Gibbs Free Energy G

In the sections that follow, we will review the main thermodynamic tools that we can use to calculate the equilibrium conditions for a system and also to determine the size of the thermodynamic deviations that occur when a system is subjected to changes in temperature, pressure, and/or composition that force it away from equilibrium. 

While you have hopefully already been acquainted with enthalpy, entropy, and Gibbs free energy before, here is a brief review of these three important thermodynamic quantities  

Enthalpy H can be considered to be a measure of the heat value of a system. For a reversible thermodynamic process at constant pressure, AH represents the heat that is released (if AH is negative) or the heat that is absorbed (if AH is positive) during the process. An exothermic process is one where AH is negative (heat is released), while an endothermic process is one where AH is positive (heat is absorbed). 

A spontaneous process is energetically favorable it is a downhill process. Although spontaneous processes are energetically favorable, spontaneity is no guarantee that a process will occur, nor does it indicate how fast a process will occur. Many spontaneous processes do not occur because they are impeded by kinetic barriers. Thus, our calculation of AG only provides us the first step in our quest to understand the rate of processes. Once we have determined AG for a process, we will then need to apply kinetic laws to determine how quickly (if at all) the process will happen  

For a closed thermodynamic system at constant temperature and pressure, the following equation can be used to relate changes experienced by the three thermodynamic quantities discussed above during a thermodynamic process  

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For spontaneous processes at constant temperature and pressure it is the Gibbs free energy G that decreases, while at equilibrium under such conditions dG = 0. 

Figure A2.5.2 shows schematically the behaviour of several thennodynamic fiinctions along a constant-pressure line (shown as a dotted line in Figure A2.5.1 )—the molar Gibbs free energy G(for a one-component system the same as...

Our discussion so far has considered the calculation of Helmholtz free energies, which a obtained by performing simulations at constant NVT. For proper comparison with expe inental values we usually require the Gibbs free energy, G. Gibbs free energies are obtaini trorn a simulation at constant NPT. 

A quantity of great importance in chemical thermodynamics is the Gibbs free energy G. The latter is defined in terms of enthalpy H as... 

Physical Equilibria and Solvent Selection. In order for two separate Hquid phases to exist in equiHbrium, there must be a considerable degree of thermodynamically nonideal behavior. If the Gibbs free energy, G, of a mixture of two solutions exceeds the energies of the initial solutions, mixing does not occur and the system remains in two phases. Eor the binary system containing only components A and B, the condition (22) for the formation of two phases is... 

The definitions of enthalpy, H, Helmholtz free energy. A, and Gibbs free energy, G, also give equivalent forms of the fundamental relation (3) which apply to changes between equiUbrium states in any homogeneous fluid system ... 

An important question for chemists, and particularly for biochemists, is, Will the reaction proceed in the direction written J. Willard Gibbs, one of the founders of thermodynamics, realized that the answer to this question lay in a comparison of the enthalpy change and the entropy change for a reaction at a given temperature. The Gibbs free energy, G, is defined as... 

Other thermodynamical functions, such as the enthalpy H, the entropy S and Gibbs free energy G, may be constructed from these relations. 

The Gibbs free energy G provides a means of defining equilibrium or of the tendency of a reaction to proceed in a given direction. It is similar to the... 

Other thermodynamic functions described above in that the change in free energy AG is determined solely by the initial and final states of the system. The maximum work, or maximum available energy, defined in terms of the Gibbs free energy G, which is now called the free enthalpy, is... 

In Chapter 1, we describe the fundamental thermodynamic variables pressure (p), volume (V), temperature (T), internal energy ((/), entropy (5), and moles (n). From these fundamental variables we then define the derived variables enthalpy (//), Helmholtz free energy (A) and Gibbs free energy (G). Also included in this chapter is a review of the verbal and mathematical language that we will rely upon for discussions and descriptions in subsequent chapters. 

To take the next step, we introduce the Gibbs free energy, G, which is defined as... 

If we consider an assembly of N molecules, each individual molecule may exist either in the HS state or in the LS state, the transformation for a fixed set of values of the external variables T, p, or x being characterized by Eq. (2). Here, N is the Avogadro number and the Gibbs free energy G per mole of the system may be expressed as ... 

The Gibbs free energy G and the chemical potentials include contributions from the internal energy, vibrational free energy, and configurational entropy. Since most relevant stmctures will have a low surface free energy, we obtain from (5.4) that... 

This expression has the advantages that the electrode potential only appears in the last term and that the Gibbs free energy G depends only on the temperamre and quantities related to the electrode, allowing one to neglect the electrolyte part of the interface. 

Whether a reaction is spontaneous or not depends on thermodynamics. The cocktail of chemicals and the variety of chemical reactions possible depend on the local environmental conditions temperature, pressure, phase, composition and electrochemical potential. A unified description of all of these conditions of state is provided by thermodynamics and a property called the Gibbs free energy, G. Allowing for the influx of chemicals into the reaction system defines an open system with a change in the internal energy dt/ given by ... 

The energy relations associated with the redox processes in wastewater follow the general rules of thermodynamics (Castellan, 1975 Atkins, 1978). The Gibbs free energy, G, of the system is the major thermodynamic function defining the state — and the change in state — of the biochemical redox processes. At constant temperature and under constant pressure, AG is equal to the maximum work, which can be produced by the redox process ... 

Let us consider a rock at temperature T whose chemical composition q (recipe) is expressed as the vector of all the molar fractions x0 of s elements or oxides. It is assumed that it can be made by an arbitrarily large number p s of mineral phases exclusive of solid solution. B is the component matrix of these minerals for the selected set of elements or oxides. Let nj be the number of moles of mineral j and gj its Gibbs free energy of formation AGf T estimated when formed from either the elements or the oxides. The function to be minimized is the Gibbs free energy G given by... 

A widely-used alternative is the free energy perturbation technique (FEP),9"11,72"74 which will be discussed for the Gibbs free energy G. It involves a thermodynamic cycle such as the following, in which X and Y are two different molecules that are undergoing solvation in a particular solvent ... 

Our goal in this chapter is to help you learn the laws of thermodynamics, especially the concepts of entropy and free energy. It might be helpful to review Chapter 6 on thermochemistry and the writing of thermochemical equations. The concept of Gibbs free energy (G) will be useful in predicting whether or not a reaction will occur spontaneously. Just like in all the previous chapters, in order to do well you must Practice, Practice, Practice. 

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