Excess activation free energy

The excess activation free energy AG, enthalpy Aff, and entropy A5, and their partial molar quantities for alcohols AG, A//, and A5 were also calculated for the dominating processes with T, in methanol, ethanol, and 1-propanol water mixtures [67-69] and are depicted in Figure 6.6. These thermodynamic quantities were calculated according to the Eyring transition state theory [93]. Based on the curves in Figure 6.6 characteristic molar fraction values (0.30,0.18, and 0.14 for methanol, ethanol, and 1-propanol water mixtures, respectively) were also reported above and below which the behavior of the partial molar excess activation quantities... 

FIGURE 6.6 Concentration dependence of the (a) excess activation free energy AG, enthalpy MP, and entropy AS, and (b) excess activation free energy of alcohol AG, enthalpy A//, and entropy AS for methanoFwater, ethanol/water, and 1-propanol/water mixtures at 25°C for the processes with the relaxation times (Reprinted from Sato, T., Chiba, A., and Nozaki, R., J. Chem. Phys., 113, 9748, 2000. With permission.)... 

For a detailed discussion of the calculation of activities (and excess Gibbs free energies) from freezing point measurements, see R. L. Snow. J. B. Ott. J. R. Goates. K. N. Marsh, S. O Shea, and R. N. Stokes. "(Solid + Liquid) and (Vapor + Liquid) Phase Equilibria and Excess Enthalpies for (Benzene + //-Tetradecane), (Benzene + //-Hexadecane). (Cyclohexane + //-Tetradecane), and (Cyclohexane +//-Hexadecane) at 293.15, 298.15, and... 

Since these mixing processes occur at constant pressure, // is the heat evolved or absorbed upon mixing. It is usually measured in a mixing calorimeter. The excess Gibbs free energy, is usually obtained from phase equilibria measurements that yield the activity of each component in the mixtureb and S is then obtained from equation (7.17). The excess volumes are usually obtained... 

For correlation of solubility, the correct thermodynamic quantities for correlation are the activity coefficient y, or the excess Gibbs free energy AG, as discussed by Pierotti et al. (1959) and Tsonopoulos and Prausnitz (1971). Examples of such correlations are given below. 

The Excess Gibbs Free Energy and the Activity Coefficients of the Nd(N03)3-HN03-H20 System at 25°C... 

Many mixtures of interest in the chemical indu.stry exhibit strong nonidealities that can not be described by the EOS with any form of the van der Waals mixing rules. Mixing rules that combine equations of state with liquid excess Gibbs free-energy (or, equivalently, activity coefficient) models are more suitable for the thermodynamic... 

This last result, with only one adjustable parameter, is too simple to be useful but does show that, to a first approximation, the Margules model is symmetric in mole fraction. This is evident because the activity coefficients are mirror images of each other, and the excess Gibbs free energy is symmetric around Xj = 0.5. The higher-order terms in eqn. (2.4.1) lead to more realistic, unsymmetric behavior. 

It should be noted that even when using activity coefficient models directly, temperature dependent parameters are needed. There is no excess Gibbs free energy model... 

In eqn. (B.I.7), the activity coefficient is obtained from an excess Gibbs free-energy... 

In eqn. (B.I.8), the activity coefficient is obtained by multiplying the molar excess Gibbs free-energy expression with total number of moles of the mixture. W, and then differentiating the resultant total excess Gibbs free-energy term with respect to the... 

Since the activity coefficient, (pf, is given in terms of molar fraction as (pf= aJX, in Equation (168), then by inserting this expression in Equation (375), the total excess Gibbs free energy for the constant temperature, pressure and mole number of other constituents can be written as... 

Since this temperature is still well below the melting points of the species, our conclusion does not change, there is no phase separation. We do, however, see the importance of accounting for the temperature dependence of the excess Gibbs free energy (and activity coefficients) ]... 

Excess Gibbs free energy of mixing from activity coefficient model... 

It is important to note that in the equation (6.19) G is excess Gibbs free energy. This function can be calculated accurately by means of liquid activity models. C is a constant depending on the particular type of EOS. Note also that in the mixing rules of Huron Vidal the parameters in the liquid activity model are not equal with those found at other pressures, and must be regressed again from experimental data. 

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