Mixing, energy partial molar

Next we differentiate Eq. (8-44) with respect to 2, obtaining the partial molar energy of mixing of 2 in 1 ... 

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... 

Similar expressions can be derived for the partial molar Gibbs energy of mixing and the activity coefficient of component B. 

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... 

There have been many attempts to describe the process of mixing and solubility of polymer molecules in thermodynamic terms. By assuming that the sizes of polymer segments are similar to those of solvent molecules, Flory and Huggins derived an expression for the partial molar Gibbs free energy of dilution that included the dimensionless Flory Higgins interaction parameter X = ZAH/RT, where Z is the lattice coordination number. It is now... 

As already pointed out, Yu is 1 if a compound forms an ideal solution. In this rather rare case, the term RTkiyu, which we denote as partial molar excess free energy of compound i in solution t, Gpe, is 0. This means that the difference between the chemical potential of the compound in solution and its chemical potential in the reference state is only due to the different concentration of the compound i in the two states. The term R In xtf=S 1 expresses the partial molar entropy of ideal mixing (a purely statistical term) when diluting the compound from its pure liquid (xiL =1) into a solvent that consists of otherwise like molecules. 

Equilibrium Vaporization. The cesium release results presented in this chapter may also be used to demonstrate our earlier conclusion that equilbirium vaporization represents the upper limit for the fractional fission-product release as a function of sodium vaporization. Figure 6 shows three cesium release curves. Curve A was calculated from the Rayleigh Equation in conjunction with the partial molar excess free energy of mixing of infinitely dilute cesium—sodium solutions reported... 

The partial molar excess Gibbs free energy and partial molar excess enthalpy of mixing are defined by the following equations ... 

Gj -G° is the change in molar free energy of / due to the change in state from the standard state to the state of solution of a particular composition. This is called the partial molar free energy of mixing or relative partial molar free energy of i and is designated... 

This is called the relative integral molar free energy or the molar free energy of mixing. Hie method of tangential intercepts which we have applied for determination of partial molar quantities from the integral molar quantities can also apply to the relative quantities ... 

The chemical potential is defined as an intensive energy function to represent the energy level of a chemical substance in terms of the partial molar quantity of free enthalpy of the substance. For open systems permeable to heat, work, and chemical substances, the chemical potential can be used more conveniently to describe the state of the systems than the usual extensive energy functions. This chapter discusses the characteristics of the chemical potential of substances in relation with various thermodynamic energy functions. In a mixture of substances the chemical potential of an individual constituent can be expressed in its unitary part and mixing part. 

We also see that the excess free enthalpy GE is differentiated with respect to the temperature and the number of moles of the solution to give the excess entropy SF and the partial molar excess free energy of mixing RTlnyi as follows ... 

The Flory-Huggins theory is generally applied to define the thermodynamic properties of a polymer solution (I). It gives an expression for experimentally obtainable quantities such as the partial molar free energy of mixing. 

In case of a solution, like the FeO-MnO solid solution, the integral molar free energy of mixing would be related to the partial molar values, as per their definition, in the following manner ... 

Since the initial work of Smidsrod and Guillet numerous investigators have used I.G.C. to determine physicochemical parameters characterising the interaction of small amounts of volatile solutes with polymers Baranyi has shown that infinite dilution weight fraction activity coefficients, interaction parameters and excess partial molar heats of mixing can be readily determined with this technique. Partial molar heats and free energies of mixing, and solubility parameters of a wide variety of hydrocarbons in polystyrene and poly(methyl methacrylete) have been determined The temperature dependence of the interaction parameter between two polymers has also been studied... 

The contribution to the partial molar free energy arising from the residual (enthalpic and non-conformational entropic) partial molar free energy of mixing of the two monomers is small relative to all other terms in the monomer droplet phase. 

The quantities pj are the densities of the pure phases at the specified pressure p, that is, with attractive forces operating to achieve experimental densities the partial molar volumes of these pure phases are i)i = 1/pi. Similarly, the densities of the mixture correspond to the same pressure p. Rememhering Eq. (4.39), a way for this mixing free energy, Eq. (4.41), to achieve the form of the initial two terms of Eq. (4.38) is that the excess quantities within the brackets of Eq. (4.41) vanish ... 

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