Solutions, ideal regular

A similar evaluation for the solid solution starts with Eiq. (2.34), since the solid solution is regular and not ideal. This equation simplifies rapidly, since the standard state free energies of the components are in the solid phase in both the separate and mixed states, such that... 

Weber [2] proposed a formula to determine the maximum retrograde temperature, assuming that the impurity behaves ideally in liquid solution and regularly in solid phase ... 

Similarities in the solvent-solute solubility parameters allow a more negative Gibbs energy of mixing. If it is assumed that the solution is regular (A S ideal)... 

It was not necessary to assume ideal solution behavior to solve this problem. One could, for example, assume that the solution is regular, in which case y (and K ) would be a nonlinear function of the mole fractions. The calculation of the vapor- and liquid-phase mole fractions is then more complicated than was the case here however, the basis of the calculation, the equality of the fugacity of each species in both phases, remains unchanged. 

Hildebrand and Rotariu [14] have considered differences in heat content, entro])v and activity and classified solutions as ideal, regular, athermal, associated and solvated. Despite much fundamental work the theory of binary liquid mixtures is still e.ssentiaUy unsatisfactory as can be seen from the. systematic treatment of binar> mi.Ktures by Mauser-Kortiim [15]. The thermodynamics of mixtures is presented most instructively in the books of Mannchen [16] and Schuberth [17]. Bittrich et al. [17a] give an account of model calculations concerning thermophysical properties of juire and mixed fluids. 

Hildebrand has found experimentally that a large number of binary mixtures show a behavior which can be represented quite well by the laws of regular solutions. A regular solution is, by definition, one in which the partial entropies of the various components have ideal forms. In this section, we discuss some of the properties of regular solutions. 

Classically, one treats phases of two components as ideal, regular, or real solutions. Usually, however, one concentrates for the non-ideal case only on solutions of salts by discussing the Debye-Huckel theory. Polymer science, in turn, adds the effect of different molecular sizes with the Hory-Huggins equation as of basic importance (Chap. 7). Considerable differences in size may, however, also occur in small molecules and their effects are hidden falsely in the activity coefficients of the general description. 

Ashakawa et al. (1997) report CMC data as shown in the figure for mixtures of a partially fluorinated lithium decyl sulfate (1) and hthium tetradecyl sulfate (2). Analyze assuming ideal solution theory in the bulk solution and regular solution theory in the micelles. Show that an azeotrope is formed in this system. Plot x, as a funetion of Xj/(x, +... 

Although they are partially ideal systems, the athermal solutions are completely different in character from regular solutions while regular solutions consist of molecules of similar shape and size, the constituents of athermal solutions are polymers whose molecular weights are much larger than those of the solvents, which are in general common organic molecules. 

The lattice theory of solution is derived from several idealized assumptions. The assumptions that components A and B are the same size and have the same number of nearest neighbors, for example, are not applicable to real solutions. Ilie regular solution concept of Hildebrand is more versatile it takes into account a mixture of molecules of different sizes, where the principal idea is an ideal entropy of mixing at constant volume irrespective of heat. The activity coefficients in the form of (3.9) due to interaction between components A and B in a liquid mixture are derived by the following equations when the mixing term is expressed as a volume fraction ... 

The mixed cmc values for mixtures of DEFUMAC with a cationic hydrocarbon surfactant DTAC were determined by plotting equivalent conductivity versus the square root of concentration. The cmc values agreed reasonably well with cmc values calculated from the regular solution theory assuming an interaction parameter value of j8 = 1. The positive (3 value indicates a repulsive interaction between the two surfactants. Hence, the cationic-cationic surfactant mixture deviates more from the ideal regular solution theory than the cationic-nonionic system. 

Evaluate ASj for ideal solutions and for athermal solutions of polymers having n values of 50, 100, and 500 by solving Eqs. (8.28) and (8.38) at regular intervals of mole fraction. Compare these calculated quantities by preparing a suitable plot of the results. 

In the first category of solutions ( regular solutions ), it is the enthalpic contribution (the heat of mixing) which dominates the non-ideality, i.e. In such solutions, the characteristic intermolecular potentials between unlike species differ significantly from the average of the interactions between Uke species, i.e. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

In this case, the melting point of the ideal solid solution should increase linearly as the ration of B/A increases. However, it usually does not. Either a negative deviation or a positive deviation is regularly observed. 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

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 model beyond the ideal solution model is the regular solution model, first introduced by Hildebrant [9]. Here A mix, S m is assumed to be ideal, while A inix m is not. The molar excess Gibbs energy of mixing, which contains only a single free parameter, is then... 

The regular solution model (eq. 3.68) is symmetrical about xA = xB =0.5. In cases where the deviation from ideality is not symmetrical, the regular solution model is unable to reproduce the properties of the solutions and it is then necessary to introduce models with more than one free parameter. The most convenient polynomial expression with two parameters is termed the sub-regular solution model. 

The entropy of mixing of many real solutions will deviate considerably from the ideal entropy of mixing. However, accurate data are available only in a few cases. The simplest model to account for a non-ideal entropy of mixing is the quasi-regular model, where the excess Gibbs energy of mixing is expressed as... 

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