Gibbs energy pure component

Figure 7.4 also introduces us to a new problem. Because the mixing curve is concave downward, the Gibbs energies of components A and B in the solution are necessarily less than the corresponding values of and G, the molar Gibbs energies of the pure compounds. The fact that this is so provides the (thermodynamic) reason why A and B form a solution. If we mix moles of A and moles of B the reaction is... 

The concentration of this species in liquid sulfur was estimated from the calculated Gibbs energy of formation as ca. 1% of all Ss species at the boihng point [35]. In this context it is interesting to note that the structurally related homocyclic sulfur oxide Sy=0 is known as a pure compound and has been characterized by X-ray crystallography and vibrational spectroscopy [48, 49]. Similarly, branched long chains of the type -S-S-S(=S)-S-S- must be components of the polymeric S o present in liquid sulfur at higher temperatures since the model compound H-S-S-S(=S)-S-S-H was calculated to be by only 53 kJ mol less stable at the G3X(MP2) level than the unbranched helical isomer of HySs [35]. 

The Gibbs energy is an additive function of all components. For systems consisting of pure components only. 

As a thermodynamicist working at the Lower Slobbovian Research Institute, you have been asked to determine the standard Gibbs free energy of formation and the standard enthalpy of formation of the compounds ds-butene-2 and trans-butene-2. Your boss has informed you that the standard enthalpy of formation of butene-1 is 1.172 kJ/mole while the standard Gibbs free energy of formation is 72.10 kJ/mole where the standard state is taken as the pure component at 25 °C and 101.3 kPa. 

It can be shown that the maximum theoretical work produced (or minimum work required) for a process is related to the change in Gibbs energy of the process, assuming again the inputs and outputs of the process are pure components at standard conditions (Denbigh, 1956 De Nevers and Seader, 1980). 

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... 

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

It should be remembered that the CALPHAD approach is based on the hypothesis that, for all the phases and structures existing across the complete alloy system, entire Gibbs energy vs. composition curves may be constructed even by extrapolation into regions where they are unstable or metastable. A particular case concerns the pure component elements for which the relative Gibbs energy for the different crystal structures (the so-called lattice stabilities) must also be established and defined as a function of temperature (and pressure). 

Figure 3.9 Conformation of Gibbs free energy curve in various types of binary mixtures. (A) Ideal mixture of components A and B. Standard state adopted is that of pure component at T and P of interest. (B) Regular mixture with complete configurational disorder kJ/mole for 500 < r(K) < 1500. (C) Simple mixture IF = 10 - 0.01 X r(K) (kJ/ mole). (D) Subregular mixture Aq = 10 — 0.01 X T (kJ/mole) = 5 — 0.01 X F (kJ/ mole). Adopting corresponding Margules notation, an equivalent interaction is obtained with IFba = 15 - 0.02 X r(kJ/mole) Bab = 5 (kJ/mole).

It is evident from equation 5.204 that the intrinsic significance of equation 5.206 is closely connected with the choice of standard state of reference. If the adopted standard state is that of the pure component at the P and T of interest, then AG%i is the Gibbs free energy of reaction between pure components at the P and T of interest. Deriving in P the equilibrium constant, we obtain... 

The first step in the model is a normative calculation (table 6.12) to establish the molar amounts of the various melt components. For each component, the molar Gibbs free energy at the standard state of pure component at T and P of interest is given by... 

The Gibbs free energy of phase y is represented by a straight line connecting the standard state potentials of the two end-members in the mixture. Because we use the term mixture, it is evident that the standard state of both end-members is the same and is that of pure component. The two components are totally immiscible in any proportion and the aggregate is a mechanical mixture of the two components crystallized in form y ... 

At Ty, the Gibbs free energy of phase a (i.e., melt) at all compositions is lower than that of mechanical mixture y + y" phase a is then stable over the whole compositional range. At T2, the chemical potential of component 1 in a is identical to the chemical potential of the same component in y . Moreover, the equahty condition is reached at the standard state condition of the pure component T2 is thus the temperature of incipient crystallization of y. At T, the Gibbs free energy of a intersects mechanical mixture y + y" on the component 1-rich side of the diagram and touches it at the condition of pure component 2. Applying the prin-... 

Roozeboom type I is obtained whenever the Gibbs free energy curve of the melt initially touches that of the mixture in the condition of pure component. This takes place at the melting temperature of the more refractory component (T2 in... 

Figure 7,8 Gibbs free energy curves and T-X phase relations for an intermediate compound (C), totally immiscible with pure components. Column 1 Gibbs free energy relations leading to formation of two eutectic minima separated by a thermal barrier. Column 2 energy relations of a peritectic reaction (incongruent melting). To facilitate interpretation of phase stability fields, pure crystals of components 1 and 2 coexisting with crystals C are labeled y and y", respectively, in T-X diagrams same notation identifies mechanical mixtures 2-C and C-1 in G-X plots.

The thermodynamic equations for the Gibbs energy, enthalpy, entropy, and chemical potential of pure liquids and solids, and for liquid and solid solutions, are developed in this chapter. The methods used and the equations developed are identical for both pure liquids and solids, and for liquid and solid solutions therefore, no distinction between these two states of aggregation is made. The basic concepts are the same as those for gases, but somewhat different methods are used between no single or common equation of state that is applicable to most liquids and solids has so far been developed. The thermodynamic relations for both single-component and multicomponent systems are developed. 

Many other tests, too numerous to discuss individually, have been devised, all of which are based on the Gibbs-Duhem equation. Only one such test, given by Redlich, is discussed here and is applicable to the case in which both components are volatile and in which experimental studies can be made over the entire range of composition. The reference states are chosen to be the pure liquid at the experimental temperature and a constant arbitrary pressure P0. The values of A/iE[T, P0, x] and A f[T, P0, x] will have been calculated from the experimental data. The molar excess Gibbs energy is given by Equation (10.62), from which we conclude that AGE = 0 when Xj = 0 and when xt = 1. Therefore,... 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

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