Gibbs function of mixing

Considerable information concerning structural effects on aqueous salt solutions has been provided by studies of the properties of mixed solutions (Anderson and Wood, 1973). In a mixed salt solution prepared by mixing YAm moles of a salt MX (molality m) with Yhm moles of a salt NX (molality m) to yield m moles of mixture in 1 kg of solvent, if W is the weight of solvent, the excess Gibbs function of mixing Am GE is given by (19) where GE is the excess function for... 

To verify the thermodjuamic consistency between the Gibbs function of mixing and the enthalpj of mixing of carbon tetrachloride + cyclohexane. 

The excess Gibbs function of mixing G for carbon tetrachloride -j-cydohexane has been determined at several temperatures by Scatchard, Wood, and Mochel (J. Amer. Chem. Soc. 1939, 61, 3206). Their results can be represented by the relation (compare problem 69)... 

In eq 5.71, i) is a constant that depends on the particular equation of state used and Gm is an excess Gibbs function of mixing obtained from an activity coefficient model. Activity coefficients are usually obtained from measurements of (vapour-f liquid) equilibria at a pressure relatively low compared with the requirement of eq 5.67 for which p- ao the activity coefficients are tabulated, for example, those in the DECHEMA Chemistry Data Series. This distinction in pressure is particularly important because the excess molar Gibbs function of mixing, obtained from experiment and estimated from an equation of state, depends on pressure d(G /7 r)/d/)<0.002MPa for (methanol-f benzene) at a temperature of 373 K. Equation 5.71 does not satisfy the quadratic composition dependence required by the boundary condition of eq 5.3. However, equations 5.70 and 5.71 form the mixing rules that have been used to describe the (vapour + liquid) equilibria of non-ideal systems, such as (propanone + water), successfully in this particular case the three-parameter Non-Random Two Liquid (known by the acronym NRTL) activity-coefficient model was used for G and the value depends significantly on temperature to the extent that the model, while useful for correlation of data, cannot be used to extrapolate reliably to other temperatures. 

At the end of this part, we would like to emphasize two important facts First, because the F-H theory is a theory of regular polymer solutions and the crossinteraction term can be expressed as a geometric average of homo-interactions, the Gibbs function of mixing can be decomposed into parts corresponding to the pure components and to the entropy of mixing. Consequently, it is possible to predict the properties of polymer solutions at a semiquantitative level on the basis of the... 

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

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. 

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... 

The way we wrote 3G in Equation (5.13) suggests the chemical potential // is the Gibbs function of 1 mol of species i mixed into an infinite amount of host material. For example, if we dissolve 1 mol of sugar in a roomful of tea then the increase in Gibbs function is /x,sugar> - An alternative way to think of the chemical potential // is to consider dissolving an infinitesimal amount of chemical i in 1 mol of host. 

Fig. 37. A portion of the Gibbs energy of mixing isotherm for a Hg-Te melt at 670°C as a function of the atom fraction of the component. Calculated with the same interaction parameters as used for Fig. 36.

In equation 33, the superscript I refers to the use of method I, a T) is the activity of component i in the stoichiometric liquid (si) at the temperature of interest, AHj is the molar enthalpy of fusion of the compound ij, and ACp[ij] is the difference between the molar heat capacities of the stoichiometric liquid and the compound ij. This representation requires values of the Gibbs energy of mixing and heat capacity for the stoichiometric liquid mixture as a function of temperature in a range for which the mixture is not stable and thus generally not observable. When equation 33 is combined with equations 23 and 24 in the limit of the AC binary system, it is termed the fusion equation for the liquidus (107-111). 

Figure 2F-1 shows the Gibbs energy of mixing, AG, as a function of volume fraction for a binary system with two liquid phases I and II in equilibrium. 

Figure 2F-1. Gibbs Energy of Mixing as a Function of Volume Fraction.

Figure 6-5. Reduced molar Gibbs energy of mixing AG "IRT as a function of the volume fraction 02, of solute monomeric unit with different interaction parameters xo and degrees of polymerization Xi of the solute in low-molecular-weight solvents (Xi = 1). Calculations according to Equation (6-32) with a = 0.

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