Activity coefficient pure condensed phases

The mathematical treatment of Sections 3.4—3.10 has been largely formal so far because only the activity or activity coefficients of pure condensed phases has been discussed up to this point In Eqs. (3.7.16) through (3.7.18) a procedure was set up for their determination by experiment. No method has yet been provided by which the activity coefficients or activities of species in solution can be determined experimentally. We now turn our attention to these matters. 

By way of review we see from Eq. (3.7.8b) that the equilibrium constant involves products of factors of the following forms (i) the quantities rs(T,P,q ) = Ys T, P, q )a (T, P), which relate to pure condensed phases, (ii) terms involving the activity coefficients yj(T, P,qj), which correct for gross deviations from ideal properties of species making up homogeneous solutions, (iii) terms involving a (7, P), which, by (3.5.17) or (3.5.20), relate to the activities and activity coefficients of jiure j at pressures other than one atmosphere, and (iv) the usual products [j leq that involve concentration units and which constitute the equi-... 

We here determine the activity coefficients for the undissolved species that are customarily omitted from the right-hand side of Eq. (3.4.11). This step is frequently summarized by the statement that the activity of all pure condensed phases is unity, whence these factors drop out. The degree to which this claim is tenable is examined below. 

Figure 1 represents the isotherms for two lipid components which are miscible in the condensed monolayer state. The major feature of the isotherms for the pure components (1 0, 0 1) is the transition region in which the surface pressure is independent of surface area here the limits of the transition region are at the low area end, Ac, and at the high area end, Ax. These areas are characteristic of each lipid and represent the area per molecule of the lipid in the condensed and vapor states (10). For an equimolar mixture of the two components (1 1), the surface pressure in the transition region depends on the surface area according to the phase rule (11, 12, 13, 14), two surface phases coexist here a condensed phase of lipids and the surface vapor phase. To obtain the activity coefficient of the ith component in the condensed phase the following relation may be used ... 

This leads to the easiest approach to understanding activities. The activity of a constituent is the ratio of the fugacity of that constituent to its fugacity in some other state, which we called a reference state. We then showed through consideration of the Lewis Fugacity Rule, which is an extension of Dalton s Law, that for ideal solutions of condensed phases, the activity of a constituent equals its mole fraction, if the reference state is the pure constituent at the same P and T. Deviations from ideal behaviour are then conveniently handled by introducing Henryan and Raoultian activity coefficients. 

When the standard states for the solid and liquid species correspond to the pure species at a pressure of 1 bar or at a low equilibrium vapor pressure of the condensed phase, the activities of the pure species at equilibrium are taken as unity at all moderate pressures. Consequently, the gas-phase composition at equilibrium will not be affected by the amount of solid or liquid present. At very high pressures, equation (2.8.1) must be used to calculate these activities. When solid or liquid solutions are present, the activities of the components of these solutions are no longer unity even at moderate pressures. In this case, to determine the equilibrium composition of the system, one needs data on the activity coefficients of the various species and the solution composition. 

For reactions involving only condensed phases, including those occurring in liquid solutions, which are our chief concern, the situation is very different. Three choices of standard state are in common use. For the solvent (i.e., the substance present in largest amount), the standard state almost universally chosen is the pure liquid. This choice is also often made for other liquid substances that are totally or largely miscible with the solvent. The activity scale is then related to the mole fraction, through the rational activity coefficient f which is unity for each pure substance. For other solutes, especially those that are solid when pure, or for ionic species in solution in a nonionic liquid, activity scales are used that are related either to the molar concentration or the molality, depending on experimental convenience. On these scales, the activity coefficients become imity in the limit of low concentration. 

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