Thermodynamics chemical potential

The thermodynamic chemical potential is then obtained by averaging the Boltzmann factor of this conditional result using the isolated solute distribution function Sa Sn). Notice that the fluctuation contribution necessarily lowers the calculated free energy. 

Electrons, holes, or other mobile charge carriers can be considered as chemically reactive species that can be allotted a thermodynamic chemical potential—the electrochemical potential, X, defined as... 

See Activity Coefficients Additivity Principle Biochemical Thermodynamics Chemical Potential Equilibrium Constants Hess s Law Innate Thermodynamic Quantities Molecular Crowding Thermodynamics, Laws of Thermodynamic Cycle Thermodynamic Equations of State... 

ACTIVITY COEEEICIENTS ADDITIVITY PRINCIPLE BIOCHEMICAL THERMODYNAMICS CHEMICAL POTENTIAL EQUILIBRIUM CONSTANTS HESS S LAW... 

In treating the fundamental equations of thermodynamics, chemical potentials of species are always used, but in making calculations when T and P are independent variables, chemical potentials are replaced by Gibbs energies of formation AfG . Therefore, we will use equation 3.1-10 in the form... 

Job G (1992) Teaching thermodynamics Chemical potential from the beginning. Proc. Taormina Conf, on Thermodynamics, Classe I di Scienze Fis. Mat. e Nat. 70 385 09... 

This presents some difficulties. The scale is a set of negative numbers, and it is always more difficult to decide which of two negative numbers is the larger More serious is the conflict with the existing usage of p, as the ordinary thermodynamic chemical potential pY-... 

For all molecules except the smallest, E is much larger than Np. Examples are given in Table 2.6. Most of the energy is not relevant to chemistry since it comes from the inner-shell electrons. For this reason, we subtract from E the energies of the constituent atoms. This gives us the so-called electronic energy of statistical thermodynamics, 7, which is by far the largest part of the thermodynamic chemical potential. ... 

It should be stressed, that the above information-theoretic, thermodynamic chemical potential co differs from the chemical potential of equations (17) and (29). 

Because of the relationships between the various energies defined by thermodynamics, chemical potential can also be defined in terms of the other energies, but with different state variables held constant ... 

This chemical potential is equal to the thermodynamic chemical potential divided by Avogadro s constant. The number of molecules is an integer, so we use a quotient of finite differences to approximate the derivative in Eq. (26.1-23) ... 

In order to compare the energetic stability of different atomic structures for a given surface orientation but different surface stoichiometries, the TEs are plotted in a surface phase diagram. Here the surface energy S2 of the various structure models is presented versus the thermodynamic chemical potential of one of its elements A/r with respect to its bulk value. 

This definition introduces electronegativity as an electronic chemical potential similar to a thermodynamic chemical potential in any system of atoms in a nonequilibrium state, there must be a flux of electronic density from the regions of high potential to the regions of lower potential. 

In thermodynamic terms the equilibrium constant is related to the standard chemical potential by the equation... 

It is generally assumed that isosteric thermodynamic heats obtained for a heterogeneous surface retain their simple relationship to calorimetric heats (Eq. XVII-124), although it may be necessary in a thermodynamic proof of this to assume that the chemical potential of the adsorbate does not show discontinu-... 

A careful analysis of the fundamentals of classical thermodynamics, using the Born-Caratheodory approach. Emphasis on constraints, chemical potentials. Discussion of difficulties with the third law. Few applications. 

The thermodynamic properties that we have considered so far, such as the internal energy, the pressure and the heat capacity are collectively known as the mechanical properties and can be routinely obtained from a Monte Carlo or molecular dynamics simulation. Other thermodynamic properties are difficult to determine accurately without resorting to special techniques. These are the so-called entropic or thermal properties the free energy, the chemical potential and the entropy itself. The difference between the mechanical emd thermal properties is that the mechanical properties are related to the derivative of the partition function whereas the thermal properties are directly related to the partition function itself. To illustrate the difference between these two classes of properties, let us consider the internal energy, U, and the Fielmholtz free energy, A. These are related to the partition function by ... 

As noted above, all of the partial molar quantities are concentration dependent. It is convenient to define a thermodynamic concentration called the activity aj in terms of which the chemical potential is correctly given by the relationship... 

The first point in developing the thermodynamic method is the observation that for equilbrium between two phases-say, a and 3-the chemical potential must be equal in both phases for all components ... 

Thermodynamics provide a straightforward method for quantifying this situation. The criterion for equilibrium is the equality of chemical potential in... 

