Mixing, entropy ideal

The last term in Equation 12.16 accounts for an ideal entropy of mixing. This ideal mixing entropy reLects the random mixing of the hydrocarbon tails in the bulk hydrocarbon phase. 

The entropy term denoted by 1 has already been discussed. It enters in alone if no interactions occur between the solvent and the solute it has been previously termed (see p. 213) the ideal mixing entropy. The terms 2, 3 and 4 are additional entropy differences based on the fact that the volume, the heat capacity and the chemical constant of a molecule when surrounded by its own species assume values different from those it would assume if incorporated in solutibn in a medium of molecules of different kinds. Finally, 5 represents the energy term, which owes its existence to the difference in the play of forces between similar and dissimilar molecules. ... 

This is nothing else but equation (53). The comparison shows that the second coefficient B always contains a small share of ideal mixing entropy, expressed by the term whether or not it can be neglected in comparison with fc, depends upon the magnitude of that constant. 

Here, most definitions are the same as in Eq. (7.1) Va, Vb, and Vp denote the volumes of A-homopolymer, B-homopolymer, and particle, respectively. The first line is the ideal mixing entropy contribution, and the second line sums up the enthalpic contributions, taking into account that particles interact with the polymers only at the surfaces. The third line describes two additional contributions due to the nature of the particles. The function Whs(Carnahan-Starling [86] non-ideal contribution to the free energy of hard spheres, given by ... 

Xi is the molar fraction of component i with Y iXi = 1. The term is the Gibbs energy of the phase relative to the reference state for the components and G " is the contribution of ideal mixing entropy. 

Figure 8.1 The entropy of mixing (in units of R) as a function of mole fraction solute for ideal mixing and for the Flory-Huggins lattice model with n = 50, 100, and 500. Values are calculated in Example 8.1.

This result is nearly equal to 4.87 J K hmoT. the value that would be calculated for the entropy of mixing to form an ideal solution. We will show in Chapter 7 that the equation to calculate AmixSm for the ideal mixing process is the same as the one to calculate the entropy of mixing of two ideal gases. That is. AmixSm = -R. Vj ln.Yj. 

The ideal molar entropy of mixing is then given by... 

Secondly, if only ideality of the mixing entropy is considered, n = ni = and the Friunkin generahzed equation of state and adsorption isotherm are obtained, giving [15,26]... 

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. 

ENTROPY CHANGE DURING IDEAL MIXING OF GASES... 

Despite the fact that the mixing entropy is small for polymer blends, it is always positive and hence promotes mixing. Mixtures with no difference in interaction energy between components are called ideal mixtures. Let us denote the volume fraction of component A by — and the corresponding volume fraction of component B becomes = 1 — The free energy of mixing per site for ideal mixtures is purely entropic ... 

Ideal mixtures are always homogeneous as a result of the mixing entropy... 

In equation (2) Ghs and Gls are the standard Gibbs free energies in the absence of any interaction for Na molecules in the HS and LS states, respectively, r(nns) is an interaction term which reflects the departure of the system from an ideal solution. S mix is the mixing entropy. For a regular solution of molecules, S mix, is determined by... 

In this appendix, we shall discuss a system of ideal gases. We shall examine the suitability of the terms mixing entropy and mixing Gibbs energy, and the validity of the statement that the mixing process is essentially reversible , see, for example, Denbigh (1966). 

AH , and A5 are the changes in heat content and entropy due to adsorption as well as dilution to the bulk concentration under consideration. Assuming ideal mixing and hence neglecting the heat of dilution ... 

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