Gibbs free energy formation species, standard

Self-Test 7.20A Calculate the standard Gibbs free energy of formation of NH,(g) at 25°C from the enthalpy of formation and the molar entropies of the species taking part in its formation. 

Table 8.17 Main predominance limits of aqueous complexes and saturation limits between solutes and condensed phases in iron-bearing aqueous solutions (see figure 8.22). Standard state Gibbs free energies of formation of species are listed in table 8.18. (c) = crystalline ... 

In a similar manner to that employed for thermochemical AH° of chemical reactions [cf. (3.106)], the reaction free energy AG° can be expressed in terms of the standard Gibbs free energy of formation AGf [AJ for each species A, namely,... 

Table 6.1. Standard Gibbs free energies of formation of minerals and aqueous species considered in development of mineral compatibility diagrams in Figure 6.1.

The results of the DFT calculations for various stable C2H.V species and transitions states on Pt(lll) and Pt(211) are summarized in Table V, which also shows entropy changes for the various steps, as estimated from DFT calculations of the vibrational frequencies of the various adsorbed C2H species and transition states on 10-atom platinum clusters (55). Table V also includes estimates of the standard Gibbs free energy changes for the formation of stable C2H surface species and activated complexes responsible for C-C bond cleavage at 623 K. These estimates were made by combining... 

Table 5.3 shows the enthalpy and Gibbs free energy of formation of species at 289.13 K and 1 atm [3]. On this basis standard AH and AG[J can be determined, as shown in Table 5.4. The hydrogenation of phenol is highly exothermic, while the dehydrogenation of cyclohexanol is moderately endothermic. The conversion...

Equation (2.16) is often used in the nucleation literature with some controversy. We have included the derivation so that the assumptions in its use are clear. We repeat that AG (n, p, T) used in Eq. (2.16) is the difference in the Gibbs free energy of and n B monomers when and B are both at pressure p. We can consider AG (n, p, T) to be the Gibbs free energy of formation of clusters of size n deflned by a standard state of pressure p, rather than p = 1 atm. When all species obey the ideal-gas law, the populations expressed in terms of AG ti, p, T) are give rigorously by Eq. (2.14). Equation (2.16) follows when the system is dominated by a monomer. 

Where, for the ith species, AG is the Gibbs free energy of formation, a,- is the activity, and Zj is the stoichiometric coefficient in the balanced reaction statement (by convention, z,- is negative for reactants and positive for products). The absolute temperature is T R is the gas constant, and P is the absolute pressure. The standard Gibbs free energy of formation, AGf, can be obtained from standard tables, from values of the standard enthalpy AH( and entropy AS of formation for each species via... 

The solubility product constant may be determined by direct measnrements or calcnlated from the standard Gibbs free energies of formation (JsGf) of the species involved at their standard states. For the reaction scheme (Equation 8.13) the Gibbs free energy change is ... 

Since Al reacts almost instantly with ferron, it would seem reasonable that it consists of only simple monomeric species—i.e., Al3+, Al(OH)2+, Al(OH)2+, and Al(OH)4 (with appropriate coordinated water molecules). Standard Gibbs free energies of formation values (AG°) for the species are available in the chemical literature. Table III... 

Species Standard Gibbs Free Energies of Formation o G°kcal) Reference... 

AGf°)i standard Gibbs free energy of formation of species i kJmol"1... 

Standard Gibbs Free Energy of Formation of Species Considered... 

Tables often indude formation properties of a species in more than one standard state. Develop a relationship between the Gibbs free energy of formation in the liquid and in the gas standard state.

A common problem is to calculate the composition of a reacting mixture at equilibrium at a specified temperature. To do this, it is always easier if we start with the stoichiometric table of the reaction. The first step is to express all the concentrations in terms of the extent of reaction, . We then calculate the activity of each species and finally, we equate the product of activities to the equilibrium constant. This produces an equation where the only unknown is Once the extent of reaction is known, all the mole fractions can be computed from the stoichiometric table. If the temperature of the calculation is at 25 C, the equilibrium constant is obtained directly from tabulated values of the standard Gibbs free energy of formation. To calculate the equilibrium constant at another temperature, an additional step is needed to obtain the heat of reaction and the Gibbs energy at the desired temperature. This procedure is demonstrated with examples below. 

The first equation expresses the equilibrium constant in terms of quantities that can be obtained from tabulated values (formation enthalpy and Gibbs free energy, heat capacities). The second equation expresses the equilibrium constant in terms of the activity of species, and ultimately, in terms of mol fractions. We must remember that activities and formation properties of each species must refer to the same standard state. 

The quantities AfG°(Pj) and AfG°(Rj) represent the free energies of formation of the species Pj and from the elements in their standard states (at a pressure of 1 atm) at temperature T. (Formerly, the Gibbs free energy was designated just free energy , and denoted by F rather than G.) The constant R is the universal gas constant (1.987 calmol" or 8.314 joule mol K" when G is expressed in units of cal mol or joule mol", respectively). 

Complexing behavior can be checked for via a thorough literature review. Consulting the extensive compilations by the National Bureau of Standards (1) and the Russian Academy of Science (2) is a good first step. Other sources to check are the Smith and Martell (3) and SUlen (4) compilations. These references provide vcdues for the Gibbs free energies and heats of formation for precipitate, ionic, vapor, aqueous molecule and complex species which can be used to calculate the various equilibrium constants needed for modeling aqueous solutions. There are also values for some of the cation hydrolysis complexes. 

Gas fraction as a function of distance x Gibbs free energy Standard Gibbs free energy Standard Gibbs free energy of formation of species j... 

The micelle sketched in Fig. 5.10 contains an asphaltene core with asphaltene molecules 2 resin molecules are adsorbed onto the surface of the core. In addition to resins that are part of the solvation shell surrounding the core, asphalt-free oil species are also present in the shell. The formation of the solvation shell around the asphaltene core lowers the Gibbs free energy. The standard Gibbs free energy of micelli-zation, AG , represents the standaird Gibbs free energy difference between (1) asphaltene molecules in the core, resin molecules in the shell, and (2) those and ri2 molecules in an infinite-dilution petroleum mixture ... 

First, Lvov and Macdonald used a free-energy minimization code, ° which employs standard Gibbs energies of formation of the species (as calculated using the SUPCR92 software package.) The activity coefficients for all charged species were calculated... 

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