Gibbs energy molar

When M = the requited derivatives are given by equations 62 and 63. Moreover, the derivative on the left side of equation 64 defines the partial molar Gibbs energy, G. Therefore,... 

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. 

Partial Molar Gibbs Energy Implicit in Eq. (4-16) is the relation... 

In view of Eq. (4-47), the chemical potential and the partial molar Gibbs energy are therefore identical ... 

Two liquids are miscible in all proportions if Ag, the molar Gibbs energy of mixing at constant temperature and pressure, satisfies the relations... 

The standard Gibbs free energy of reaction, AG°, is defined like the Gibbs free energy of reaction but in terms of the standard molar Gibbs energies of the reactants and products ... 

The transfer of one mole of ions from a vacuum into the solution is connected with work Na(wi + vv2). This work is identical with the molar Gibbs energy of solvation A Gs i ... 

When the adsorbed components are electrically charged, then the partial molar Gibbs energy of the charged component depends on the charge of the given phase, and thus the chemical potentials in the above relationships must be replaced by the electrochemical potentials. The Gibbs adsorption isotherm then has the form... 

The quantity a is the anodic transfer coefficient-, the factor l/F was introduced, because Fcf> is the electrostatic contribution to the molar Gibbs energy, and the sign was chosen such that a is positive - obviously an increase in the electrode potential makes the anodic reaction go faster, and decreases the corresponding energy of activation. Note that a is dimensionless. For the cathodic reaction ... 

There is a fundamental difference between electron-transfer reactions on metals and on semiconductors. On metals the variation of the electrode potential causes a corresponding change in the molar Gibbs energy of the reaction. Due to the comparatively low conductivity of semiconductors, the positions of the band edges at the semiconductor surface do not change with respect to the solution as the potential is varied. However, the relative position of the Fermi level in the semiconductor is changed, and so are the densities of electrons and holes on the metal surface. 

The third law of thermodynamics can be verified experimentally. The stable rhombic low-temperature modification of sulfur transforms to monoclinic sulfur at 368.5 K (p = 1 bar). At that temperature, Ttrs, the two polymorphs are in equilibrium and the standard molar Gibbs energies of the two modifications are equal. We therefore have... 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

Thus the molar Gibbs energies of the two phases are the same at equilibrium. 

For any single-component system such as a pure gas the molar Gibbs energy is identical to the chemical potential, and the chemical potential for an ideal gas is thus expressed as... 

The value of this standard molar Gibbs energy, p°(T), found in data compilations, is obtained by integration from 0 K of the heat capacity determined by the translational, rotational, vibrational and electronic energy levels of the gas. These are determined experimentally by spectroscopic methods [14], However, contrary to what we shall see for condensed phases, the effect of pressure often exceeds the effect of temperature. Hence for gases most attention is given to the equations of state. 

Since AmixGA = fiA - pA, the integral molar Gibbs energy of mixing can alternatively be expressed in terms of the chemical potentials as... 

The excess molar Gibbs energy of mixing is thus... 

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... 

Figure 3.5 The molar Gibbs energy of mixing and the molar excess Gibbs energy of mixing of molten Fe-Ni at 1850 K. Data are taken from reference [3].

Binary solutions have been extensively studied in the last century and a whole range of different analytical models for the molar Gibbs energy of mixing have evolved in the literature. Some of these expressions are based on statistical mechanics, as we will show in Chapter 9. However, in situations where the intention is to find mathematical expressions that are easy to handle, that reproduce experimental data and that are easily incorporated in computations, polynomial expressions obviously have an advantage. 

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