Ideal Solution as a Reference System

Suppose that the two components A and B are similar in the sense of section 6.8, which, in this case, means [see Eq. (6.85)] 

Note that is the chemical potential of pure A at this particular T and P, and therefore it includes the effect of A-A interactions through Baa If, on the other hand, the system is not SI, then we define the activity coefficient as 

Note that and p f do not include the term Baa which reflects the extent of solute-solute interactions. The word interaction is appropriate in the present context since, in the present limiting case, we know that gap P) depends only on the direct interaction between the pair of species a and j3, as we have assumed in (6.10.4). 

The activity coefficients defined for the two representations (6.10.18) and (6.10.19) are obtained from comparison with (6.10.10) as 

Note that in (6.10.20) and (6.10.21), we retained only the first-order terms in Xa and in Pa, respectively. Using these activity coelficients, the chemical potential in (6.10.10) can be rewritten in two alternative forms  

If A is diluted in B, i.e., when - 0, we also have 1. Hence, in this case, we have a DI solution. Equation (4.168) reduces to 

The notation and has been introduced to distinguish between the two cases. Table 4.2 summarizes the three different ways of splitting the chemical potential according to the various reference systems. 

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We bear in mind however that the values of p (T,p) and y, depend upon the choice of the ideal reference system. If we choose for the solvent a reference system in which y, becomes unity as xt approaches unity, the unitary chemical potential p (T,p) is given by the chemical potential p (T,p) of the pure solvent i ut(T,p) = p (T,p). On the other hand, if we choose for the solute substances a reference system in which y, becomes unity as xt approaches zero, the unitary chemical potential ju (r,p) is given by the chemical potential p (T,p) of the solute i at infinite dilution p ( T,p) = p (T,p). 

We first take as a reference system an infinitely dilute solution of solute 2 in solvent 1. The chemical potentials of solvent 1 and solute 2, then, are given in the form of Eq. 8.13 for an ideal solution and in the form of Eq. 8.14 for a non-ideal solution ... 

The study of mixtures of ideal gases is important for two reasons first, these systems serve as a reference system for the study of real mixtures and solutions and second, these systems are special cases of systems in which a chemical reaction occurs. As we shall see in section 2.4, a system of reacting species in an ideal-gas mixture reduces to a nonreacting ideal-gas mixture whenever we block the flow of material from one species to another— e.g., by adding an inhibitor or by removing a catalyst. 

First, the term A ix° refers to the difference in Gibbs energies of products and reactants when each product and each reactant, whether solid, liquid, gas, or solute, is in its pure reference state. This means the pure phase for solids and liquids [e.g., most minerals, H20( ), H20(/), alcohol, etc.], pure ideal gases at Ibar [e.g., 02( ), H20( ), etc.], and dissolved substances [solutes, e.g., NaCl(ag), Na+, etc.] in ideal solution at a concentration of Imolal. Although we do have at times fairly pure solid phases in our real systems (minerals such as quartz and calcite are often quite pure), we rarely have pure liquids or gases, and we never have ideal solutions as concentrated as 1 molal. 

The potential of the mercury electrode is controlled against a suitable reference electrode. It is not essential to use a three-electrode system in this case, since the mercury/solution interface is studied in the range of potentials where it behaves essentially as an ideally polarizable interface. A reference electrode is commonly used, nevertheless, to ensure stability and reproducibility of the measured potential. 

You will recognize Equation (8.3) as Raoult s law, which you have undoubtedly seen before. It directly results from the criteria for equilibrium [Equation (8.1)] under the special circumstances described above (ideal gas, ideal solution, Lewis/Randall reference state). This equation is convenient, since the saturation pressure of species i depends only on the temperature of the system. The relation between Pf and T is commonly fit to the Antoine equation. Appendix A.l provides Antoine equation parameters for several species. 

An alternative approach to improve upon Hartree-Fock models involves including an explicit term to account for the way in which electron motions affect each other. In practice, this account is based on an exacf solution for an idealized system, and is introduced using empirical parameters. As a class, the resulting models are referred to as density functional models. Density functional models have proven to be successful for determination of equilibrium geometries and conformations, and are (nearly) as successful as MP2 models for establishing the thermochemistry of reactions where bonds are broken or formed. Discussion is provided in Section II. 

In this section we shall always define the activity coefficients with respect to the symmetrical reference system. Comparing Eq. 8.7 and Eq. 8.17, we define the excess free enthalpy (excess Gibbs energy) gE per mole of a non-ideal binary solution as Eq. 8.18 ... 

The surface excess amount, or Gibbs adsorption (see Section 6.2.3), of a component i, that is, /if, is defined as the excess of the quantity of this component actually present in the system, in excess of that present in an ideal reference system of the same volume as the real system, and in which the bulk concentrations in the two phases stay uniform up to the GDS. Nevertheless, the discussion of this topic is difficult on the other hand for the purposes of this book, it is enough to describe the practical methodology, in which the amount of solute adsorbed from the liquid phase is calculated by subtracting the remaining concentration after adsorption from the concentration at the beginning of the adsorption process. 

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