Molar reaction Gibbs function

The entire term within parentheses in Eq. (2.7) is called the molar reaction Gibbs function, ArG. More precisely, it is the molar free enthalpy change accompanying the reaction at a given instant of its evolution, that is, for an extent for which the instantaneous chemical potentials are p. ... 

The molar reaction Gibbs function varies with respect to the extent reaction. After Eq. (2.7), it is the partial derivative of the system free enthalpy with respect to at constant pressure and temperature. 

We must not confuse the free enthalpy change AGsyst accompanying a chemical reaction and the molar reaction Gibbs function change ArG. They do not have the same mathematical status. The former change is a difference, the latter a partial... 

The change t/Gsyst is negative when the process is spontaneous. As a result, at constant pressure and temperature, the molar reaction Gibbs function ArG must be negative in the case of a spontaneous process ... 

The molar reaction Gibbs function ArG quantity, whose algebraic sign has been inversed, is called the chemical affinity (de Donder s definition). It is positive for a spontaneous process ... 

Fig. 2.2 EHfference between the molar reaction Gibbs function and the free enthalpy change during a chemical reaction...

The expression of the molar reaction Gibbs function A G given by Eq. (2.8) is valid for each extent value After introducing the chemical potentials expressions (2.1) into it, we find... 

The terms enclosed within parentheses in Eqs. (2.10) and (2.11) are respectively called the standard molar reaction Gibbs function change A,G and the standard chemical affinity A°. By setting up... 

It is interesting to note that the standard molar reaction Gibbs function A G° does not have the same mathematical status as ArG at each extent value. A G°, indeed, is not a derivative, unlike ArG. ArG is simply the system free enthalpy change AGsyst between two particular states, which happen to be the standard ones. 

The molar reaction Gibbs function of acid ionization is given by the equation... 

In order to determine the standard molar reaction Gibbs function change ArG°, the standard states of the reaction reactants and products must be defined. They must be chosen or, at a minimum, they must correspond to physical states, such as the physical property differences between them being endowed with an unambiguous physical meaning. As an example, a possible standard state of a solute is the state in which its concentration is 1 mol/L and in which the solution it forms with the solvent is an ideal one. Standard states are chosen conventionally for practical reasons. Fortunately, the conventions are universally agreed upon. 

The fact that standard states are conventional may be somewhat troublesome. Indeed, the question immediately arises about equilibrium constant values with different arbitrarily chosen standard states. Quite evidently, when standard states other than the usual ones are chosen, the value of the standard molar reaction Gibbs function change ArG° is different according to Eq. (2.14), it is also the case with K°. However, this is not the case with A G and AGgyst, which remain constant for a given process regardless of the adopted conventions. Actually, in Eq. (2.12),... 

The molar reaction Gibbs functions of reactions (2.15) and (2.16) are given by the following equations ... 

We must emphasize two points. The first one has already been mentioned. The molar reaction Gibbs function change is endowed with an instantaneous value. It depends on the reaction extent and, of course, on the initial reactants and products concentrations. As a result, the potential difference E is also instantaneous. This is the reason why the above reasoning involved differential quantities. 

The thermodynamic equilibrium constant K, for a given reaction equation and a given choice of reactant and product standard states, is a function of T and only of T. By equating two expressions for the standard molar reaction Gibbs energy, AfG° = lA ArG° = —RT nK (Eqs. 11.8.3 and 11.8.10), we obtain... 

Here, aHr, Asr, and A r denote the molar enthalpy, entropy, and Gibbs function, respectively, of the reversible combustion reaction of the fuel with oxygen. HHV is the molar higher heating value of the fuel, and vjt(v, ) is the stoichiometric coelRcient of the (/ th) substance in this reaction. 

The standard molar chemical exergy of any substance not present in the environment can be determined using the change in the specific Gibbs function Ag for the reaction of this substance with substances present in the environment (Bejan, Tsatsaronis, and Moran, 1996 Moran and Shapiro 1998) ... 

This condition of chemical equilibrium can also be expressed in terms of chemical potentials /x (the partial molar Gibbs functions), and, for example, for an A —> B reaction we would obtain ... 

The thermodynamic function used as the criterion of spontaneity for a chemical reaction is the Gibbs free energy of reaction, AG (which is commonly referred to as the reaction free energy ). This quantity is defined as the difference in molar Gibbs free energies, Gm, of the products and the reactants ... 

In the theoretical treatment of diffusive reactions, one usually works with diffusion coefficients, which are evaluated from experimental measurements. In a multicomponent system, a large number of diffusion coefficients must be evaluated, and are generally interrelated functions of alloy composition. A database would, thus, be very complex. A superior alternative is to store atomic mobilities in the database, rather than diffusion coefficients. The number of parameters which need to be stored in a multicomponent system will then be substantially reduced, as the parameters are independent. The diffusion coefficients, which are used in the simulations, can then be obtained as a product of a thermodynamic and a kinetic factor. The thermodynamic factor is essentially the second derivative of the molar Gibbs energy with respect to the concentrations, and is known if the system has been assessed thermodynamically. The kinetic factor contains the atomic mobilities, which are stored in the kinetic database. 

Here, AjG° is the standard molar Gibbs energy change and is the equiUbrium constant for a reaction R is the gas constant (8.314 472 J K mol ). The subscripts T and 9 denote the temperature to which a quantity pertains, the subscript p denotes constant pressure, and the subscript r denotes that the quantity refers to a reaction. Combination of equations (1) and (2) yields the following equation that gives pK as a function of temperature ... 

The formation reaction (Eq. (4.62)) can be used to calculate thermodynamic functions of the UPD phase. From the cell voltage AB = E — Eq one can calculate the partial molar Gibbs energy AG pp of the UPD modification of the metal B... 

Determine the molar Gibbs energy as a function of composition and the equilibrium concentration for the isomerization reaction ... 

K(T), as defined above, is called the equilibrium constant. The equilibrium constant as defined above is a function of T only, and this is an important thermodynamic result. It is called the law of mass action. In terms of the tabulated molar Gibbs free energies of formation AG [A ] = it is convenient to define a Gibbs free energy of reaction AGrxn as... 

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