Allowing for non-ideality activity coefficients

In this chapter the relationship between activity and concentration is developed 

As defined, the activity has units of moles dm . Occasionally, and more rigorously, activities are defined in terms of molalities, m, where Sa = yAmA.The quantity Wa has units of moles kg and, unlike a concentration it Is temperature Independent. For aqueous solutions rr A [A] since one litre of water has a mass of approximately 1 kilogram. Both definitions will be used in this Primer. 

Clearly if Ya is unity then the solution is ideal. Otherwise the solution is nonideal and the extent to which ya deviates from unity is a measure of the solution s non-ideality. In any solution we usually know [A] but not either a a or Ya- However we shall see in this chapter that for the special case of dilute electrolytic solutions it is possible to calculate ya- This calculation involves the Debye-Hdckel theory to which we turn in Section 2.4. It provides a method by which activities may be quantified through a knowledge of the concentration combined with the Debye-Huckel calculation of ya- First, however, we consider some relevant results pertaining to ideal solutions and, second in Section 2.3, a general interpretation of Ya- 

Consider what happens when two separate solutions containing a and moles of A and B respectively are mixed together. The initial and final free energies will be given by  

We have therefore shown that the enthalpy of mixing is zero for ideal solutions. Physically this can be interpreted in the terms that the intermolecular forces between the molecules in the mixture are equal to those in the pure liquids. In other words A-A, A-B and B -B interactions are the same. Equality of interaction forces is therefore an alternative way of describing an ideal solution 

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Summary This chapter has presented a set of variations on the theme of free energy changes. We have seen how accurate values of AG° may be derived at any temperature, how this data may be summarized either as free energy functions or in terms of Ellingham diagrams, and how the data may be applied in a few instances. In virtually all cases, we have seen that activity can simplify the calculations of equilibrium constants and that allowances can always be made for non-ideal behaviour, assuming that activity coefficient data are available. Complete thermodynamic data have been published for relatively few compounds, however, and there are for example many common organic compounds for which only an enthalpy of formation has been determined. As more complete information is circulated, the number of applications of chemical... 

In both cases it is necessary to convert the concentrations of indicator in the two compartments into chemical activities by allowing for binding, or non-ideal behaviour of the indicator ion in the two compartments. It is here that the major problems arise for precise quantitation. The mitochondrial matrix compartment (or the bacterial cytosol) is about as far removed from an ideal solution as it is possible to be. If some 50% of the mitochondrial protein is soluble in the matrix, which typically has a volume of 1 /il/mg total protein, then this implies that protein in the matrix is present as a 50% solution, ignoring the additional metabolites and nucleotides. Little is known about activity coefficients under these conditions. The... 

It should be emphasised that the solvent activity coefficients recorded to date are of greatest value in reactions involving at least one ionic species as a reactant or product, in particular bimolecular nucleophilic attack by anions and molecular solvolyses producing ionic products. These reactions show the greatest sensitivity to solvent change and thus the relatively imprecise values of these activity coefficients do not endanger the validity of the interpretation. Allowance for solute non-ideality in terms of Debye-Huckel activity coefficients and on association can be made in principle, but is time consuming and requires both additional care and more experiments than have been done, indeed warranted, to date. 

The term general solution was introduced by Flory to characterize polymer solutions whose enthalpy of mixing is not zero. The model of general solutions borrows the formula of excess enthalpy from regular systems and the excess entropy from athermal solutions. Thus, a treatment of non-ideal polymer solutions arises which is simpler than the conventional methods applied to real systems this allows the deduction, on the basis of the known relationships, of the expressions of functions of deviation from ideality. Thus, for the activity coefficients of components in a binary system the following relations were established ... 

Since B and B2 were chosen so that all the relevant concentrations can be determined by U V/ vis spectroscopy, the unknowns in Eq. 5.16 are K -b and the activity coefficients. A reasonable assumption is that the activity coefficients for the B2 entities are the same as for the Bi entities in the new solution, becau.se aggregation and non-ideal behavior are related to molecular structure, and both Bi and B2 are anilines. Given this assumption, Eq. 5.16 reduces to Eq. 5.17. Now fCa.B2H- can be determined. The next step is to choose an even weaker aniline base, B3, which requires a higher percent acid for appreciable protonation, but for which the protonation state of B3 and B2 can both be measured in the same acidic solution. This allows calculation of Ka.B,n, and so on. 

Our present understanding of the thermodynamics of HNO3/H2SO4/ H2O ternary solutions under stratospheric conditions still depends to a high degree on predictions made by thermodynamic models, which allow to calculate the properties of non-ideal, i.e. highly concentrated, electrolytic solutions. The interactions between the species in such solutions are expressed in terms of activity coefficients (/). For example, the solubility of a species HX which dissolves and dissociates in solution can be calculated according to... 

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