Types of Ideal Solutions

The concept of ideal solutions (41) was used by the industry early in the period covered by this discussion. Hydrocarbons follow this type of behavior with reasonable accuracy at pressures somewhat above their vapor pressures. However, important divergences occur at higher pressures. Serious deviations from ideal solutions are experienced for components at reduced temperatures markedly greater than unity. Lewis (48) proposed a modified type of ideal solution by neglecting the volume of the liquid phase. This modification simplified the application of the concept. The Lewis generalization has been widely employed by the industry. 

In this chapter, we have discussed three types of ideal solutions. We stress here that the sources of ideality are different for each case. All of the three cases can be derived from the KB theory, specifically, from the relation (5.58), which we rewrite as... 

In the previous chapter, we described three types of ideal solution, and the conditions under which these behaviors are attained. In this chapter, we discuss... 

TYPES OF IDEAL SOLUTIONS 10.2.1. Ideal Gaseous Solutions... 

The real usefulness of the ideal solution or ideal mixing concept is that it serves as a model with which real solutions are compared. Solute activities are compared to the activities they would have if the solution were ideal, and this ratio is called an activity coefficient. Care is required in using this number, however, because the two types of ideal solution behavior described above give rise to two types of activity coefficients (still more types will be introduced later). 

Ideal solutions have proved to be a very useful reference point for the analysis of real data on solutions obtained by inversion of FST (Ben-Naim 2006). They can also be used to provide approximate behavior in situations where the required experimental data are not available. In principle, ideal behavior will depend on the concentration scale used. The most common type of ideal solution involves species that are fuUy miscible and where the composition is described by mole fractions. Ideal solutions of this type are characterized by chemical potentials of the form = d nx, together with zero excess enthalpies and volumes of solution for the whole composition range. This is also referred to as symmetric ideal (SI) behavior. Application of the above conditions in Equations 1.54 provides the following general relationships for any number of components (Ploetz, Bentenitis, and Smith 2010b) ... 

A particular type of nonideal solution is the regular solution which is characterized by a nonzero enthalpy of mixing but an ideal entropy of mixing. Thus, for a regular solution,... 

The simplest solution one can imagine is a mixture of ideal gases. Let us simplify the case by assuming only two types of ideal gas molecules, A and B, in the mixture. The total pressure in this case is the sum of the partial pressures of the two components (this is termed Dalton s law). Thus,... 

Strong Electrolytes. Solutes of this type, such as HCl, are completely dissociated in ordinary dilute solutions. However, their colligative properties when interpreted in terms of ideal solutions appear to indicate that the dissociation is a little less than complete. This fact led Arrhenius to postulate that the dissociation of strong electrolytes is indeed incomplete. Subsequently this deviation in colligative behavior has been demonstrated to be an expected consequence of interionic attractions. 

This section is devoted to illustrating explicitly the three fundamentally different types of ideal mixtures. The first and simplest case is that of the ideal-gas (IG) mixtures, which, as in the case of an ideal gas, are characterized by the complete absence (or neglect) of all intermolecular forces. This case is of least importance in the study of solution chemistry. 

It is convenient to represent the departure from both types of ideality (ideal gas law and ideal gas solution) by defining the following mixture fugacity coefficients. 

The occurrence of all three types of ideality can be demonstrated by the use of Eq. (4.88) from the Kirkwood-Buff theory of solutions. We limit the discussion to a two-component system ... 

Before studying the characteristics of mixtures which deviate markedly from those just described, let us consider the equilibria for the limiting case of mixtures whose vapors and liquids are ideal. The nature of ideal solutions and the types of mixtures which approach ideality were discussed in Chap. 8. 

When gases that are somewhat soluble in a Hquid concentrate are used, both concentrate and dissolved gas are expeUed. The dissolved gas then tends to escape into the atmosphere, dispersing the Hquid into fine particles. The pressure within the container decreases as the product is dispersed because the volume occupied by the gas increases. Some of the gas then comes out of solution, partially restoring the original pressure. This type of soluble compressed gas system has been used for whipped creams and toppings and is ideal for use with antistick cooking oil sprays. It is also used for household and cosmetic products either where hydrocarbon propeUants cannot be used or where hydrocarbons are undesirable. 

Most of the assumptions are based on idealized models, indicating the limitations of the mathematical methods employed and the quantity and type of experimental data available. For example, the details of the combinatorial entropy of a binary mixture may be well understood, but modeling requires, in large measure, uniformity so the statistical relationships can be determined. This uniformity is manifested in mixing rules and a minimum number of adjustable parameters so as to avoid problems related to the mathematics, eg, local minima and multiple solutions. 

The simplest type of solutions which exhibit non-randomness are those in which the non-randomness is attributable solely to geometric factors, i.e. it does not come from non-ideal energetic effects, which are assumed equal to zero. This is the model of an athermal solution, for which... 

Equation 13 has an important implication a clathrate behaves as an ideally dilute solution insofar as the chemical potential of the solvent is independent of the nature of the solutes and is uniquely determined by the total solute concentrations 2K yK1.. . 2x yKn in the different types of cavities. For a clathrate with one type of cavity the reverse is also true for a given value of fjiq (e.g. given concentration of Q in a liquid solution from which the clathrate is being crystallized) the fraction of cavities occupied 2kVk s uniquely determined by Eq. 13. When there are several types of cavities, however, this is no longer so since the individual occupation numbers 2k2/ki . ..,2k yKn, and hence the total solute concentration... 

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