Gibbs’ excess enthalpy

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

J. B. Ott, K. N. Marsh and R. H. Stokes. "Excess Enthalpies. Excess Gibbs Free Energies, and Excess Volumes for (Cyclohexane + //-Hexane). and Excess Gibbs Free Energies and Excess Volumes for (Cyclohexane + Methylcyclohexane) at 298.15 and 308.15 K". J.Chem. Thermodyn., 12, 1139-1148 (1980). 

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... 

As has been the approach for most of the author s other reviews on organic thermochemistry, the current chapter will be primarily devoted to the relatively restricted scope of enthalpy of formation (more commonly and colloquially called heat of formation) and write this quantity as A//f, instead of the increasingly more commonly used and also proper A//f° and AfHm No discussion will be made in this chapter on other thermochemical properties such as Gibbs energy, entropy, heat capacity and excess enthalpy. Additionally (following thermochemical convention), the temperature and pressure are tacitly assumed to be 25 °C ( 298 K ) and 1 atmosphere (taken as either 101,325 or 100,000 Pa) respectively3 and the energy units are chosen to be kJmol-1 instead of kcalmol-1 (where 4.184 kJ = 1 kcal, 1 kJ = 0.2390 kcal). 

Garriga, R., Sanchez, F., Perez, P., and Gracia, M. Excess Gibbs free energies at eight temperatnres and excess enthalpies and volnmes at 7 = 198.15 for bntanenitrile + 2-bntanol, J. Chem. Eng. Data, 42(l) 78-83, 1997. 

GLC is a well-established and accurate method used to obtain and the partial molar excess enthalpies at infinite dilution values AHf" , which is determined from the Gibbs-Helmholtz equation ... 

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

There are two common and widely used definitions of the interfacial excess enthalpy. We can argue that enthalpy is equal to the internal energy minus the total mechanical work 7A-PVa. Since in the Gibbs convention PVa = 0 we define... 

Polak, J., Murakami, S., Lam, V.T., Benson, G.C. (1970) Excess enthalpy, volume, and Gibbs free energy of cyclopentane-tetrachlo-roethylene mixtures at 25°C. J. Chem. Eng. Data 16, 323-328. 

D.2. Determination of Kx from Thermodynamic Data for Alcohol—Hydrocarbon Mixtures. Using the available excess Gibbs energy and excess enthalpy data for alcohol—hydrocarbon mixtures,16 the value of Kx can be estimated as described below. The Gibbs energy of the... 

By fitting the available excess Gibbs energy data to eq D.14, the excess enthalpy data to eq D.18, the average aggregation number of the alcohol to eq D.7, and the ratio between the total and the monomeric alcohol to eq D.8 and incorporating the temperature dependence provided by eq D.19, we have developed the following expression for an alcohol with n, A carbon atoms ... 

Gibbs functions for a real salt solution and the corresponding ideal salt solution containing m2 moles of salt in a kilogram of solvent. GE can be calculated for many aqueous salt solutions from published values of 0 and y . In the same way, the corresponding excess enthalpy HE can be defined and this equals the apparent partial molar enthalpy. Thus the properties of salt solutions can be examined in plots of GE, HE, and T SE against m2, where SE is the... 

Equations (13.23) and (13.24) allow direct calculation of the effects of pressure and temperature on the excess Gibbs energy. For example, an equimolar mixture of benzene and cyclohexane at 25°C and 1 bar has an excess volume of about 0.65 cm3 mol-1 and an excess enthalpy of about 800 J mol- . Thus at these conditions,... 

The above equations are all based on the internal energy. Similar equations can be written with the enthalpy since the surface excess enthalpy and energy are identical in the Gibbs representation when 1 =0 (Harkins and Boyd, 1942). Therefore the various energies of immersion defined by Equations (5.6)—(5.8) are all virtually equal to the corresponding enthalpies of immersion, i.e. (A inmH°, AimmHr and Ah 1), thus ... 

When the thermodynamics of surfaces are discussed in terms of excess quantities relative to a Gibbs surface, there is only one way of defining the excess enthalpy, that is, these quantities depend on (y, /4,) but not on (p, V) because... 

For the implied infinitesimal changes of y with T the factor RTF remains constant. Generally, however, the derivative dy/dT also depends on T. From (4.3.22) S° will eventually be obtained as a function of x and T. As, for each T, F is accessible as a function of x, it is also possible to derive the surface excess entropy as a function of the monolayer composition. Accurate data are, as before, a prerequisite. From S the surface excess enthalpy = TS is obtainable. Alternatively, one can differentiate y /T with respect to the temperature, obtaining the enthalpy directly using the appropriate Gibbs-Helmholtz relation. 

At constant temperature and pressure, the concentration-dependent activity coefficient can be determined from the free excess enthalpy by differentiation through the mole fraction. These equations are the basis for the methods of Wilson and Prausnitz to calculate the activity coefficient [19, 20], The Gibbs-Duhem equation is again a convenient method for checking the obtained equilibrium data ... 

---