Ideal solutions Gibbs energy

The excess Gibbs energy is of particular interest. Equation 160 may be written for the special case of species / in an ideal solution, with replaced by xj in accord with the Lewis-RandaH rule ... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

The residual Gibbs energy and the fugacity coefficient are useful where experimental PVT data can be adequately correlated by equations of state. Indeed, if convenient treatment or all fluids by means of equations of state were possible, the thermodynamic-property relations already presented would suffice. However, liquid solutions are often more easily dealt with through properties that measure their deviations from ideal solution behavior, not from ideal gas behavior. Thus, the mathematical formahsm of excess properties is analogous to that of the residual properties. 

Thus the formation of an ideal solution from its components is always a spontaneous process. Real solutions are described in terms of the difference in the molar Gibbs free energy of their formation and that of the corresponding ideal solution, thus ... 

Gibbs free energy, 311 molar volume, 151 ideal gas law, 147 ideal solution, 331 ilmenite, 662 iminodisuccinate ion. 675 implant, 344 incandescence, 8, 647 inch, A4... 

Solntions in which the concentration dependence of chemical potential obeys Eq. (3.6), as in the case of ideal gases, have been called ideal solutions. In nonideal solntions (or in other systems of variable composition) the concentration dependence of chemical potential is more complicated. In phases of variable composition, the valnes of the Gibbs energy are determined by the eqnation... 

Here G is the Gibbs free energy of the system without external electrostatic potential, and qis refers to the energy contribution coming from the interaction of an apphed constant electrostatic potential s (which will be specified later) with the charge qt of the species. The first term on the right-hand side of (5.1) is the usual chemical potential /r,(T, Ci), which, for an ideal solution, is given by... 

The Gibbs energy of mixing of an ideal solution is negative due to the positive entropy of mixing obtained by differentiation of Ald.xGm with respect to temperature ... 

Figure 3.3 Thermodynamic properties of an arbitrary ideal solution A-B at 1000 K. (a) The Gibbs energy, enthalpy and entropy, (b) The entropy of mixing and the partial entropy of mixing of component A. (c) The Gibbs energy of mixing and the partial Gibbs energy of mixing of component A.

For a large number of the more commonly used microscopic solution models it is assumed, as we will see in Chapter 9, that the entropy of mixing is ideal. The different atoms are assumed to be randomly distributed in the solution. This means that the excess Gibbs energy is most often assumed to be purely enthalpic in nature. However, in systems with large interactions, the excess entropy may be large and negative. 

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 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... 

For an ideal solution AmixG = -T Amjx,V and the partial molar Gibbs energy of mixing of the solute and solvent is obtained from eq. (9.57) as... 

A binary ionic solution must contain at least three kinds of species. One example is a solution of AC and BC. Here we have two cation species A+ and B+ and one common anion species C . The sum of the charge of the cations and the anions must be equal to satisfy electro-neutrality. Hence NA+ + NB+ = N(. = N where NA+, AB+ and Nc are the total number of each of the ions and N is the total number of sites in each sub-lattice. The total number of distinguishable arrangements of A+ and B+ cations on the cation sub-lattice is M/N A, JVg+ . The expression for the molar Gibbs energy of mixing of the ideal ionic solution AC-BC is thus analogous to that derived in Section 9.1 and can be expressed as... 

The first term on the right-hand side is in this ideal solution approach given by the standard Gibbs energy of oxidation... 

Solid electrolytes are frequently used in studies of solid compounds and solid solutions. The establishment of cell equilibrium ideally requires that the electrolyte is a pure ionic conductor of only one particular type of cation or anion. If such an ideal electrolyte is available, the activity of that species can be determined and the Gibbs energy of formation of a compound may, if an appropriate cell is constructed, be derived. A simple example is a cell for the determination of the Gibbs energy of formation of NiO ... 

The papers of Wagner and Schottky contained the first statistical treatment of defect-containing crystals. The point defects were assumed to form an ideal solution in the sense that they are supposed not to interact with each other. The equilibrium number of intrinsic point defects was found by minimizing the Gibbs free energy with respect to the numbers of defects at constant pressure, temperature, and chemical composition. The equilibrium between the crystal of a binary compound and its components was recognized to be a statistical one instead of being uniquely fixed. 

As in the nonelectrolyte case, the problem of representing the thermodynamic properties of electrolyte solutions is best regarded as that of finding a suitable expression for the non-ideal part of the chemical potential, or the excess Gibbs energy, as a function of composition, temperature, dielectric constant and any other relevant variables. 

Assuming this standard state, the AC° value expresses a change in the Gibbs energy of adsorption of one molecule B upon being moved from the hypothetical ideal solution onto the electrode surface. This enables the particle-particle interactions on the surface to be separated from any other interactions and to be included in the term/(/i). 

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