Reduced standard-state chemical potential

In equations 27-29, P(j is the partial distribution coefficient of component ij, Tij is the ratio of activity coefficients, 0 is the reduced standard-state chemical potential difference, xiop is the standard-state chemical potential of component i in phase p, and yf and yxjp are the activity coefficients of components i and ij, respectively, in phase p. The working equations (equations 23-26) describing phase equilibria, along with the equation defining a mole fraction, are implicitly complex relations for T, P, x, y, xAC, xA, xc, and xD but involve only two thermodynamic quantities, 0 and Tiy Equations 23-25 are implicit in composition only through the term, which is itself only a weak function of composition. 

The thermodynamic quantity 0y is a reduced standard-state chemical potential difference and is a function only of T, P, and the choice of standard state. The principal temperature dependence of the liquidus and solidus surfaces is contained in 0 j. The term is the ratio of the deviation from ideal-solution behavior in the liquid phase to that in the solid phase. This term is consistent with the notion that only the difference between the values of the Gibbs energy for the solid and liquid phases determines which equilibrium phases are present. Expressions for the limits of the quaternary phase diagram are easily obtained (e.g., for a ternary AJB C system, y = 1 and xD = 0 for a pseudobinary section, y = 1, xD = 0, and xc = 1/2 and for a binary AC system, x = y = xAC = 1 and xB = xD = 0). 

Reduced Standard-State Chemical Potential Difference. The... 

From a Solution Model. Calculation of the difference in reduced standard-state chemical potentials by methods I or III in the absence of experimental thermodynamic properties for the liquid phase necessitates the imposition of a solution model to represent the activity coefficients of the stoichiometric liquid. Method I is equivalent to the equation of Vieland (106) and has been used almost exclusively in the literature. The principal difference between methods I and III is in the evaluation of the activity coefficients... 

By using the procedures just outlined, the reduced standard-state chemical potential can be estimated for all compounds. This value of Gy is valid for any solid-liquid phase equilibrium problem that contains the compound... 

Two types of variables appear in Equations 3 and 4, 0 and r The variable 0 is a reduced standard state chemical potential difference and is defined by... 

With the standard state for each component chosen as the pure component in the phase of interest and at the temperature of interest, Chang et al. (4-) have discussed three thermodynamic sequences for the calculation of the reduced standard state chemical potentials. The pathways for each sequence are shown in Figure 2. 

Figure 2. Three thermodynamic sequences for evaluating the reduced standard state chemical potential change.

Equilibrium between a pseudobinary III—V solid solution and a ternary liquid solution is described by Equations 3 and 4. By the methods presented in the previous section, the determination of the reduced standard state chemical potential change, 0jq, can proceed in a reliable manner. The other term contained in Equations 3 and 4 is and its determination is discussed here. 

Four different methods were presented to determine the reduced standard state chemical potential change and applied to the Ga-Sb system. It is common practice to use Equation 7 and a solution model representing the stoichiometric liquid activities to determine 0. The solution model parameters are then estimated from a fit of the binary phase diagram. It has been shown that this procedure can lead to large errors in the value of 0. The use of Equation 9, however, gave the correct temperature dependence of 0 and the inclusion of activity measurements in the data base replicated the recommended values of 0Tp. 

We need a way to obtain values for the standard-state chemical potential appearing in (10.3.38). Each standard state is a pure species, so the chemical potential reduces to the pure molar Gibbs energy, and the pure molar property g° is simply related to the Gibbs energy of formation by (10.4.15). So we rewrite (10.4.15),... 

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. 

Equation 7.15 implies that, for an electrochemical reaction involving a redox reaction, there exists an electrode potential that is related to the chemical potentials of the reactants and the reaction products and is calculated by this equation. This electrochemical potential is called the redox potential . This potential is positive for an oxidation reaction, where a constituent involved will gain in valency, while it is negative for a reduction reaction, where the valency is reduced for the constituent. In the standard thermodynamic state (i.e., for an ideal condition where each of the species is 1 mol at standard temperature and pressure), the standard redox potential is... 

In voltaic cells, it is possible to carry out the oxidation and reduction halfreactions in different places when suitable provision is made for transporting the electrons over a wire from one half-reaction to the other and to transport ions from each half-reaction to the other in order to preserve electrical neutrality. The chemical reaction produces an electric current in the process. Voltaic cells, also called galvanic cells, are introduced in Section 17.1. The tendency for oxidizing agents and reducing agents to react with each other is measured by their standard cell potentials, presented in Section 17.2. In Section 17.3, the Nernst equation is introduced to allow calculation of potentials of cells that are not in their standard states. 

The most of chemical reactions accompanied by electron transfer from an atom of one reagent (reducer) to an atom of another reagent (oxidizer). Each element can have some oxidation states. The standard oxidation-reduction potential between two oxidation states of element is bonded with standard thermodynamic free energy of the transition from one state to another by the following equation ... 

In this equation e9 is the potential for a standard state of 1 M conc tration the species in brackets relates to the chemical activities in the particular solution phase. This relationship indicates that the redox potential of a solution is independent of the total conc tration of the species and dq)ends only on the ratio of the oxidized and reduced forms. This has be a confirmed since concentrations of trace amounts of ions show the same redox behavior as macro concentrations. Reduction and oxidation reactions can, therefore, be carried out in solutions with trace amounts of radioactive species. 

We first consider an artificial special case which itself is very instructive. Assume that the interactions between molecules in the aggregated and monodispersed states are the same then the standard chemical potentials are all equal /ij = = M3 = = Miv- In that event, Eq. (5.4.23b) reduces to... 

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