Molar free enthalpy

The driving force for the transport of all particles is a change in the electrochemical potential /i, which is related to the partial molar free enthalpy /i, and the electric potential 0 as follows ... 

Numerous disperse dyes are marketed in a metastable crystalline form that gives significantly higher uptake than the corresponding more stable modification. The molar free enthalpy difference can be used as a criterion of the relative thermodynamic stabilities of two different modifications [53]. Certain dyes can be isolated in several different morphological forms. For example, an azopyrazole yellow disperse dye (3.52) was prepared in five different crystal forms and applied to cellulose acetate fibres. Each form exhibited a different saturation limit, the less stable modifications giving the higher values [54]. 

Thermodynamic stability. Let us consider a liquid binary mixture of two species, a and b, crystallizing to a solid solution. Let G be the free enthalpy (Gibbs) function of each phase, either solid or liquid. Calculate the change AG in molar free enthalpy when a liquid of molar composition XUqb crystallizes to a solid of molar composition... 

The terms on the right-hand side of the first line represent the difference between the molar free enthalpies of the solid and liquid solutions at composition X Mb. In addition, a standard result for binary systems (e.g., Swalin, 1962) states for G and n the following relationship... 

The only thermodynamic condition then required for this reaction to be driven from left to right is that the standard molar free enthalpy of the reaction be negative, that is, the following inequality must hold E pq < E ac, where E ac represents the standard redox potential of the A/C couple. 

These simple equations for the mixing terms of the molar free enthalpy and entropy are characteristic for perfect solutions and are identical with those for ideal gas mixtures. 

Since an ion has an electric charge, the partial molar free enthalpy gt of an ion i consists not only of the chemical potential ju, but also of the electrostatic energy zfffy of the ion where z, is the ionic valence, F is the Faraday constant, and is the electrostatic inner potential of the solution. This partial molar free enthalpy gt defines the electrochemical potential rj of an ion in an electrolyte solution as shown in Eq. 8.38 ... 

Charged particles such as ions and electrons play an important role in what is called electrochemical processes. We shall now discuss the energy level of ions and electrons in an electrochemical system. The partial molar free enthalpy (partial molar Gibbs energy) of a charged particle i, as described in the foregoing chapter (section 8.7), is represented by the electrochemical potential r)t shown in Eq. 9.1 ... 

In chemical thermodynamics the standard chemical potential ut of a compound i is defined as the molar free enthalpy Ag° for the formation of the compound from its constituent elements j in their stable molecular form in the standard state, and their chemical potential values are set zero in the standard state fit-Ag°f. In exergy engineering the standard molar exergy e° of a compound i is defined as consisting of the molar free enthalpy Ag°f for the formation of the compound in the standard state from its constituent elements and the stoichiometrical sum of the standard chemical exergy values e° of the constituent elements j in their stable state at the standard temperature T° and pressure p° ef- Ag°f + 2 vy e°. 

H = qp, heat content F = wp, work function G/N = /r, partial molar free enthalpy... 

The molar free enthalpy G, in analogy to a mechanical system, is called the chemical potential and is designated with p ( i = G). In a mechanical system, a body moves in the direction of decreasing potential (e.g. an object falls to earth or a ground state) and from this comes the analogy to the chemical potential. 

Thermo chemical properties (Chaps. 20-22) molar free enthalpy of formation... 

Molar elastic wave functions, 383,391 Molar free enthalpy of formation, 792 Molar functions, classification, 62 Molar heat... 

The chemical potential or the partial molar free enthalpy (5G/5wi) of the... 

The combination of eqns. (11) and (7) allows the formulation of an alternative expression of the second law, it introduces the partial molar free enthalpy, g., (also termed Gibbs free energy) ... 

The molar free enthalpies and enthalpies of combustion at standard conditions will be termed Ag°. and Ah , respectively. 

Now we subdivide the system into small subsystems and we assume that the molar free enthalpy is varying with position. Thus, in addition, the molar free enthalpy will become a function of position (jc, y, z) = r and in addition, if we allow a variation in time, also a function of time t. 

Free enthalpy characterizes maximum useful work, which is performed between atoms and molecules on the account of potential energy of only electrons. In this coimection it may be assumed that the free enthalpy of elements per se is equal to zero. Then the values of median (molar) free enthalpy and of any compounds may be characterized as energy of its formation in the amoimt of 1 mole. In order to compare free enthalpy of the formation of different compounds, it is necessary to measure the energy of their formation from individual elements under some identical conditions. 

In pure water, Cr may interact only with hydroxyl ion OH and have 4 migration forms Cr, Cr(OH), Cr(OH)2% Cr(OH)j°. Values of molar free enthalpy of the... 

Then is identified the number and nature of compoimds, which the selected basis component B, is capable of forming in water of given composition within H O stability boimd-aries. For all compoimds are found values of molar free enthalpy of their formation among them are identified soluble and insoluble (minerals) under assigned conditions. This allows the identification among them of migration forms and determination of the nature of boundaries between their stability fields. 

However, the concept of current flow is only applicable to aqueous systems. In the gaseous phase of air, electron exchange occurs within the transition state of two molecular entities, basically in a wider sense of charge transfer complexes. Any substance in a specified phase has an electrochemical potential consisting of the chemical potential Pi (partial molar free enthalpy) and a specified electric potential ... 

It was shown before that the phase equilibrium of a single component system can be described by the free enthalpy G. The partial molar free enthalpy G, is... 

The variable p, is called the chemical potential of component i. The total differential of the molar free enthalpy is then... 

These excess quantities can be closely coimected to the activity coefficients. With the excess molar free enthalpy g = Ag - Agthis gives... 

By means of the preliminary results it has been possible to thermodynamically model the presence of chlorine in nickel silicides. Chlorine-containing silicides may be taken as diluted solid solutions of chlorine in nickel silicides, which in the thermodynamic sense can be described by a modified Wagner model [5]. The molar free enthalpy of the solution of chlorine in silicide (Gm) is derived from Eq. 4. 

Solvation processes occurring in a solvent mixture, i.e., the interactions between the solvent and the solute, are even more involved than the interactions between the solvent components themselves. Padova [Pa 68] stated that it is the partial molar free enthalpy of solvation of the components that determines which of the components of the solvent mixture will solvate the dissolved ion. Naturally, this is true in general, but it hardly gives a factual basis for the interpretation of the special interactions. 

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