Infinite dilution standard state

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

All data in Table IV-1 and Table lV-2 refer to a temperature of 298.15 K, the standard state pressure of 0.1 MPa and, for aqueous species and reactions, to the infinite dilution standard state (/ = 0). 

Since the value of an activity coefficient depends on the standard state, an activity coefficient based on (10.2.21) will differ numerically from one that is based on a pure-component standard state. To emphasize that difference, we make a notational distinction between the two we use y for an activity coefficient in a pure-component standard state and use y for an activity coefficient in the solute-free infinite-dilution standard state. Then for y, the generic definition of the activity coefficient (5.4.5) gives... 

At this point you should note that we have not used the infinite dilution standard state for aqueous solutes, as we will for other properties in Chapter 10. Having m- 0 in Equation (8.24) would obviously be inconvenient. 

In summary, then, for dissolved substances we use the ideal one molal standard state for Gibbs energy, and the infinite dilution standard state for enthalpy, volume and heat capacity. What about entropy ... 

Infinite dilution standard state whereby the standard slate value of fugacily or activity of a component at the temperature and pressure of the solution is given by the ratio of the fugacily or activity to the mole fiacUon" under conditions of infinite dilution... 

Case 2 Pure solute i does not exist as a liquid at P and T-, an infinite dilution standard state is necessary (item (5), Table 3.3.2). In general, such standard state values dependent on phase j. Therefore, from relation (3.3.72),... 

If the solute i Is such that an infinite dilution standard state is necessary, then, from relation (3.3.79), we get... 

The estimation of Ki or i2 for cases where an infinite dilution standard state for the solute(s) is employed, can be made from equation (4.1.1) as fallows ... 

All in aqueous solution at 25 C standard states are IM ideal aqueous solution with an infinitely dilute reference state, and for water the pure liquid. 

The standard chemical potential // q corresponds to the pure oil phase, the standard chemical potential /i° () refers to the standard state of the monomeric alcohol m pure alcohol, and the standard chemical potentials //g0 and / wo °f the surfactant and water, respectively, correspond to their infinitely dilute solution states in the oil phase. For the droplets, the chemical potential is written as... 

Many nonionizable organic solutes in water are described thermodynamically on the mole fraction scale, although their solubilities may commonly be reported in practical units, for example, molality. [Refer to Schwarzenbach et al. (1993) and Klotz (1964) for detailed discussion of such aqueous solutions.] Here, the standard state is the pure liquid state of the organic solute, that is, Xj = 1. The reference state is Xi - 1, that is, a solution in which the organic solute molecules interact with one another entirely. Activity coefficients of solute molecules in dilute aqueous solutions are generally much greater than unity for this reference state choice, jc, 1. For example, with this reference state, aqueous benzene has an experimental infinitely dilute solution activity coefficient, T nzeno of 2400 for an infinite dilution reference state, jc, - 0, the activity coefficient would be approximately 1 (Tanford, 1991). 

In summary, thermodynamic models of natural water systems require manipulation of chemical potential expressions in which three concentration scales may be involved mole fractions, partial pressures, and molalities. For aqueous solution species, we will use the moial scale for most solutes, with an infinite dilution reference state and a unit molality standard state (of unit activity), l or the case of nonpolar organic solutes, the pure liquid reference and standard states are used. Gaseous species will be described on the partial pressure (atm — bar) scale. Solids will be described using the mole fraction scale. Pure solids (and pure liquids) have jc, = 1, and hence p, = pf. 

The next step is to perform a simultaneous regression of NaCl(aq) apparent molal volumes from 25-350 C. Over this wide range of temperature, however, and particularly above 300 C, standard-state properties based on the infinitely dilute reference state exhibit a very complex behavior (7,8), which is related to various peculiarities of the solvent. Thus in their representation of NaCl(aq) volumetric properties, Rogers and Pitzer (7) adopted a reference composition of a hydrated fused salt, NaCl IOH2O, to minimize the P and T dependence of the reference state volume and to adequately fit volumetric ta to 300°C and 1 kb. In this study the (supercooled) fused salt is used as the reference state. The equation for the apparent molal volume on this basis can be easily derived from that for the excess Gibbs energy of Pitzer and Simonson (, and is given by ... 

Of more interest are solubility calculations in the ternary system NaCl-KCl-H20. The equations for the excess Gibbs energy and activity coefficients in a mixture of a solvent and two salts with a common ion, MX and NX, and with cation fraction F of M are given by Pitzer and Simonson (5). Their equation for the activity coefficient of the solute MX in the ternary mixture MX-NX-H2O based on a pure fused salt standard state can be converted to one based on the infinitely dilute reference state. This is given by ... 

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.

Infinite-diluiion standard states. When the standard state is based on an infinitely dilute solution, then the standard-state fugacity is a Henry s constant. In 10.2 we introduced two kinds of Henry s constants for multicomponent mixtures the solute-free form Hj-g and the reference-solvent form H,y. For binary mixtures these two are the same. Here we use Hj-g to illustrate the response to changes in T and P analogous expressions apply for Hjy. 

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

However, as can be seen in Figure 6.15, which is a graph of the fugacity of HC1 against molality in dilute aqueous solutions of HC1 (near. i = 1), f2 approaches the m axis with zero slope. This behavior would lead to a Henry s law constant, kn.m = 0. given the treatment we have developed so far. Since the activity with a Henry s law standard state is defined as a —fi/kwnu this would yield infinite activities for all solutions. 

Thus, with a Henry s law standard state, H° is the enthalpy in an infinitely dilute solution. For mixtures, in which we choose a Raoult s law standard state for the solvent and a Henry s law standard state for the solute, we can... 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

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