Ion, chemical potential

In the definitions of T, two variables in addition to the ion chemical potential must also be specified as constant. In an equilibrium dialysis experiment, these are temperature and the chemical potential of water. This partial derivative is known as the Donnan coefficient. (Note that the hydrostatic pressure is higher in the RNA-containing solution.) In making connections between T and the Gibbs free energy, it is more convenient if temperature... 

Figure 44. Dependence of single ion chemical potentials on mole fraction of methyl alcohol, 6m(i° (ion), for various ions in methyl alcohol + water mixtures (a) Cl-, (b) Br-, (c) I", (d) K+, (e) Na+, (f) Li+ and H+ (Wells, 1973).

For an 1 1 electrolyte the measurable chemical potentials pj3 and P23 are equated to their inaccessible single ion chemical potentials p, as shown... 

If the solute Y in a binary system is an electrolyte composed of a cation C + of valency z+ and an anion A of valency z (i.e., Y = C +A I), the appropriate form of the chemical potential of the solute is based on the single-ion chemical potentials of its cation and anion and is given by the relationship... 

The definition of single-ion chemical potentials [Eqs. (16)] and the properties derived from them are nonoperational. There is no way of adding to the solution ions of only one species. That is, the ions in a solution are not components according to the Gibbs definition only the elec-... 

The silver ion chemical potential is then obtained by numerical solution of equation (23). The result for different choices of the parameters B, are shown in figure (17). At low temperatures the silver ion chemical potential has the limiting value B (figure (18)) as expected from the analogous electron problem and approaches the intrinsic value, equation (8), at sufficiently high temperatures. It is possible using only this set of curves... 

We see that the solute chemical potential in this case is the sum of the single-ion chemical potentials. 

Equation 10.3.3 relates the chemical potential of electrolyte B in a binary solution to the single-ion chemical potentials of its constituent ions ... 

To find an expression for the Donnan potential, we can equate the single-ion chemical potentials of the salt cation (0 ) = When we use the expression of Eq. 

Reciprocal screening length Larger-to-smaller particle size ratio Characteristic wavelength Stokes law correction factor Electrochemical potential of an ion Reference electrochemical potential of an ion Chemical potential of a particle Reference chemical potential of a particle Fluid kinematic viscosity Hydrodynamic pressure tensor Pressure between plates (disjoining pressure)... 

This is Kirkwood s expression for the chemical potential. To use it, one needs the pair correlation fimction as a fimction of the coupling parameter A as well as its spatial dependence. For instance, if A is the charge on a selected ion in an electrolyte, the excess chemical potential follows from a theory that provides the dependence of g(i 2, A) on the charge and the distance r 2- This method of calculating the chemical potential is known as the Gimtelburg charging process, after Guntelburg who applied it to electrolytes. 

The McMillan-Mayer theory offers the most usefiil starting point for an elementary theory of ionic interactions, since at high dilution we can incorporate all ion-solvent interactions into a limitmg chemical potential, and deviations from solution ideality can then be explicitly coimected with ion-ion interactions only. Furthemiore, we may assume that, at high dilution, the interaction energy between two ions (assuming only two are present in the solution) will be of the fomi... 

Photosystem II Inhibitors. The PSII complex usually is assumed to be that stmctural entity capable of light absorption, water oxidation, plastoquiaone reduction, and generation of transmembrane charge asymmetry and the chemical potential of hydrogen ions (41). The typical PSII complex... 

Ion-Dipole Forces. Ion-dipole forces bring about solubihty resulting from the interaction of the dye ion with polar water molecules. The ions, in both dye and fiber, are therefore surrounded by bound water molecules that behave differently from the rest of the water molecules. If when the dye and fiber come together some of these bound water molecules are released, there is an increase in the entropy of the system. This lowers the free energy and chemical potential and thus acts as a driving force to dye absorption. 

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). 

Fiber-reactive dye is also hydrolyzed by reaction with free OH ions in the aqueous phase. This is a nonreversible reaction and so active dye is lost from the system. Hydrolysis of active dye can take place both in the dyebath and on the fiber, although in the latter case there is a competition between the reactions with free hydroxyl ions and those with ionized ceUulose sites. The hydrolyzed dye estabHshes its own equUibrium between dyebath and fiber which could be different from the active dye because the hydrolyzed dye has different chemical potentials in the two phases. The various reactions taking place can be summarized as in Figure 2. 

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. 

One criterion for the anode material is that the chemical potential of lithium in the anode host should be close to that of lithium metal. Carbonaceous materials are therefore good candidates for replacing metallic lithium because of their low cost, low potential versus lithium, and wonderful cycling performance. Practical cells with LiCoOj and carbon electrodes are now commercially available. Finding the best carbon for the anode material in the lithium-ion battery remains an active research topic. 

Thermodynamic information can also be obtained from simulations. Currently we are measuring the differences in chemical potential of various small molecules in dimethylimidazolium chloride. This involves gradually transforming one molecule into another and is a computationally intensive process. One preliminary result is that the difference in chemical potential of propane and dimethyl ether is about 17.5 kj/mol. These molecules are similar in size, but differ in their polarity. Not surprisingly, the polar ether is stabilized relative to the non-polar propane in the presence of the ionic liquid. One can also investigate the local arrangement of the ions around the solute and the contribution of different parts of the interaction to the energy. Thus, while both molecules have a favorable Lennard-Jones interaction with the cation, the main electrostatic interaction is that between the chloride ion and the ether molecule. 

In view of the importance of the hydronium ion, HjO, and dissolved oxygen as electron acceptors in corrosion reactions, some values of the redox potentials E and chemical potentials n for the equilibria... 

As with all determinations of thermodynamic stability, we comihehce by defining all stable phases possible, and their standard, chemical, potentials. For inost, metals there are many such phases, including oxides, hydroxides and dissolved ions. For brevity, here, only the minimum number of phases is Considered. The siriiplest system is a metal, ilf, which can oxidise lo form a stable dissolved pro,duct, (qorrpsipn), or to form a stable oxide MO (passivation), lit aqueous environments thfbe equilibria Can thereby be... 

In the case of ions in solution, and of gases, the chemical potential will depend upon concentration and pressure, respectively. For ions in solution the standard chemical potential of the hydrogen ion, at the temperature and pressure under consideration, is given an arbitrary value of zero at a specified concentration... 

Standard chemical potentials for ions and compounds are given in Chapter 21, Table 21.5. 

The chemical potential of the hydrogen ion, or of any other ion, will vary with activity... 

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