Chemical potential, worked example

All these examples demonstrate that mechanical work can be transferred to chemical potential energy. Examples of the conversion of free energy change of association between a solvated polymer or drug and a membrane by stretching and contracting of the membrane will be shown later (Fig. 17, 18). 

Various types of work in addition to pV work are frequently involved in experimental studies. Research on chemical equilibria for example may involve surfaces or phases at different electric or magnetic potentials [11], We will here look briefly at field-induced transitions, a topic of considerable interest in materials science. Examples are stress-induced formation of piezoelectric phases, electric polarization-induced formation of dielectrica and field-induced order-disorder transitions, such as for environmentally friendly magnetic refrigeration. 

Is there any relevance of this new potential, work function, to electrochemistry The main idea is that because of its nature, the work function can be considered fingerprints of individual metals. If the electrode studied is a metal, then the work function is expected to be a relevant physical property in electrochemistry. It is involved in all electrochemical processes and accounts for effects observed on metals with different surface orientations. An example of these effects is given in Fig. 6.46. Obviously, different metals would have different chemical potentials, and that would account for the different values of d> in Fig. 6.46. But what about the differences observed, for example, for two of the crystalline faces of silver (Ag) For both crystals He is clearly the same thus the work function difference arises from different dipole layers at surfaces with different surface geometry. Another important involvement of in electrochemistry is in the determination of the absolute electrode potential, as will be explained in the next section. 

Because wrev is the maximum available work of any type, we can say from (5.53) that AG is the maximum available non-PV work. Here, available (or free ) refers to the idealized reversible limit in which no useful work is dissipated. Practically speaking, the major non-PV work of interest to chemists is the chemical energy (as manifested, for example, in electrochemical or osmotic phenomena), associated with the chemical potential terms that will be introduced in Chapter 6. 

We will not discuss microscopy and structure determinations since special monographs are available. Let us mention, however, that hot stages are available these days which allow imaging and diffraction work to be done at high temperatures. The limits for high spatial resolution are often not set by the temperature but rather by the ambient atmospheres. For example, the electron probe beam requires vacuum, whereas the component chemical potentials of a sample are undefined in a vacuum. 

The thermodynamic treatment of systems in which at least one component is an electrolyte needs special comment. Such systems present the first case where we must choose between treating the system in terms of components or in terms of species. No decision can be based on thermodynamics alone. If we choose to work in terms of components, any effect of the presence of new species that are different from the components, would appear in the excess chemical potentials. No error would be involved, and the thermodynamic properties of the system expressed in terms of the excess chemical potentials and based on the components would be valid. It is only when we wish to explain the observed behavior of a system, to treat the system on the basis of some theoretical concept or, possibly, to obtain additional information concerning the molecular properties of the system, that we turn to the concept of species. For example, we can study the equilibrium between a dilute aqueous solution of sodium chloride and ice in terms of the components water and sodium chloride. However, we know that the observed effect of the lowering of the freezing point of water is approximately twice that expected for a nondissociable solute. This effect is explained in terms of the ionization. In any given case the choice of the species is dictated largely by our knowledge of the system obtained outside of the field of thermodynamics and, indeed, may be quite arbitrary. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

A frequent reason for the dependence of catalyst structure on the chemical potential in the gas phase containing all the reactants is the incorporation of molecules or atoms from the reaction mixture into the catalyst phases. Formation of subphases, often only in the near-surface region of the solid, fails to create phases with individual reflections but modifies the reflections of the starting precatalyst phase notably (see previous sections). This complication presents a massive problem in the analysis of working catalysts when significant partial pressures of products are important to the phase formation and when the necessary conversions cannot be reached in the experimental cell. The investigation of ammonia synthesis catalysts when insufficient partial pressures of the product ammonia prevent the formation of the relevant nitride phases is a prominent example of this limitation (Herzog et al., 1996 Walker et al., 1989). 

In general, the term SW represents all different forms of work. Work is the product of an intensive variable and a differential of an extensive variable. For example, if the system is displaced by a distance dl under a force F, it performs the work of -Fdl. If dNt moles of substance / with the chemical potential /a, flow from the system to its surroundings, the chemical work of -pdNi occurs. Thus the total work becomes... 

We recall from thermodynamics that a component s contribution to a mixture s ability to perform mechanical work (the Gibbs free energy) is called the chemical potential p. . The chemical potential increases with temperature, pressure, and concentration of the component in the mixture. For example, the chemical potential for an ideal gas component can be expressed as... 

The main difference between a solid and a liquid is that the molecules in a solid are not mobile. Therefore, as Gibbs already noted, the work required to create new surface area depends on the way the new solid surface is formed [ 121. Plastic deformations are possible for solids too. An example is the cleavage of a crystal. Plastic deformations are described by the surface tension y also called superficial work, The surface tension may be defined as the reversible work at constant elastic strain, temperature, electric field, and chemical potential required to form a unit area of new surface. It is a scalar quantity. The surface tension is usually measured in adhesion and adsorption experiments. 

Problem 2.5(a) (Worked Example) From the Flory-Huggins free energy per unit volume, Eq. (2-33), show that the excess chemical potential of mixing of the solvent, — yLig, in a polymer... 

Different kinds of driving forces tend to bring about different kinds of change. For example, imbalance of meehanical forces such as pressure on a piston tend to cause energy transfer as work temperature differences tend to eause the flow of heat gradients in chemical potential tend to cause substances to be transferred from one phase to another. At equilibrium all sueh forees are in balance. 

The work of Gibbs was essentially theoretical and its full importance in physical chemistry was appreciated only after its wide applicability had been demonstrated by extensive experimental researches. Among these may be mentioned, for example, the work of Bakhuis Rooseboom which focused attention on the phase rule. At the same time Planck, van Laar, Duhem and van der Waals demonstrated clearly the importance of the concept of chemical potential and completed several aspects of Gibbs work. 

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