The tme driving force for any diffusive transport process is the gradient of chemical potential rather than the gradient of concentration. This distinction is not important in dilute systems where thermodynamically ideal behavior is approached. However, it becomes important at higher concentration levels and in micropore and surface diffusion. To a first approximation the expression for the diffusive flux may be written... 

The interface region in a composite is important in determining the ultimate properties of the composite. At the interface a discontinuity occurs in one or more material parameters such as elastic moduli, thermodynamic parameters such as chemical potential, and the coefficient of thermal expansion. The importance of the interface region in composites stems from two main reasons the interface occupies a large area in composites, and in general, the reinforcement and the matrix form a system that is not in thermodynamic equiUbhum. 

Internal and External Phases. When dyeing hydrated fibers, for example, hydrophUic fibers in aqueous dyebaths, two distinct solvent phases exist, the external and the internal. The external solvent phase consists of the mobile molecules that are in the external dyebath so far away from the fiber that they are not influenced by it. The internal phase comprises the water that is within the fiber infrastmcture in a bound or static state and is an integral part of the internal stmcture in terms of defining the physical chemistry and thermodynamics of the system. Thus dye molecules have different chemical potentials when in the internal solvent phase than when in the external phase. Further, the effects of hydrogen ions (H" ) or hydroxyl ions (OH ) have a different impact. In the external phase acids or bases are completely dissociated and give an external or dyebath pH. In the internal phase these ions can interact with the fiber polymer chain and cause ionization of functional groups. This results in the pH of the internal phase being different from the external phase and the theoretical concept of internal pH (6). 

Determining the cell potential requites knowledge of the thermodynamic and transport properties of the system. The analysis of the thermodynamics of electrochemical systems is analogous to that of neutral systems. Eor ionic species, however, the electrochemical potential replaces the chemical potential (1). 

Perhaps the most significant of the partial molar properties, because of its appHcation to equiHbrium thermodynamics, is the chemical potential, ]1. This fundamental property, and related properties such as fugacity and activity, are essential to mathematical solutions of phase equihbrium problems. The natural logarithm of the Hquid-phase activity coefficient, Iny, is also defined as a partial molar quantity. For Hquid mixtures, the activity coefficient, y, describes nonideal Hquid-phase behavior. 

Thermodynamics of Liquid—Liquid Equilibrium. Phase splitting of a Hquid mixture into two Hquid phases (I and II) occurs when a single hquid phase is thermodynamically unstable. The equiUbrium condition of equal fugacities (and chemical potentials) for each component in the two phases allows the fugacitiesy andy in phases I and II to be equated and expressed as ... 

Equation (4-8) is the fundamental property relation for singlephase PVT systems, from which all other equations connecting properties of such systems are derived. The quantity is called the chemical potential of ecies i, and it plays a vital role in the thermodynamics of phase ana chemical equilibria. 

Since the infinite dilution values D°g and Dba. re generally unequal, even a thermodynamically ideal solution hke Ya = Ys = 1 will exhibit concentration dependence of the diffusivity. In addition, nonideal solutions require a thermodynamic correction factor to retain the true driving force for molecular diffusion, or the gradient of the chemical potential rather than the composition gradient. That correction factor is ... 

This expression can be used to describe both pore and solid diffusion so long as the driving force is expressed in terms of the appropriate concentrations. Although the driving force should be more correctly expressed in terms of chemical potentials, Eq. (16-63) provides a qualitatively and quantitatively correct representation of adsorption systems so long as the diffusivity is allowed to be a function of the adsorbate concentration. The diffusivity will be constant only for a thermodynamically ideal system, which is only an adequate approximation for a limited number of adsorption systems. 

Processes in which solids play a rate-determining role have as their principal kinetic factors the existence of chemical potential gradients, and diffusive mass and heat transfer in materials with rigid structures. The atomic structures of the phases involved in any process and their thermodynamic stabilities have important effects on drese properties, since they result from tire distribution of electrons and ions during tire process. In metallic phases it is the diffusive and thermal capacities of the ion cores which are prevalent, the electrons determining the thermal conduction, whereas it is the ionic charge and the valencies of tire species involved in iron-metallic systems which are important in the diffusive and the electronic behaviour of these solids, especially in the case of variable valency ions, while the ions determine the rate of heat conduction. 

The ionic and elecU oii or positive hole chemical potentials are related tluough thermodynamic relations such as... 

A thermodynamic inhibitor alters the chemical potential of the hydrate pha.se such that the hydrate formation point is displaced to a lower temperature and/or a higher pressure. 

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