Thermodynamics Gibbs energy calculations

When the kinetics are unknown, still-useful information can be obtained by finding equilibrium compositions at fixed temperature or adiabatically, or at some specified approach to the adiabatic temperature, say within 25°C (45°F) of it. Such calculations require only an input of the components of the feed and produc ts and their thermodynamic properties, not their stoichiometric relations, and are based on Gibbs energy minimization. Computer programs appear, for instance, in Smith and Missen Chemical Reaction Equilibrium Analysis Theory and Algorithms, Wiley, 1982), but the problem often is laborious enough to warrant use of one of the several available commercial services and their data banks. Several simpler cases with specified stoichiometries are solved by Walas Phase Equilibiia in Chemical Engineering, Butterworths, 1985). 

In order to examine the possible relationship between the bulk thermodynamics of binary transition metal-aluminum alloys and their tendency to form at underpotentials, the room-temperature free energies of several such alloys were calculated as a function of composition using the CALPHAD (CALculation of PHAse Diagrams) method [85]. The Gibbs energy of a particular phase, G, was calculated by using Eq. (14),... 

In the case of hydrogen, for example, at a temperature of 2500 K, the equilibrium constant for dissociation has the value, calculated from the thermodynamic relation between the Gibbs energy of formation and the equilibrium constant of 6.356 x 10 4 and hence at a total pressure of 10 2 atmos, the degree of dissociation is 0.126 at 2500 K, which drops to 8.32 x 10 3 at 2000 K. 

ArV is not necessarily positive, and to compare the relative stability of the different modifications of a ternary compound like AGSiOs the volume of formation of the ternary oxide from the binary constituent oxides is considered for convenience. The pressure dependence of the Gibbs energies of formation from the binary constituent oxides of kyanite, sillimanite and andalusite polymorphs of A SiOs are shown in Figure 1.10. Whereas sillimanite and andalusite have positive volumes of formation and are destabilized by pressure relative to the binary oxides, kyanite has a negative volume of formation and becomes the stable high-pressure phase. The thermodynamic data used in the calculations are given in Table 1.7 [3].1... 

Figure 4.12 (a) Gibbs energy representation of the phases in the system Zr02-Ca0 at 1900 K. McaO - MzrO = TSZ n°t deluded for clarity, (b) Calculated phase diagram of the system Zr02 Ca0. Thermodynamic data are taken from reference [9]. 

Considerable use has been made of the thermodynamic perturbation and thermodynamic integration methods in biochemical modelling, calculating the relative Gibbs energies of binding of inhibitors of biological macromolecules (e.g. proteins) with the aid of suitable thermodynamic cycles. Some applications to materials are described by Alfe et al. [11]. 

Chapter 9 deals with the general principles of computational thermodynamics, which includes a discussion of how Gibbs energy minimisation can be practically achieved and various ways of presenting the output. Optimisation and, in particular, optimiser codes, such as the Lukas progranune and PARROT, are discussed. The essential aim of these codes is to reduce the statistical error between calculated phase equilibria, thermodynamic properties and the equivalent experimentally measured quantities. 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

Owing to the allotropic forms of oxygen, to its various redox states, and related chemical species that are thermodynamically stable or exist for kinetic reasons, a lot of redox reactions are usually described. However, many of them are not really important for the common works, particularly for those in solutions consequently, only some of them have been described here. The publications cited earlier can be searched for data useful for the calculation of Gibbs energy or potentials of particular reactions. 

K is the thermodynamic equilibrium constant which is only dependent on T, and ArG° is the standard reaction Gibbs energy of the reaction, which can be calculated with... 

Summing changes in Gibbs energy. A convenient feature of thermodynamic calculations is that if two or more chemical equations are summed, AG for the resulting overall equation is just the sum of the AG s for the individual equations as illustrated in Eqs. 6-17 to 6-20. The same applies for AH and AS. 

Biochemists sometimes divide AG for the ATP synthesis in a coupled reaction sequence (in this case +69 kj) by the overall Gibbs energy decrease for the coupled process (196 or 235 kj mol 4) to obtain an "efficiency." In the present case the efficiency would be 35% and 29% for coupling of Eq. 17-21 (for 2 mol of ATP) to Eqs. 17-19 and 17-20, respectively. According to this calculation, nature is approximately one-third efficient in the utilization of available metabolic Gibbs energy for ATP synthesis. However, it is important to realize that this calculation of efficiency has no exact thermodynamic meaning. Furthermore, the utilization of ATP formed by a cell for various purposes is far from 100% efficient. 

It is understood that the (local) Gibbs energy depends on the local stress, and thus aH(NH) and (A/h) reflect the self- and coherency stresses in the Me-H system. In addition, if coherency is lost due to plastic deformation or cracking, the Me atoms in the deformation zone may well become mobile and Me then is well defined near the interface. This could explain the fact that aK(N (P)) (= aH(Ajj(a))) corresponds, in essence, to the value of the a/p equilibrium calculated using independent thermodynamic data. 

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