Mixed thermodynamic function

Figure 7.2 Excess thermodynamic functions at 7= 298.15 K for. Y1C10H22 +. Y2C6H14, an example of a system where nonpolar chain-like molecules are mixed.

Figure 7.3 Excess thermodynamic functions at 7"= 318.15 K for x +. X2CH3CN, an example of a system in which polar molecules are mixed...

In systems with different components, the values of the thermodynamic functions depend on the nature and number of these components. One distinguishes components forming independent phases of constant composition (the pure components) from the components that are part of mixed phases of variable composition (e.g., solutions). 

In the case of reciprocal systems, the modelling of the solution can be simplified to some degree. The partial molar Gibbs energy of mixing of a neutral component, for example AC, is obtained by differentiation with respect to the number of AC neutral entities. In general, the partial derivative of any thermodynamic function Y for a component AaCc is given by... 

Local association of the reduced cation and the oxygen vacancy is clearly suggested by the thermodynamics of the hypo-stoichiometric mixed oxides (Ui yPUy)02 x, where the thermodynamic functions do not depend on x and y separately, but rather on a quantity, called plutonium valence , which contains the ratio x/ y73,87) Q sters consisting of this association have been proposed in order to explain the thermodynamics of actinide hypostoichiometric dioxides. 

The original densities, heat capacities per unit volume and enthalpies of mixing from which the various thermodynamic functions are calculated for the ternary systems are given elsewhere. ... 

The magnitude and sign of the distribution constants and of the thermodynamic functions of the transfered solute to the mixed micelle, when compared with those predicted from the binary systems, indicate that the formation of a mixed micelle between BE and NaDec is a highly favorable event. 

Excess Thermodynamic Functions The excess molar thermodynamic function Z is defined as the difference between AmjXZm, the change in Zm for mixing components to form a real solution, and AmjxZ , the change in Zm to form the ideal solution. Thus,... 

The thermodynamic functions for the gas phase are more easily developed than for the liquid or solid phases, because the temperature-pressure-volume relations can be expressed, at least for low pressures, by an algebraic equation of state. For this reason the thermodynamic functions for the gas phase are developed in this chapter before discussing those for the liquid and solid phases in Chapter 8. First the equation of state for pure ideal gases and for mixtures of ideal gases is discussed. Then various equations of state for real gases, both pure and mixed, are outlined. Finally, the more general thermodynamic functions for the gas phase are developed in terms of the experimentally observable quantities the pressure, the volume, the temperature, and the mole numbers. Emphasis is placed on the virial equation of state accurate to the second virial coefficient. However, the methods used are applicable to any equation of state, and the development of the thermodynamic functions for any given equation of state should present no difficulty. 

The changes of the thermodynamic functions on mixing of ideal gases... 

It can easily be shown that simple thermodynamic relationships also hold for changes of thermodynamic functions on mixing. For example,... 

In conclusion, the partial molar quantity in thermodynamics functions consists of its unitary term and its mixing term as shown above. 

Figure 31. Excess thermodynamic functions of mixing for ethyl alcohol + water mixtures at 298-15 K.

The TNAN aqueous mixtures are characterized by the following conditions for the excess molar thermodynamic functions of mixing GE <0 and i//E > T- SE. ... 

This chapter is concerned primarily with the computation of potentials of a cell using the hydrogen electrode as a probe for studying ionic equilibrium processes in mixed-organic-aqueous solvent systems. Computation of a number of other thermodynamic functions of the ionic process under investigation or of the solvent used is rather straightforward once the standard potential of the measuring cell has been calculated. 

Electromotive Forces and Thermodynamic Functions of the Cell Pt, H2 HBr(m), X% Alcohol, Y% Water AgBr-Ag in Pure and Mixed Solvents... 

Thermodynamic effects of directional forces in liquid mixtures.— The theory applied to pure liquids in the last two sections can be generalized to liquid mixtures and can be used to discuss the effects of directional forces on the thermodynamic functions of mixing. Classical statistical mechanics leads to a complete expression for the free energy of a multicomponent system in terms of the intermolecular energies Ust for all pairs of components s and t. Each Ust can be expanded in the general manner (2.1), so that it is separated into a spherically symmetric part and various directional terms. 

The thermodynamic functions of mixing two substances, a and A, are conveniently expressed in terms of the difference in solubility parameters (5a Sb)- The applicability of this treatment is limited to systems for which the interaction between a and b molecules is the geometric mean of the separate interactions among a molecules and among b molecules. This is rarely true for H bonding liquids. 

We have already introduced in 3 of chap. XX the thermodynamic functions of mixing in the case of perfect solutions. These definitions are easily extended to non-ideal solutions. The results obtained provide a useful basis for the classification of non-ideal solutions which will be made in paragraph 5 of this chapter. 

The difference between the thermodynamic function of mixing (denoted by superscript M) for an actual system, and the value corresponding to an ideal solution at the same T and jp, is called the thermodynamic excess function (denoted by superscript E). This quantity represents the excess (positive or negative) of a given thermodynamic property of the solution, over that in the ideal reference solution. nnhn< ... 

It will be seen, by reference to tables 7.2 and 7.1, that quite generallj" the thermodynamic excess function is the difference between the thermodynamic function of mixing (table 7.2) for the system concerned, and the same function for an ideal system (table 7.1). 

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