Entropy and Gibbs free energy

Entropy, Gibbs Free Energy, and Spontaneous Reactions... 

ENTROPY, GIBBS FREE ENERGY, AND SPONTANEOUS REACTIONS... 

This chapter reviews the fundamental concepts in thermodynamics that a user should master to obtain reliable results in simulation. The thermodynamic network (equations 5.39 to 5.42, and 5.68 to 5.74) links the fundamental thermodynamic properties of a fluid, as enthalpy, entropy, Gibbs free energy and fiigacity, with the primary measurable state parameters, as temperature, pressure, volumes, concentrations. The key consequence of the thermodynamic network is that a comprehensive computation of properties is possible with a convenient PVT model and only a limited number of fundamental physical properties, as critical co-ordinates and ideal gas heat capacity. 

Skill 26.1 Recognize the relationships among enthalpy, entropy, Gibbs free energy, and the equilibrium constant. 

The reversible potential can be evaluated from the Gibbs free energy [10,11,16]. Although thermodynamic data at 25°C are abundant, corresponding values at high temperatures are relatively few. DeBethune and coworkers published very useful papers on the temperature coefficients of electrode potential [17] and of enthalpy, entropy, Gibbs free energy, and specific heat at constant pressure [9]. 

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. 

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... 

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

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. 

Vq is the frequency of the small oscillation, and AG and AS are, respectively, the difference in Gibbs free energy and entropy of the adatom at the saddle point and the equilibrium adsorption site. Ed is the activation energy of surface diffusion, or the barrier height of the atomic jumps. 

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).

The following equations further define Gibbs free energy and relate it to enthalpy and entropy. 

Thermodynamic Functions for Solids.—In the preceding section we have seen how to express the equation of state and specific heat of a solid as functions of pressure, or volume, and temperature. Now we shall investigate the other thermodynamic functions, the internal energy, entropy, Helmholtz free energy, and Gibbs free energy. For the internal... 

Of the three quantities (temperature, energy, and entropy) that appear in the laws of thermodynamics, it seems on the surface that only energy has a clear definition, which arises from mechanics. In our study of thermodynamics a number of additional quantities will be introduced. Some of these quantities (for example, pressure, volume, and mass) may be defined from anon-statistical (non-thermodynamic) perspective. Others (for example Gibbs free energy and chemical potential) will require invoking a statistical view of matter, in terms of atoms and molecules, to define them. Our goals here are to see clearly how all of these quantities are defined thermodynamically and to make use of relationships between these quantities in understanding how biochemical systems behave. 

The relationship between the change in Gibbs free energy and enthalpy, H, and entropy, S, is... 

Printed outputs Cartesian Coordinates of Atoms Molecular Orbital Energies and Eigenfunctions Mulliken Population Analysis Atom Occupancies and Charges Vibrational Frequencies and Intensities Raman Active, yes/no Zero Point Energy Enthalpy Entropy Gibbs Free Energy, Cy. 

The Effect of Temperature on Gibbs Free Energy and Electro motive Force. When the entropy S is eliminated from equations (18) and (22) we obtain... 

Since both phases have the same Gibbs free energy at the temperature, T, this implies that the substance with the larger entropy (which arises from larger heat capacity) will have the lower Gibbs free energy, and therefore be the stable phase. 

---