Gibbs molar free energy potential

Chemical potential also is called Gibbs molar free energy. 

The behaviour of most metallurgically important solutions could be described by certain simple laws. These laws and several other pertinent aspects of solution behaviour are described in this section. The laws of Raoult, Henry and Sievert are presented first. Next, certain parameters such as activity, activity coefficient, chemical potential, and relative partial and integral molar free energies, which are essential for thermodynamic detailing of solution behaviour, are defined. This is followed by a discussion on the Gibbs-Duhem equation and ideal and nonideal solutions. The special case of nonideal solutions, termed as a regular solution, is then presented wherein the concept of excess thermodynamic functions has been used. 

Equation 9.20 gives the pressure dependence of the Gibbs free energy of a pure substance. More generally, for a mixture one should consider the chemical potential /r, which is defined as the partial molar free energy of species k ... 

For a pure substance, the molar Gibbs free energy is also known as the chemical potential8 p. In a solution, the partial molar free energy is the chemical potential Pi. Hence,... 

If the liquid junction is formed between two aqueous solutions of electrolytes containing many types of ions of different valency and at different concentrations, the electrochemical potentials of all species are linked by the Gibbs-Duhem equation ((A.21), Appendix A). For any moving species, the change of its electrochemical potential is caused by the change of its molar free energy G . 

Although the partial molar Gibbs free energy (G<) or the chemical potential (pi) defined by the equation given below pertains to the individual components of the system, it is a property of the system as a whole. The value of the partial molar free energy depends not only the nature of the particular substance in question but also on the nature and relative amounts of the other components present as well. 

Measurements of the potentials of galvanic cells at open circuit give information about the thermodynamics of cells and cell reactions. For example, the potential of the cell in Figure 1, when the solution concentrations are 1 molar (1 M) at 25°C, is 1.10 V. This is called the standard potential of the cell and is represented by E°. The available energy (the Gibb s free energy AG°) of the cell reaction given in equation (3) is related to E° by... 

Partial Molar Free Energy Chemical Potential.—The partial molal free energy is an important thermodynamic property in connection with the study of electrolytes it can be represented either as G, where G is employed for the Gibbs, or Lewis, free energy, or by the symbol /i, when it is referred o as the chemical potential thus the appropriate form... 

The symbols and nomenclature are essentially those which have been widely adopted in the American chemical literature however, for reasons given in the text, and in accordance vith a modern trend, the Gibbs symbol fjL and the shorter term chemical potential" are employed for the partial molar free energy. Because atmospheric pressure is postulated for the conventional standard state of a liquid, some confusion has resulted from the use of the same S3rmbol for the standard state as for the liquid at an arbitrary pressure. Hence, the former state is indicated in the text in... 

It s the molar Gibb s free energy and it s intensive. Conceptually, chemical potential is to Gibb s free energy what specific heat capacity is to heat capacity in the former it s per mole and the latter is typically per mass unit. 

In a homogeneous mixture each component i has a chemical potential pt, defined as the partial molar free energy of that component (i.e., the change in Gibbs energy per mole of component ti added, for addition of an infinitesimally small amount). It is given by... 

In the case of the first two partial derivatives, the subscript n, means that the moles of all components (i = 1, 2,. .., c) are held fixed. The subscript njti which appears on the derivatives included in the summation means that the moles of all components except i are held fixed. The partial derivative (dG/dw,) IS called the partial molar free energy, and denoted by G,. The partial molar free energy G, was introduced by Gibbs who called it //,, the chemical potential. Thus... 

The equilibrium state of a system at constant temperature and pressure is characterized by a minimum in the Gibbs free energy of the system. For a multicomponent, multiphase system, the minimum free energy corresponds to uniformity of the chemical potential (gi) of each component throughout the system. For a binary system, the molar free energy (G) and chemical potentials are related by Equation (2.1),... 

Clearly, this state can be attained by transferring a volume vxic of pure solvent from the particular volume concerned to the rest of the solution. To that end we must transfer vx/eVo moles of solvent, if lA represents the molar volume of the solvent. Now, if go is the molar potential of the solvent, the increase in Gibb s free energy when vdxjcVo moles of solvent are transferred from a volume in which the concentration is c -f JC to another volume in which the concentration is c, is given by... 

Solubility is defined by the thermodynamic equilibrium of a solute between two phases, which in the context of this chapter are a solid phase and a liquid solution phase.The criterion for equilibrium between coexisting phases is that the temperature, pressure and molar free energies or chemical potentials of each individual species in each phase are equal.For a co-crystal, however, the sum of the molar free energies or chemical potentials of each co-crystal component plays a key role in determining phase equilibria. The molar Gibbs energy of the co-crystal A B in equilibrium with a solution phase is given by ... 

The chemical potential is an example of a partial molar quantity /ij is the partial molar Gibbs free energy with respect to component i. Other partial molar quantities exist and share the following features ... 

We divide by Avogadro s number to convert the partial molar Gibbs free energy to a molecular quantity, and the minus sign enters because the force and the gradient are in opposing directions. Recalling the definition of chemical potential [Eq. (8.13)], we write jUj + RT In aj = ii2 + RT In 7jC, where aj... 

The energy of a system can be changed by means of thermal energy or work energy, but a further possibility is to add or subtract moles of various substances to or from the system. The free energy of a pure substance depends upon its chemical nature, its quantity (AG is an extensive property), its state (solid, liquid or gas), and temperature and pressure. Gibbs called the partial molar free heat content (free energy) of the component of a system its chemical potential... 

Hence, for a pure substance, the chemical potential is a measure of its molar Gibbs free energy. We next want to describe the chemical potential for a component in a mixture, but to do so, we first need to define and describe a quantity known as a partial molar property. 

Before leaving our discussion of partial molar properties, we want to emphasize that only the partial molar Gibbs free energy is equal to n,-. The chemical potential can be written as (cM/<9 ,)rv or (dH/dnj)s p H partial molar quantities for fi, into equations such as those given above. 

The quantity of primary interest in our thermodynamic construction is the partial molar Gibbs free energy or chemical potential of the solute in solution. This chemical potential reflects the conformational degrees of freedom of the solute and the solution conditions (temperature, pressure, and solvent composition) and provides the driving force for solute conformational transitions in solution. For a simple solute with no internal structure (i.e., no intramolecular degrees of freedom), this chemical potential can be expressed as... 

It is also evident from figure 2.1 that the molar Gibbs free energy of a pure phase composed of a single component is equivalent to the chemical potential of the component itself... 

Linear regions (constant slope, hence constant potentials) define the composition interval over which a two-phase assemblage is stable. Because the minimum Gibbs free energy curve of the system is never convex, the chemical potential of any component will always increase with the increase of its molar proportion in the system. 

Once the standard state potentials at the P and T of interest have been calculated (ix° = Gf for a pure single-component phase), the ideal and excess Gibbs free energy of mixing terms are easily obtained on the basis of the molar fractions of the various melt components and the binary interaction parameters listed in table 6.15 (cf eq. 6.78). 

We can then derive the calculated Gibbs free energy of mixing with respect to the molar amount of the component of interest, thus obtaining the difference between the chemical potential of the component in the mixture and its chemical potential at standard state ... 

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