Gibbs energy availability function

The Gibbs function is the energy available for reaction after adjusting for the entropy changes of the surroundings. 

Figure 4.6 The value of the Gibbs function AG decreases as the extent of reaction until, at (eq), there is no longer any energy available for reaction, and AG = 0. =0 represents no reaction and = 1 mol represents complete reaction...

We return to the graph in Figure 4.6 of Gibbs function (as y) against extent of reaction (as x). At the position of the minimum, the amounts of free acid and ionized products remain constant because there is no longer any energy available for reaction, as explained in the example above. 

One of the main models which is available in CALPHAD calculation programmes is that based on Pitzer (1973, 1975), Pitzer and Mayorga (1973) and Pitzer and Kim (1974). The model is based on the development of an explicit function relating the ion interaction coefficient to the ionic strength and the addition of a third virial coefficient to Eq. (5.83). For the case of an electrolyte MX the excess Gibbs energy is given by... 

It is commonplace to assume a form of the Gibbs energy function which excludes the pressure variable for solid-state phase transformations, as the magnitude of the PAV term is small at atmospheric pressures. This is of course not the case in geological systems, or if laboratory experiments are deliberately geared to high-pressure environments. Klement and Jayaraman (1966) provide a good review of the data available at the time when some of the earliest CALPHAD-type calculations were made (Kaufman and Bernstein 1970, Kaufman 1974). Much work was also carried out on specific alloy systems such as Fe-C (Hilliard 1963) and the Tl-In system (Meyerhoff and Smith 1963). 

The emphasis in the previous sections has been on the accuracy with which the Gibbs energy, particularly the entropy component above T , can be calculated. However, as the number of components, C, and the number of atoms in the chosen cluster, n, increases, the number of simultaneous equations that have to be solved is of the order of C". This number is not materially reduced by redefining the equations in terms of multi-site correlation functions (Kikuchi and Sato 1974). The position may be eased as extra computing power becomes available, but a choice will inevitably have to be made between supporting a more complex model or extending a simpler model to a greater number of components. 

Similar data for the two-component system water-ammonia are also available and complete, because of the use of this system in absorption refrigeration. The data of Scatchard and coworkers are the most recent 24), and are unique among such compilations in that the availability function is tabulated as well as the usual enthalpy, entropy, and Gibbs free energy. These data have been converted to graphical form (charts) by Kohloss and Scott 16) and Bulkley and Swartz 4). Older data, but more complete in the low concentration range, are those of Jennings and Shannon 11). 

By convention, thermodynamic functions of state refer to the system and not the environment, so - AG (exergonic) represents the Gibbs energy potentially available for expenditure and potentially dissipated to the environment. Under suitable conditions, this energy could be made to perform work. An endergonic reaction (+ AG) cannot proceed spontaneously and requires an input of Gibbs energy to proceed from its initial to its final state. 

Enthalpy is an intrinsic property of a substance and a function of temperature and pressure.19 In practice the Gibbs free energy is the net internal energy available to do work, less work done by changes in pressure and temperature.20 Exergy, on the other hand, is defined as the total amount of work that can be harnessed and becomes more relevant in high-temperature and high-pressure electrolysis. 

Transfer functions can also be defined for the thermodynamic state functions AH° and AS° [102], The ease of calorimetric measurements has made the standard molar transfer enthalpy, AH X,1 II), readily available. If both transfer Gibbs energies and... 

When very accurate data In on K as a function of T are available, the corresponding standard Gibbs energies (-RT In Ky) can be split into their enthalpic and entropic parts (sec. 1.2.15), of which the former virtually represents the enthalpy of the exchange of 1 against J under standard conditions, which can be related to the difference A, H - A, H ... 

Oxides. Decomposition pressure measurements on the TbO system by Eyring and his collaborators (64) have been supplemented by similar and related studies on the PrO system (46) and on other lanthanide-oxygen systems (43, 44). Extensive and systematic studies of vaporization processes in lanthanide-oxide systems have been undertaken by White, et al. (6, 188,196) using conventional Knudsen effusion measurements of the rates of vaporization of the oxides into high vacuum. Combination of these data with information on the entropies and Gibbs energy functions of reactants and products of the reaction yields enthalpies of reaction. In favorable instances i.e., if spectroscopic data on the gaseous species are available), the enthalpies of formation and the stabilities of previously undetermined individual species are also derived. The rates of vaporization of 17 lanthanide-oxide systems (196) and the vaporization of lanthanum, neodymium, and yttrium oxides at temperatures between 22° and 2700°K. have been reported (188). 

At the boiling point and higher temperatures sodium vapor contains an appreciable proportion of diatomic moleculses. Thompson and Garelis (j ) have made a careful analysis of the available vapor pressure data. Their results are consistent with the Gibbs energy functions calculated in the present work and have been adopted. 

The thermodynamic data in the selected set refer to a temperature of 298.15 K (25.00°C), but they can be recalculated to other temperatures if the corresponding data (enthalpies, entropies, heat capacities) are available [97PU1/RAR]. For example, the temperature dependence of the standard reaction Gibbs energy as a function of the standard reaction entropy at the reference temperature (7o= 298.15 K), and of the heat capacity function is ... 

The data obtained by the third law approach in Table V-24 were calculated from primary vapour pressures, when available, or from the estimated pressure at the mean temperature of the interval, when only the A and B coefficients were published. The Gibbs energy function data were extracted from [74BEH/LEIVI]. 

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