Chemical potential concept

Chemical Potential. Equilibrium calculations are based on the equaHty of individual chemical potentials (and fiigacities) between phases in contact (10). In gas—soHd adsorption, the equiHbrium state can be defined in terms of an adsorption potential, which is an extension of the chemical potential concept to pore-filling (physisorption) onto microporous soHds (11—16). 

The chemical potential concept provides a useful way to think about the tendency for spontaneous chemical change in complex environmental systems involving gases, liquids, and solids (cf. Wood and Fraser 1976 Stumm and Morgan 1981). In a particular phase, the chemical potential, /U, of component i is related to the activity of i through the expression... 

Understanding the Chemical Potential Concept Substitution of Eq. (2.11) into (2.9) leads to... 

Eck B, Dronskowski R (2002) Atomistic simulations of solid-state materials based on crystal-chemical potential concepts basic ideas and implementation. J Alloys Comp 338 136... 

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). 

The idea of having two distinct quasi-Fermi levels or chemical potentials within the same volume of material, first emphasized by Shockley (1), has deeper implications than the somewhat similar concept of two distinct effective temperatures in the same block of material. The latter can occur, for example, when nuclear spins are weakly coupled to atomic motion (see Magnetic spin resonance). Quasi-Fermi level separations are often labeled as Im p Fermi s name spelled backwards. 

Besides the already mentioned Fukui function, there are a couple of other commonly used concepts which can be connected with Density Functional Theory (Chapter 6). The electronic chemical potential p is given as the first derivative of the energy with respect to the number of electrons, which in a finite difference version is given as half the sum of the ionization potential and the electron affinity. Except for a difference in sign, this is exactly the Mulliken definition of electronegativity. ... 

Activity can be thought of as the quantity that corrects the chemical potential at some pressure and/or composition condition" to a standard or reference state. The concept of a standard state is an important one in thermodynamics. The choice of the pressure and composition conditions for the standard state are completely arbitrary, and unusual choices are sometimes made. The common choices are those of convenience. In the next section, we will describe and summarize the usual choices of standard states. But, first, we want to describe the effect of pressure and temperature on a,. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

The concept of chemical potentials, the equilibrium criterion involving chemical potentials, and the various relationships derived from it (including the Gibbs phase rule derived in Chapter 5) can be used to explain the effect of pressure and temperature on phase equilibria in both a qualitative and quantitive way. 

Chapter 4 presents the Third Law, demonstrates its usefulness in generating absolute entropies, and describes its implications and limitations in real systems. Chapter 5 develops the concept of the chemical potential and its importance as a criterion for equilibrium. Partial molar properties are defined and described, and their relationship through the Gibbs-Duhem equation is presented. 

In Chapter 6, fugacity and activity are defined and described and related to the chemical potential. The concept of the standard state is introduced and thoroughly explored. In our view, a more aesthetically satisfying concept does not occur in all of science than that of the standard state. Unfortunately, the concept is often poorly understood by non-thermodynamicists and treated by them with suspicion and mistrust. One of the firm goals in writing this book has been to lay a foundation and describe the application of the standard state in such a way that all can understand it and appreciate its significance and usefulness. 

Here we shall consider a different concept, which has an interesting potential, particularly in liquid phase reactions used for the production of fine chemicals. The concept is schematically illustrated in Fig. 3. The modification of the metal catalysts is achieved by very small quantities (usually a sub-monolayer) of adsorbed auxiliaries (modifiers), which are either simply added to the reaction mixture (in-situ), or brought onto the catalyst surface in a... 

Eor galvanic circuits (cells) the OCV generally is not zero. In contrast to metal circuits, where electrons are the sole carriers, in galvanic circuits the current is transported by different carriers in the different circuit parts (i.e., by electrons and by ions). Hence when substituted into Eq. (2.9), the chemical potentials of the carriers in the intermediate circuit parts will not cancel. The concept of OCV in the case of... 

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. 

Suspension Model of Interaction of Asphaltene and Oil This model is based upon the concept that asphaltenes exist as particles suspended in oil. Their suspension is assisted by resins (heavy and mostly aromatic molecules) adsorbed to the surface of asphaltenes and keeping them afloat because of the repulsive forces between resin molecules in the solution and the adsorbed resins on the asphaltene surface (see Figure 4). Stability of such a suspension is considered to be a function of the concentration of resins in solution, the fraction of asphaltene surface sites occupied by resin molecules, and the equilibrium conditions between the resins in solution and on the asphaltene surface. Utilization of this model requires the following (12) 1. Resin chemical potential calculation based on the statistical mechanical theory of polymer solutions. 2. Studies regarding resin adsorption on asphaltene particle surface and... 

The same pseudo-ensemble concept has been used by Camp and Allen [44] to obtain a pseudo-Gibbs method in which particle transfers are substituted by volume fluctuations of the two phases. The volume fluctuations are unrelated to the ones required for pressure equality (10.7) but are instead designed to correct imbalances in the chemical potentials of some of the components detected, for example, by test particle insertions. 

Concepts Spontaneous chemical reactions The use of thermodynamics to determine what reactions are possible in a particular prebiotic environment, including the ideas of chemical potential, equilibrium and extent of reaction... 

Since the interplay of theory and experiment is central to nearly all the material covered in this chapter, it is appropriate to start by defining the various concepts and laws needed for a quantitative theoretical description of the thermodynamic properties of a dilute solid solution and of the various rate processes that occur when such a solution departs from equilibrium. This is the subject matter of Section II to follow. There Section 1 deals with equilibrium thermodynamics and develops expressions for the equilibrium concentrations of various hydrogen species and hydrogen-containing complexes in terms of the chemical potential of hy-... 

The concept of potential energy in mechanics is one example of a scalar field, defined by a simple number that represents a single function of space and time. Other examples include the displacement of a string or a membrane from equilibrium the density, pressure and temperature of a fluid electromagnetic, electrochemical, gravitational and chemical potentials. All of these fields have the property of invariance under a transformation of space coordinates. The numerical value of the field at a point is the same, no matter how or in what form the coordinates of the point are expressed. 

Be careful when searching the Web, though, because typing the phrase chemical potential will locate a great many pages that relate to solid-state and atomic physics both disciplines use the term to mean different concepts. 

The concept of substance activity was derived by Gilbert N. Lewis in 1907 from the laws of equilibrium thermodynamics and is described in detail in the text entitled Thermodynamics and the Free Energy of Chemical Substances by Lewis and Randell (1923). In a homogeneous mixture, each component has a chemical potential (jjl), which describes how much the free energy changes per mole of substance added to the system. The chemical potential of water (pw) in a solution is given by... 

The starting point of the DFT of chemical reactivity is the identification of the concept of electronegativity, y, with the chemical potential, through the relationship [7]... 

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