Chemical potential corresponding species

In this case, the standard chemical potential corresponds to the standard free energy of formation of the species i in aqueous solution, that is ... 

Figure 2-6. Possible changes in the chemical potential of species j that can accompany a transition from initial state A to final state B, as might occur in a chemical reaction or in crossing a membrane. Hie heights of the bars representing correspond to the relative values of the chemical potential.

To proceed fiirther, to evaluate the standard free energy AG , we need infonnation (experimental or theoretical) about the particular reaction. One source of infonnation is the equilibrium constant for a chemical reaction involving gases. Previous sections have shown how the chemical potential for a species in a gaseous mixture or in a dilute solution (and the corresponding activities) can be defined and measured. Thus, if one can detennine (by some kind of analysis)... 

Let us consider a simple model of a quenched-annealed system which consists of particles belonging to two species species 0 is quenched (matrix) and species 1 is annealed, i.e., the particles are allowed to equlibrate between themselves in the presence of 0 particles. We assume that the subsystem composed of 0 particles has been a usual fluid before quenching. One can characterize it either by the density or by the value of the chemical potential The interparticle interaction Woo(r) does not need to be specified for the moment. It is just assumed that the fluid with interaction woo(r) has reached an equlibrium at certain temperature Tq, and then the fluid has been quenched at this temperature without structural relaxation. Thus, the distribution of species 0 is any one from a set of equihbrium configurations corresponding to canonical or grand canonical ensemble. We denote the interactions between annealed particles by Un r), and the cross fluid-matrix interactions by Wio(r). 

Transfer matrix calculations of the adsorbate chemical potential have been done for up to four sites (ontop, bridge, hollow, etc.) or four states per unit cell, and for 2-, 3-, and 4-body interactions up to fifth neighbor on primitive lattices. Here the various states can correspond to quite different physical systems. Thus a 3-state, 1-site system may be a two-component adsorbate, e.g., atoms and their diatomic molecules on the surface, for which the occupations on a site are no particles, an atom, or a molecule. On the other hand, the three states could correspond to a molecular species with two bond orientations, perpendicular and tilted, with respect to the surface. An -state system could also be an ( - 1) layer system with ontop stacking. The construction of the transfer matrices and associated numerical procedures are essentially the same for these systems, and such calculations are done routinely [33]. If there are two or more non-reacting (but interacting) species on the surface then the partial coverages depend on the chemical potentials specified for each species. 

When repulsion forces exist between the particles, the chemical potential of the corresponding species will increase (an additional energy j > 0 must be expended to place a particle into a given volume), and hence, the activity coefficient will be larger than unity. When attraction forces are present, the activity coefficient will be smaller than unity. 

Note, in using Equations 50 and 53 above, that tabulations of thermodynamic data for electrolytes tend to employ a 1 molar ess concentration for all species in solution. For situations defined to have a standard-state pH value different from 0 (which corresponds to a 1 molar concentration of solvated protons), the standard-state chemical potentials for anions and cations are determined as... 

Results of the ideal solution approach were found to be identical with those arrived at on the basis of a simple quasichemical method. Each defect and the various species occupying normal lattice positions may be considered as a separate species to which is assigned a chemical potential , p, and at equilibrium these are related through a set of stoichiometric equations corresponding to the chemical reactions which form the defects. For example, for Frenkel disorder the equation will be... 

Thus the relative chemical potential of each component equals that of the corresponding uncombined species and we shall no longer distinguish between them. We note then that we can rewrite Eq. (26) as... 

These conditions can be satisfied by drawing the common tangent to the G curves of M(O) and MO. As shown in Fig. 1.7, the chemical potentials of M and O for the M(O) phase with the composition x, are equal to those for the MO phase with the composition Xj, and the values correspond to MqMj and OgO, respectively. If the experimental conditions are similar to those described in Section 1.1, the solid phases must coexist with the gas phase. It may be adequate for the gas phase to be pure O2, because the vapour pressure of other species is very low in this case. The chemical potential of O for the gas phase is equal to OgO, which corresponds to the oxygen pressure. Thus we can understand the coexistence of the M(O) phase with Xj and the MO phase with X2 from the free energy change of composition. 

The coefficients (dU/drii)s vn of the dnt in (6.7) are evidently an important new set of intensive properties that control the chemical flows (analogous to the manner in which T controls the entropy flow and P the volume flow). Following Gibbs, we identify each coefficient (dU/dni)s v n as the chemical potential (/ ) of the corresponding species At ... 

The uphill reservoir, which is the state of high (gravitational) potential, corresponds to an electrochemical reservoir (= electrode), where an electrochemically active species is stored with high chemical potential (see Figure 3.5.10). This electrode is called negative electrode in a battery context, and during discharge, the anodic reaction takes place here.1... 

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