipole, and ion-dipoles. 

Clegg SL, Brimblecombe P (1990a) Equilibrium partial pressures and mean activity and osmotic coefficients of 0-100% nitric acid as a function of temperature. J Phys Chem 94 5369-5380 Clegg SL, Brimblecombe P (1990b) The solubility and activity coefficient of oxygen in salt solutions and brines. Geochim Cosmochim Acta 54 3315-3328... 

K. S. Pitzer, G. Mayorga, Thermodynamics of electrolytes. II. Activity and osmotic coefficients for strong electrolytes with one... 

In the mean spherical approximation (MSA) treatment of the ion association in aqueous solutions, the linearity of the relative permittivity and of the hydrated cation diameters with the electrolyte concentration was taken into account and a good fit of the experimental activity and osmotic coefficient was obtained [72-75]. The MSA model was elaborated on the basis of cluster expansion considerations involving the direct correlation function the treatment can deal with the many-body interaction term and with a screening parameter and proved expedient for the interpretation of experimental results concerning inorganic electrolyte solutions [67,75-77]. 

Formalism According to Pitzer. The most common method for the evaluation of the activity and osmotic coefficients of an electrolyte in a binary mixture of strong electrolytes with a common ion is by Scatchard s Equations (23), the McKay-Perring treatment (24), Mayers Equations... 

The activity and osmotic coefficients of sodium thiocyanate in water have been determined (531). The solvation number of NCS has been reported as zero. (588), and the ion tends to be less structure-breaking than most anions (136). Its transport number and ionic conductance have been measured in formamide (581), and 1 1 solvates have been reported from dimethylformamide solutions of M—NCS (M = NH4, Na, K) (595). 

For any imaginary ideal solution of an electrolyte, at any given T and P, in which all activity and osmotic coefficients are unity, we can write for the chemical potential of a solute s. 

Temperature Effects. The temperature range for which this model was assumed to be valid was 0°C through 40°C, which is a range covering most natural surface water systems (28). Equilibrium constants were adjusted for temperature effects using the Van t Hoff relation whenever appropriate enthalpy data was available (23, 24, 25). Activity and osmotic coefficients were temperature corrected by empirical equations describing the temperature dependence of the Debye-Huckel parameters of equations 20 and 21. These equations, obtained by curve-fitting published data (13), were... 

Goldberg. R. N. 1979. Evaluated activity and osmotic coefficients for aqueous solutions Bi-univalent compounds of lead, copper, manganese and uranium. J. Phys. Chem. Ref Data ft(4) i005-50. 

Values of the water activity and osmotic coefficient for NaCl solutions in water for concentrations up to 6 m are shown in fig. 3.3. First, it is apparent that the vapor pressure of water decreases continuously with increase in salt concentration as one would expect. The value of at the most dilute concentration considered (0.1 m) is 0.99665. Measurements of vapor pressure lowering for lower concentrations are extremely difficult. The concentration dependence of the osmotic coefficient 9 reported in the same figure is quite different from that of the water activity. This quantity at first decreases, and then rises to values which are significantly... 

Activity and osmotic coefficients for 2-2 electrolytes, J. Solution Chem., 3, (1974), 539-546. Cited on page 590. 

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