Activity coefficient infinite-dilution value

Figure 4. Solubilities of halite (NaCl) in water to 350°C. The curve represents values calculated using the Margules expansion model for activity coefficients (infinite dilution reference state), and standard state Gibbs energies for NaCl(aq) derived from the equations of Pitzer et al. to 300°C, and of Tanger and Helgeson above 300 C.

The symmetrical nature of these relations is evident. The infinite-dilution values of the activity coefficients are In yF = Iri JT = B. 

Outlined below are the steps required for of a X T.E calciilation of vapor-phase composition and pressure, given the liquid-phase composition and temperature. A choice must be made of an equation of state. Only the Soave/Redlich/Kwong and Peng/Robinson equations, as represented by Eqs. (4-230) and (4-231), are considered here. These two equations usually give comparable results. A choice must also be made of a two-parameter correlating expression to represent the liquid-phase composition dependence of for each pq binaiy. The Wilson, NRTL (with a fixed), and UNIQUAC equations are of general applicabihty for binary systems, the Margules and van Laar equations may also be used. The equation selected depends on evidence of its suitability to the particular system treated. Reasonable estimates of the parameters in the equation must also be known at the temperature of interest. These parameters are directly related to infinite-dilution values of the activity coefficients for each pq binaiy. 

The solvent and the key component that show most similar liquid-phase behavior tend to exhibit little molecular interactions. These components form an ideal or nearly ideal liquid solution. The ac tivity coefficient of this key approaches unity, or may even show negative deviations from Raoult s law if solvating or complexing interactions occur. On the other hand, the dissimilar key and the solvent demonstrate unfavorable molecular interactions, and the activity coefficient of this key increases. The positive deviations from Raoult s law are further enhanced by the diluting effect of the high-solvent concentration, and the value of the activity coefficient of this key may approach the infinite dilution value, often aveiy large number. 

The effect of solvent concentration on the activity coefficients of the key components is shown in Fig. 13-72 for the system methanol-acetone with either water or methylisopropylketone (MIPK) as solvent. For an initial-feed mixture of 50 mol % methanol and 50 mol % acetone (no solvent present), the ratio of activity coefficients of methanol and acetone is close to unity. With water as the solvent, the activity coefficient of the similar key (methanol) rises slightly as the solvent concentration increases, while the coefficient of acetone approaches the relatively large infinite-dilution value. With methylisopropylketone as the solvent, acetone is the similar key and its activity coefficient drops toward unity as the solvent concentration increases, while the activity coefficient of the methanol increases. 

A unitless correction factor that relates the relative activity of a substance to the quantity of the substance in a mixture. Activity coefficients are frequently determined by emf (electromotive force) or freezing-point depression measurements. At infinite dilution, the activity coefficient equals 1.00. Activity coefficients for electrolytes can vary significantly depending upon the concentration of the electrolyte. Activity coefficients can exceed values of 1.00. For example, a 4.0 molal HCl solution has a coefficient of 1.76 and a 4.0 molal Li Cl has a value of... 

A new theory of electrolyte solutions is described. This theory is based on a Debye-Hiickel model and modified to allow for the mutual polarization of ions. From a general solution of the linearized Poisson-Boltzmann equation, an expression is derived for the activity coefficient of a central polarized ion in an ionic atmosphere of non-spherical symmetry that reduces to the Debye-Hiickel limiting laws at infinite dilution. A method for the simultaneous charging of an ion and its ionic cloud is developed to allow for ionic polarization. Comparison of the calculated activity coefficients with experimental values shows that the characteristic shapes of the log y vs. concentration curves are well represented by the theory up to moderately high concentrations. Some consequences in relation to the structure of electrolyte solutions are discussed. 

In highly dilute aqueous solution, the activity coefficients approach the value 1. That is, in aqueous solution, K and become practically equal at infinite dilution. If the equilibrium constant, expressed in concentration terms, is denoted by Ash for the solvent SH, and AhjO is the value of in water at infinite dilution, then it follows that ... 

Because the parameters of 2-parameter correlations of G data are directly related to infinite-dilution values of the activity coefficients, our primary interest in Eq. (14.59) is its application to binary systems at infinite dilution of one of tlie constituent species. For this purpose, we divide Eq. (14.59) by the product xixi- For Cp independent of T (and thus with... 

Van Ness and Abbott, Int. DATA Ser., Ser. A, Sel. Data Mixtures, 1978 67 (1978)] and excess enthalpy data [Morris et al.,/, Chem. Eng. Data 20 403-T05 (1975)] are available. The VLE data are well correlated by the Margules equations. As noted in connection with Eq. (4-270), parameters Ai and A i relate directly to infinite dilution values of the activity coefficients. Thus, we have from the VLE data at 323.15 K ... 

In order for us to have flexibility in our modeling of natural water chemistry we need a way to obtain individual ion activity coefficients from mean values. To do so requires that we make an assumption, called the Macinnes convention (Macinnes 1919), which states = 7c - The convention is based on the observation that and Cr ions are of the same charge and nearly the same size, have similar electron structures (inert gas), and similar ionic mobilities. In support of this assumption, tracer diffusion coefficients, D°, of K+ and Cl" at infinite dilution are nearly equal at 19.6 and 20.3 X 10" cmVs (Lerman 1979). Also, limiting equivalent conductances, A°, of and Cl" are comparable at 73.50 and 76.35 cmV(ohm) (equiv.) at 25°C (Robinson and Stokes 1970),... 

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