Gibbs energy ideal

Evaluation of the integrals requires an empirical expression for the temperature dependence of the ideal gas heat capacity, (3p (8). The residual Gibbs energy is related to and by equation 138 ... 

The entropy and Gibbs energy of an ideal gas do depend on pressure. By equation 85 (constant T),... 

For the Gibbs energy of an ideal gas mixture, — T the parallel relation for partial properties is equation 149 ... 

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 ... 

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

Cmpd. no. Name Formula CAS no. Mol wt Ideal gas enthalpy of formation, J/kmol X lE-07 Ideal gas Gibbs energy of formation, J/kmol X lE-07 Ideal gas entropy, J/(kmol-K) X lE-05 Standard net enthalpy of combustion, J/kmol X lE-09... 

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. 

The oxidation of nickel-copper alloys provides an example of die dependence of the composition of the oxide layer on the composition of the alloy. Nickel-copper alloys depart from Raoult s law, but as a first approximation can be taken as ideal. The Gibbs energy change for the reaction... 

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... 

The standard Gibbs energy of formation of NaCl is — 384 kJ mol 1 and that of NiCl2 is — 62kJmol 1. Calculate the ideal voltage of a ZEBRA cell. 

Using the ideal gas law the Gibbs energy expression becomes... 

For any single-component system such as a pure gas the molar Gibbs energy is identical to the chemical potential, and the chemical potential for an ideal gas is thus expressed as... 

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 ... 

The partial molar Gibbs energy of mixing of a component i in a non-ideal mixture can in general be expressed in terms of activity coefficients as... 

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... 

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