Formation, Gibbs free energy change

A solution is a single-phase mixture of more than one compound, and the driving force for its spontaneous formation from the pure compounds at constant T and p is the negative Gibbs free energy change of the mixing process, —AG, as... 

The Gibbs free energy change involved in equation 8.157 corresponds to the partial molal Gibbs free energy of formation of Fe from the element at stable state (cf table 8.13) ... 

A recent paper gives a method for the calculation of the Gibbs free energy changes and heats of reaction for the formation of amide bonds in the solid-to-solid approach [47]. 

Similar relationships can be derived for the Gibbs free energy changes (AG = AGsoin) of solution formation. Starting from (6.22c), we obtain in a similar manner... 

We represent A///° and A/G° as the standard enthalpy and Gibbs free energy changes for the reaction in which the chemical substance is formed from the elements in their stable form, as they occur in nature at T = 298.15 K.rr For ions in solution, the values tabulated are relative to the standard enthalpy and Gibbs free energy of formation of the H+ ion being set equal to zero.ss... 

Gm = RT(Na InNA +Ng lnNB) Gibbs free energy change for the formation of... 

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... 

AG° is the standard Gibbs free energy change of reaction obtained from the standard energy of formation of pure components AG at 25 °C, P = 1 atm and a suitable aggregation state. Once having determined IQq in standard conditions, the van t Hoff equation may be used to calculate fQq at other temperatures, as follows ... 

Calculate AG° and Kfor each independent reaction. This may be done as in the relevant examples earlier in this section, with determination of AG° as a function of temperature. An easier route, however, is to use the standard Gibbs free-energy change of formation A Gy for each compound at the temperature of interest in the relationship... 

J is the number of nuclei formed per unit time per unit volume, No is the number of molecules of the crystallizing phase in a unit volume, v is the frequency of atomic or molecular transport at the nucleus-liquid interface, and AG is the maximum in the Gibbs free energy change for the formation of clusters at a certain critical size, 1. The nucleation rate was initially derived for condensation in vapors, where the preexponential factor is related to the gas kinetic collision frequency. In the case of nucleation from condensed phases, the frequency factor is related to the diffusion process. The value of 1 can be obtained by minimizing the free energy function with respect to the characteristic length. 

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