Free enthalpy Gibbs function

Thermodynamic stability. Let us consider a liquid binary mixture of two species, a and b, crystallizing to a solid solution. Let G be the free enthalpy (Gibbs) function of each phase, either solid or liquid. Calculate the change AG in molar free enthalpy when a liquid of molar composition XUqb crystallizes to a solid of molar composition... 

From the absolute entropy andi T - the free enthalpy (Gibbs function) Gt -... 

The determination of Nemst s law involves thermodynamic notions. We use the free enthalpy (Gibbs function) notated as AG. Taking n moles of electrons to be involved in the chemical reaction, we get ... 

Fuel Cell Efficiency The theoretical energy conversion efficiency of a fuel cell e° is given by the ratio of the free energy (Gibbs function) of the cell reaction at the cell s operating temperature AG, to the enthalpy of reaction at the standard state AH°, both quantities being based on a mole of fuel ... 

Exergy therefore results from a difference in free enthalpy (Gibbs energy) between the energy carriers under consideration and the common reference substances in the natural environment exergy is thus a function of the thermodynamic state of the substances under consideration and of the thermodynamic state of the common reference substances in the natural environment. In other words, exergy arises from an interaction between the substances under consideration and the common reference substances in the environment. 

The thermodynamic characteristics of solutions are often expressed by means of excess functions. These are the amounts by which the free energy, entropy, enthalpy, etc. exceed those of a hypothetical ideal solution of the same composition (Denbigh, 1981). The excess free energy is closely related to the activity coefficients. The total free enthalpy (Gibbs free energy) of a system is ... 

Phase relationships in equilibrium are determined by the free enthalpy (Gibbs free energy) of the system. The thermodynamic bdiaviour of polymer solutions can be very well described with the free enthalpy of mixing function derived, independently, by Florv (6,7) and Huggins (8—10) on the basis of the lattice theory of the liquid state. For the simplest case conceivable — a solution of a polydisperse polymer in a single solvent quasi-binary system) — we have... 

From the absolute entropy and i/x - Ho , the free enthalpy (Gibbs fimction) Gt - Ho can be calculated for amorphous solids. For amorphous linear macromolecules, the reported thermodynamic functions listed in the sources for Table 1 are... 

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... 

The well-known thermodynamic rule says that the two substances of different nature are miscible if the process brings about a gain in the value of the Gibbs function, AG, also called Gibbs energy or free enthalpy—that is, if AG > 0. The Gibbs function is connected with further basic thermodynamic quantities enthalpy and entropy, by the relation... 

Early chemists thought that the beat of reaction, —AH. should be a measure of the "chemical affinity" of a reaction. With the introduction of the concepl of netropy (q.v.) and ihe application of the second law of thermodynamics lo chemical equilibria, it is easily shown that the true measure of chemical affinity and Ihe driving force for a reaction occurring at constant temperature and pressure is -AG. where AG represents the change in thermodynamic slate function, G. called Gibbs free energy or free enthalpy, and defined as the enthalpy, H, minus the entropy. S. times the temperature, T (G = H — TS). For a chemical reaction at constant pressure and temperature ... 

Figure 15.1 Standard enthalpy, Gibbs free energy, and entropy of formation as a function of temperature for the Haber reaction 3H2(g) + N2(g) = 2NH3(g).

Gibbs used the symbol for this function, and G. N. Lewis used F. Sometimes this is referred to as the free energy or the Gibbs free energy. The term free enthalpy has also been used. The IUPAC recommendation, which is followed in this book, is to use the symbol G for the Gibbs energy. For simplicity we omit the word function. ... 

We then introduce two new energy functions called free energy / (Helmholtz energy) for the independent variables temperature T and volume V, and free enthalpy G (Gibbs energy) for the independent variables temperature T and pressure p as defined, respectively, in Eqs. 3.21 and 3.22 ... 

As mentioned above, free energy F is occasionally called the Helmholtz energy, and free enthalpy G is frequently called the Gibbs energy. These two energy functions F and G correspond to the amounts of energy that are freed from the restriction of entropy and hence can be fully utilized for irreversible processes to occur at constant temperature. 

Among the four principal thermodynamic energy functions, U, H, F, and G, the free enthalpy G (Gibbs energy) associated with the intensive variables T and p is a homogeneous function of the first degree with respect to the extensive independent variable of the number of moles n. of the constituent substances present in the system considered, so that it can be expressed as the sum of the chemical potentials of all constituent substances at constant temperature and pressure. 

Comparing these four equations from 5.15 to 5.18, we realize that the free enthalpy G (Gibbs energy) is the most convenient in that it is directly proportional to the chemical potentials of the constituent substances and is a function of the characteristic intensive variables T and p. 

Henceforth we concentrate on the use of Eqs. (l.lS.lf), (1.13.2f), (1.13.3f), (1.13.4e) as the fundamental building blocks (as applied to equilibrium processes) for all subsequent thermodynamic operations. The enormous advantage accruing to their use is that by the First Law all of these functions depend solely on the difference between the initial and the final equilibrium state. We no longer rely on the use of quantities such as heat and work that are individually path dependent. As will be shown shortly and in much of what is to follow, these functions of state may be manipulated to obtain useful information for characterizing experimental observations. One should note that the choice of the functions E, H, A, or G depends on the experimental conditions. For example, in processes where temperature and pressure are under experimental control one would select the Gibbs free energy as the appropriate function of state. Processes carried out under adiabatic and constant pressure conditions are best characterized by the enthalpy state function. 

Description of thermochemical properties of chemical compounds, including that of polymers can be done using a few thermodynamic functions. One basic function is Gibbs free enthalpy that is expressed as follows [1] ... 

The heat capacity quantifies the amount of thermal energy absorbed by a material upon heating, or released by it upon cooling. The heat capacity can be used to calculate all of the other thermodynamic properties, such as the enthalpy, entropy and Gibbs free energy, as functions of the temperature and pressure. The thermodynamic properties are often called calorimetric properties because they are usually measured by calorimetry [1-6]. 

Gef(r), Gibbs energy function (free enthalpy function)... 

Fig. 2.5 Gibbs energy function (free enthalpy function) of silicon for the solid and liquid phases (a) and the gaseous phase (b) as a function of temperature at 1 bar.

One typically starts with an internal energy of a macroscopic system, expressed as the internal energy of the periodically repeated unit cell. This state function is part of another state function H, the enthalpy, which is a very useful energetic measure for conditions of constant pressure p. For a complete picture, one also needs to know the value of the state function T, the temperature, and that of the state function S, the entropy, a measure of chaos and also probability. These functions may be combined to yield the Gibbs energy (or free enthalpy) G, the true and final measure of stability. In its difference form, the so-called Gibbs-Helmholtz formula reads... 

To use entropy as a criterion of spontaneous change, it is necessary to investigate both system and surroundings. For that reason, a further thermodynamic function, the free energy, or Gibbs function G, is used. This combines the enthalpy H and the entropy S and allows the combination of the effects of both H and S on the system only, generally at constant pressure. The quantities U, if, G and S are referred to as state functions, since they depend only on the state of the system. 

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