Gibbs free energy properties

At the melt is absent and 7 and 7" coexist stably in a mechanical mixture of bulk composition C. The crystallization process in a closed system is thus completely defined at all T (and P) conditions by the Gibbs free energy properties of the various phases that may form in the compositional field of interest. 

Figure 4.3a shows schematically how the Gibbs free energy of liquid (subscript 1) and crystalline (subscript c) samples of the same material vary with temperature. For constant temperature-constant pressure processes the criterion for spontaneity is a negative value for AG, where the A signifies the difference final minus initial for the property under consideration. Applying this criterion to Fig. 4.3, we conclude immediately that above T , AGf = Gj - G. is negative... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Equilibrium combustion product compositions and properties may be readily calculated using thermochemical computer codes which minimize the Gibbs free energy and use thermodynamic databases... 

The Gibbs free energy is given in terms of the enthalpy and entropy, G — H — TS. The enthalpy and entropy for a macroscopic ensemble of particles may be calculated from properties of the individual molecules by means of statistical mechanics. 

This expression shows that the maximum possible useful work (i.e., reversible work) that can be obtained from any process occurring at constant temperature and pressure is a function of the initial and final states only and is independent of the path. The combination of properties U + PV - TS or H - TS occurs so frequently in thermodynamic analysis that it is given a special name and symbol, F, the free energy (sometimes called the Gibbs Free Energy). Using this definition, Equation 2-143 is written... 

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. 

In most applications, thermodynamics is concerned with five fundamental properties of matter volume (V), pressure (/ ), temperature (T), internal energy (U) and entropy (5). In addition, three derived properties that are combinations of the fundamental properties are commonly encountered. The derived properties are enthalpy (//). Helmholtz free energy (A) and Gibbs free energy ) ... 

In addition to the fundamental variables p, V, T, U, and S that we have described so far, three other thermodynamic variables are commonly encountered enthalpy Helmholtz free energy and Gibbs free energy. They are extensive variables that do not represent fundamental properties of the... 

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. 

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. 

What Are the Key Ideas Equilibrium between two phases is reached when the rates of conversion between the two phases are the same in each direction. The rates are equal when the molar Gibbs free energy of the substance is the same in each phase and therefore there is no tendency to change in either direction. The same concepts apply to the dissolving of a solute. The presence of a solute alters the entropy of a solvent and consequently affects its thermodynamic properties. 

Because osmosis is a thermodynamic property, we can expect it to be related to the effect of the solute on the enthalpy and entropy of the solution solvent flows until the molar Gibbs free energy of the solvent is the same on each side of the membrane We have already seen several times that a solute lowers the molar Gibbs free energy of the solution below that of the pure solvent, and solvent therefore has a tendency to pass into the solution (Fig. 8.33). 

Another property of the system, G, the free energy, or the Gibbs free energy, is related to enthalpy and entropy by ... 

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 ... 

Values of the equilibrium constants at 298°K can also be calculated from tabulated thermodynamic properties. The standard Gibbs free energy of the reaction at 298°K is first calculated, and the equilibrium constant at 298°K is then determined from the equation... 

An entirely different approach to equilibrium adsorption is to assume that adsorbed layers behave like liquid films, and that the adsorbed molecules are free to move over the surface. It is then possible to apply the equations of classical thermodynamics. The properties which determine the free energy of the film are pressure and temperature, the number of molecules contained and the area available to the film. The Gibbs free energy G may be written as ... 

The most important property of a liquid-gas interface is its surface energy. Surface tension arises at the boundary because of the grossly unequal attractive forces of the liquid subphase for molecules at its surface relative to their attraction by the molecules of the gas phase. These forces tend to pull the surface molecules into the interior of the liquid phase and, as a consequence, cause liquids to minimize their surface area. If equilibrium thermodynamics apply, the surface tension 7 is the partial derivative of the Helmholtz free energy of the system with respect to the area of the interface—when all other conditions are held constant. For a phase surface, the corresponding relation of 7 to Gibbs free energy G and surface area A is shown in eq. [ 1 ]. 

Thermodynamic properties for explosion calculations are presented for major organic chemical compounds. The thermodynamic properties include enthalpy of formation, Gibbs free energy of formation, internal energy of formation and Helmholtz free energy of formation. The major chemicals include hydrocarbon, oxygen, nitrogen, sulfur, fluorine, chlorine, bromine, iodine and other compound types. 

Equilibrium combustion product compositions and properties may be readily calculated using thermochemical computer codes which minimize the Gibbs free energy and use thermodynamic databases containing polynomial curve-fits of physical properties. Two widely used versions are those developed at NASA Lewis (Gordon and McBride, NASA SP-273, 1971) and at Stanford University (Reynolds, STANJAN Chemical Equilibrium Solver, Stanford University, 1987). 

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