Gibbs free energy generalized

Polymorphic form also influences dissolution rate and solubility. By definition, metastable polymorphs should have higher solubility and faster dissolution rates than those of their more stable crystalline counterparts because they possess a higher Gibbs free energy. Generally, only a moderate enhancement of solubility and dissolution rate can be achieved through polymorphic modification, although... 

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. 

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

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. 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

The changes in free energy of formation of Reaction (1) are shown in Fig. 2.1 as a function of temperature. " The values of AG were calculated using Eq. (1) above for each temperature. The Gibbs free-energy values of the reactants and products were obtained from the JANAF Tables.1 Other sources of thermodynamic data are listed inRef 6. These sources are generally accurate and satisfactory forthe thermodynamic calculations of most CVD reactions they are often revised and expanded. 

At sufficiently high temperatures, the term TS in the Gibbs free energy will dominate and the stable isomer will be that of greater entropy which is in general the HS state. 

Bornian theory of the Gibbs free energy of ion resolvation, a vast amount of work dealing with ion solvation and resolvation could not fully be reviewed. The reader is referred to some books [2-5] and review articles [6-10] for a general survey. 

This example illustrates the principle that values of AG° and AH0 may be calculated from values of the enthalpies and Gibbs free energies of formation of the products and reactants. In more general form,... 

The standard Gibbs free energy change for a reaction refers to the process wherein the reaction proceeds isothermally, starting with stoichiometric quantities of reactants each in its standard state of unit activity and ending with products each at unit activity. In general it is nonzero and given by... 

The general equation for a straight line is given below with the slightly modified Gibbs Free-Energy equation as a reference AG° = - AS°T + AH° (here AH° is assumed to be constant)... 

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 ... 

One of the goals of chemists is to be able to predict whether or not a reaction will be spontaneous. Some general guidelines for a spontaneous reaction have already been presented (negative A//and positive AS), but neither is a reliable predictor by itself. Temperature also plays a part. A thermodynamic factor that takes into account the entropy, enthalpy, and temperature of the reaction should be the best indicator of spontaneity. This factor is called the Gibbs free energy. 

More precise relative Gibbs free-energy scales were established using equation 9. Other metal cations have also been considered, such as Li, A1 and Mn in general, the order of basicity found in the K+ scale was not altered33. 

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