Solution, Gibbs free energy

Figure 1. Free energy and enthalpy for bond dissociation in solution. (+)Gibbs Free Energy, (-) Enthalpy.

COSMO [30] was used to model effect of water solution. Gibbs free energy (AG) of the most stable structures was defined in terms of the COSMO model. To study electronic properties of the considered system the wavelength of the specify electronic transitions were calculated by the TD-DFT/B3PW91 approach. 

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... 

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. 

A solution is a single-phase mixture of more than one compound, and the driving force for its spontaneous formation from the pure compounds at constant T and p is the negative Gibbs free energy change of the mixing process, —AG, as... 

Thus the formation of an ideal solution from its components is always a spontaneous process. Real solutions are described in terms of the difference in the molar Gibbs free energy of their formation and that of the corresponding ideal solution, thus ... 

Real solutions are rarely completely athermal, even when there is considerable similarity between the nature of the molecules. For cases in which some energy effects must be taken into account, Flory introduced an additional term into the expression for excess Gibbs free energy. Adapting the format of the Scatchard-Hildebrand equation, the additional contribution to the excess Gibbs free energy is assumed to be of the form ... 

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

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... 

Table 9.2 Standard heat capacities, entropies, enthalpies, and Gibbs free energies of formation of some common ions in aqueous solution at T= 298.15 K...

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. 

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