Activity coefficients Henryan

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. 

Mole Fraction—Molality Conversion for Henryan Activity Coefficients... 

Note that the first of these is essentially the same as the equation derived in 12.4.5 (I = ln(l + 0.0180153m)) for the conversion of Henryan activity coefficients of nonelectrolytes from the molality scale to the mole fraction scale, the only difference being the introduction of u. 

But we do have a choice as to what kind of activity coefficient we want to use, Raoultian or Henryan. You might think that if the standard state consists of pure i, normally a pure solid or liquid, it might be difficult to use a dilute solution (Henryan) standard state. However, using hypothetical states makes it quite simple, and quite instmctive. But first we consider the Raoultian standard state. 

Figure 8.4 Henryan activity and activity coefficient data from Figure 8.3, with the Henryan slope normalized to 1.0.

In this case, in which we have continued our example of a regular solution having Wq = 2000Jmol", the solution does not deviate from the ideal very greatly until molalities well above 1 m. Activity coefficients based on mole Ifactions and molalities are shown in Table 8.3. The reason for two slightly different values of 7h> ynx nd y, is that molality is not exactly proportional to mole fraction except in the limit of infinite dilution, so that a Henryan tangent... 

It will be useful to have an expression for the Gibbs energy of mixing of real solutions. This is a bit more complicated for aqueous systems which are unsymmetrical, that is, which have different standard states for the solvent and solute, and a completely different method of expressing deviations from ideality - osmotic coefficients for the solvent, and Henryan activity coefficients for the solutes. This development follows Pitzer (1991). 

An interesting application of regular solution theory is presented by Nesbitt (1984). He shows that activity coefficients for COj in aqueous NaCl solutions to quite high temperatures ( 500°C) and NaCl concentrations ( 6 m) can be fit very well by a slight modification of (10.98). As written, the activity coefficients in (10.98) are based on Raoultian activities that is, 7b 1 as Xg 1. Solubility studies on the other hand normally use Henryan coefficients, where 7b 1 as Wb 0, where is the molality of the solute. 

The Debye-Hiickel equation in terms of stoichiometric mean ionic activity coefficients is (where yn indicates it is a Henryan activity coefficient)... 

The excess term in the chemical potential = /xa — Ma hence, RT In fA is obtained from AmG and is ° W(1 —xa). This term goes to zero when xa 1 (cf. Raoult s law). The activity coefficient just considered therefore, is referred to as the Raoultian activity coefficient. When xa 0 it is constant (cf. Hemy s law). The displacement of the constant W from the term to the /x° term makes possible another normalization method, which is advantageous for describing dilute states. The first normalization chosen above and characterized by 1a —1 for xa 1 is known as the Raoultian normalization, and the second possibility with fA 1 for xa 0 as the Henryan normalization. There are then two equivalent representations of /xA) namely as + RTlnxA -I- RTln fA or as -h RTlnxA + RTln fA- In the regular model /Xa — W and, hence, In fA = W(xa — 2xa)/RT while... 

Figure 8.7 Henryan activity of sucrose, Raoultian activity of water, and osmotic coefficients in sucrose solutions at 25°C. The inset is an enlargement of the region up to 1 molal, and the circle shows the ideal one molal standard state.

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