Gibbs Free Energy and Equilibria

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 ... 

Because the chemical potential is a thermodynamic property of species i, it must have the same value irrespective of the particular convention chosen for a,. It follows that the value of the standard chemical potential h% and consequently the values of he standard Gibbs free energy and equilibrium constant should depend on that choice. As Hi is the value of Hi for unit activity, the state having such activity in the scale chosen is the standard state. There are lUPAC recommendations for most common situations (Cox et al. 1982). Eor the solutes in the solution phase activities af in all cases collected in Table 5.1, the recommended and commonly anployed Henry law convention is used... 

Exploring the relationship between Gibbs free energy and equilibrium further, consider again the Haber process for the production of ammonia (arguably one of the key industrial processes ever developed) ... 

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

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... 

FIGURE 7.24 At constant temperature and pressure, the direction of spontaneous change is toward lower Gibbs free energy. The equilibrium state of a system corresponds to the lowest point on the curve. 

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). 

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. 

In this chapter, we discuss classical non-stoichiometry derived from various kinds of point defects. To derive the phase rule, which is indispensable for the understanding of non-stoichiometry, the key points of thermodynamics are reviewed, and then the relationship between the phase rule, Gibbs free energy, and non-stoichiometry is discussed. The concentrations of point defects in thermal equilibrium for many types of defect structure are calculated by simple statistical thermodynamics. In Section 1.4 examples of non-stoichiometric compounds are shown referred to published papers. 

A system has the minimum value of the Gibbs free energy at equilibrium. Suppose we have a system which consists of three phases, namely gas, liquid and solid solutions, with a number of different species (1,2,3,...) ... 

AU,) - the differences between the depths of different minima so going down from a shallower to a deeper minimum of the molecular PES means decreasing the Gibbs free energy and such a process generally has an equilibrium constant larger than unity. However, for precise calculations, the terms coming from translations, rotations and vibrations also must be taken into account. 

At equilibrium, the extensive properties U, S, V, Nh and the linear combination of them are functions of state. Such combinations are the Helmholtz free energy, the Gibbs free energy, and enthalpy, and are called the thermodynamic potentials. Table 1.13 provides a summary of the thermodynamic potentials and their differential changes. The thermodynamic potentials are extensive properties, while the ordinary potentials are the derivative of the thermodynamic potentials and intensive properties. 

A system at constant temperature, pressure, and mole numbers tries to decrease its Gibbs free energy. At equilibrium, the Gibbs free energy of the system is minimized. 

It will be shown below with examples that the morphology of a multiphase material is the result of an interplay between the thermodynamic drive towards its equilibrium morphology of minimum Gibbs free energy and kinetic barriers inhibiting it from reaching that morphology. 

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