Gibbs free energy potential

The standard state Gibbs free energy potential is eliminated by use of the following relation ... 

Equation ( A2.1.39) is the generalized Gibbs-Diihem equation previously presented (equation (A2.1.27)). Note that the Gibbs free energy is just the sum over the chemical potentials. 

The chemical potential p, of the adsorbate may be defined, following standard practice, in terms of the Gibbs free energy, the Helmholtz energy, or the internal energy (C/,). Adopting the last of these, we may write... 

The chemical potential is an example of a partial molar quantity /ij is the partial molar Gibbs free energy with respect to component i. Other partial molar quantities exist and share the following features ... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

N, Number of particles P, Pressure V, Volume T, Temperature E, Energy fi. Chemical potential A, Helmholtz free energy S, Entropy G, Gibbs free energy. 

At finite temperature the chemical potentials can be calculated as follows. In the dilute solution approximation, the Gibbs free energy is given by ... 

The Gibbs free energy change of a system will depend not only on temperature and pressure but upon the chemical potentials of the species involved, and this statement may be expressed in the form of the partial differential... 

The importance of the Gibbs free energy and the chemical potential is very great in chemical thermodynamics. Any thermodynamic discussion of chemical equilibria involves the properties of these quantities. It is therefore worthwhile considering the derivation of equation 20.180 in some detail, since it forms a prime link between the thermodynamics of a reaction (AG and AG ) and its chemistry. 

Hence, for a pure substance, the chemical potential is a measure of its molar Gibbs free energy. We next want to describe the chemical potential for a component in a mixture, but to do so, we first need to define and describe a quantity known as a partial molar property. 

Equation (5.21) is especially important in that it indicates that p, the chemical potential of the ith component in the mixture is the contribution (per mole) of that component to the total Gibbs free energy/... 

Before leaving our discussion of partial molar properties, we want to emphasize that only the partial molar Gibbs free energy is equal to n,-. The chemical potential can be written as (cM/<9 ,)rv or (dH/dnj)s p H partial molar quantities for fi, into equations such as those given above. 

Cell Potential and Reaction Gibbs Free Energy... 

To find the connection between cell potential and Gibbs free energy, recall that ir Section 7.14 (Eq. 21) we saw that the change in Gibbs free energy is the maximum nonexpansion work that a reaction can do at constant pressure and temperature ... 

CELL POTENTIAL AND REACTION GIBBS FREE ENERGY... 

The standard potential of the AI3+/A1 couple is —1.66 V. Calculate the standard Gibbs free energy of formation for Al +(aq). Account for any differences between the standard Gibbs free energy of formation of Tl,+(aq) (see Exercise 14.65) and that of Al +(aq). 

The Gibbs free energy for the reaction is related to the equilibrium cell potential ( 0) (Equation 6.4). For the reaction between hydrogen and oxygen to produce water, n, the number of electrons per molecule participating in the electrochemical reaction is 2 and AG has a value of —37.2 kJ mol giving Eq a value of 1.23 V... 

To see how the catalyst accelerates the reaction, we need to look at the potential energy diagram in Fig. 1.2, which compares the non-catalytic and the catalytic reaction. For the non-catalytic reaction, the figure is simply the familiar way to visualize the Arrhenius equation the reaction proceeds when A and B collide with sufficient energy to overcome the activation barrier in Fig. 1.2. The change in Gibbs free energy between the reactants, A -r B, and the product P is AG. 

Here, AS° = AS i + AS n, but since identical vibrational levels have been assumed for the two electronic levels, AS jb = 0. In addition, AS j is related to the electronic degeneracies of the two levels by ASei = K In ( l/ h)- Finally, if the transformation takes place at constant pressure, AH° = NAE where AE is defined as above. Consideration of the Gibbs free energy for an assembly of N molecules thus produces the same relation for the HS fraction Uh as the potential energy for the isolated molecule, if only the interaction between the molecules is neglected. 

Here G is the Gibbs free energy of the system without external electrostatic potential, and qis refers to the energy contribution coming from the interaction of an apphed constant electrostatic potential s (which will be specified later) with the charge qt of the species. The first term on the right-hand side of (5.1) is the usual chemical potential /r,(T, Ci), which, for an ideal solution, is given by... 

In order to evaluate which of these scenarios leads to the most stable interfacial structure, we have to analyze the relation between the chemical potentials of both reservoirs and the overall energy. Therefore, we begin with the Gibbs free energy of the interface. 

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