Gibbs free energy and

Figure 4.3 Behavior of thermodynamic variables at T for an idealized phase transition (a) Gibbs free energy and (b) entropy and volume.

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... 

Thermodynamic data Data associated with the aspects of a reaction that are based on the thermodynamic laws of energy, such as Gibbs free energy, and the enthalpy (heat) of reaction. 

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. 

For a reversible cell at equilibrium the Gibbs free energy and the reversible e.m.f. E, are related 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... 

J. B. Ott, K. N. Marsh and R. H. Stokes. "Excess Enthalpies. Excess Gibbs Free Energies, and Excess Volumes for (Cyclohexane + //-Hexane). and Excess Gibbs Free Energies and Excess Volumes for (Cyclohexane + Methylcyclohexane) at 298.15 and 308.15 K". J.Chem. Thermodyn., 12, 1139-1148 (1980). 

The challenge that we now face is to justify these remarks and to derive a quantitative relation between the Gibbs free energy and the maximum nonexpansion work that a system can do. 

From values in Appendix 2A, determine the standard Gibbs free energy and the standard entropy for the reaction. 

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

Relation between standard reaction Gibbs free energy and equilibrium constant van t Hoff equation ... 

Relation between Gibbs free energy and maximum nonexpansion work ... 

When an element enters into a reaction, its standard Gibbs free energy and standard enthalpy of formation are taken as zero if its state of aggregation is that selected as the basis for... 

The enthalpies of solution and solubilities reviewed here provide much of the experimental information required in the derivation of single-ion hydration and solvation enthalpies, Gibbs free energies, and entropies for scandium, yttrium, and lanthanide 3+ cations. 

Whereas a thermal reaction from R to P2 or P3 involves an increase in Gibbs free energy and so will not occur spontaneously, the photochemical reactions from R involve a decrease in free energy and so are more likely to occur spontaneously. This allows the photochemical production of so-called energy-rich or strained compounds such as P2 and P3 to be carried out at low temperatures, as these products may undergo decomposition at higher temperatures. 

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). 

Relationships Between Gibbs Free Energy and Other Thermodynamic Magnitudes... 

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