Enthalpy regular solution

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. ... 

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,... 

Thus the integral molar excess free energy of mixing as well as the enthalpy of mixing are independent of temperature for a regular solution. 

Still, the strain enthalpy is of particular importance. An elastic continuum model for this size mismatch enthalpy shows that, within the limitations of the model, this enthalpy contribution correlates with the square of the volume difference [41,42], The model furthermore predicts what is often observed experimentally for a given size difference it is easier to put a smaller atom in a larger host than vice versa. Both the excess enthalpy of mixing and the solubility limits are often asymmetric with regard to composition. This elastic contribution to the enthalpy of mixing scales with the two-parameter sub-regular solution model described in Chapter 3 (see eq. 3.74) ... 

The first term is the ideal entropy of mixing while the second term is the enthalpy of mixing in the regular solution approximation ... 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

Consideration of the thermodynamics of nonideal mixing provides a way to determine the appropriate form for the activity coefficients and establish a relationship between the measured enthalpies of mixing and the regular solution approximation. For example, the excess free energy of mixing for a binary mixture can be written as... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

One of the approaches to calculating the solubility of compounds was developed by Hildebrand. In his approach, a regular solution involves no entropy change when a small amount of one of its components is transferred to it from an ideal solution of the same composition when the total volume remains the same. In other words, a regular solution can have a non-ideal enthalpy of formation but must have an ideal entropy of formation. In this theory, a quantity called the Hildebrand parameter is defined as ... 

Figure 7.15. Phase diagram of a phase showing spinodal decomposition, (a) In a regular solution having positive mixing enthalpy, has an opposite sign on the left and...

A particularly simple approximation known as regular-solution theory was developed by Hildebrand and co-workers [J. H. Hildebrand. /. Am. Chem. Soc. 51, 66-80 (1929)]. The regular-solution model assumes that the excess enthalpy of mixing can be represented as a simple one-parameter correction... 

C contains the formation entropy and r is the coordination number of the vacancy. Thus, AJf j/r is the enthalpy per V-A bond in the sense of the thermodynamics of regular solutions [H. Schmalzried, A. Navrotsky (1975)]. For random A-B distributions, the probability of the configuration (/ a b) in the nearest neighbor shell of the vacancy V is... 

Zinc and cadmium liquid alloys conform to regular solution behaviour. The following table shows the relative integral molar enthalpies (or the molar heats of mixing) at various zinc concentrations at 723K. 

For so-called regular solutions, in which small solute molecules disperse randomly among like-size solvent molecules, AS° can be taken as zero [14]. The enthalpy change AH% for transferring (mixing) pure solute of molar volume Vi into solvent p at high dilution is approximately [14]... 

For regular solutions [i , the partial free enthalpy (chemical potential) of substance B in solution, calculated with respect to the solid state, also contains the partial heat of mixing Au (the entropy is equal to that of the ideal case). From the expression for A U on p. 358 we have for the partial heat of mixing ... 

Table G. 1 reproduces values calculated by Miedema s model (Niessen et al. 1983) for the partial enthalpy of solution at infinite dilution of a liquid metal solute i in a liquid metal solvent i, AH, (in kJ/mole). For a i-j alloy, the regular solution parameter k can be approximated by [AHj(j( + AHJ(l)]/2.

The Flory-Huggins model differs from the regular solution model in the inclusion of a nonideal entropy term and replacement of the enthalpy term in solubility parameters by one in an interaction parameter x- This parameter characterizes a pair of components whereas each S can be deduced from the properties of a single component. 

For regular solutions the enthalpy of mixing is the only cause of departure from ideality, and... 

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