Reference states of the solute

When the infinitely dilute solution, with respect to all solutes, is used as the reference state of the solution at all temperatures and pressures, Ap c approaches zero as all cfs approach zero. Thus, the standard state of the solvent is the pure solvent at all temperature and pressures and is identical to the reference state of the solvent for all thermodynamic functions. 

For any method, care must be taken to define the reference state of the solute, which can be either the solution at equilibrium with the surface or the solution at infinite dilution state [4, 52]. An adsorption isotherm determined independently is needed to relate the calorimetric data with the surface excess amount. 

Similarly, we are able to apply this relation to the reference state of the solution, as follows ... 

However, the two cases differ both with respect to the relaxation of the molecular orbitals (MO) of the Hartree-Fock reference state of the solute, and with respect to the presence of non-equilibrium solvation effects. 

The AG can then be parated into the re ective enthalpic (A7/ ) and entropic (A5 ) contributions to the activity coefficient, using the well known relationship that is also given in Eq. (9). The p al molar enthalpy (Af/ ) and entropy (AS ° ) of solution, with the reference state of the solute at infinite dilution in an ideal gas, can be calculated using Eqs. (10) and (11), respectively, where A// is the solute s molar heat of vapourization. The AH required can be determined from the Clausius-Cla-peyron equation. 

One has to keep in mind that the excess parts of the chemical potentials depend on the selection of the reference state for a solute component, as both the activity of a solute component and the activity of the solvent in an ideal mixture depend on the reference states of the solutes. The activity coefficients of a solute on molality scale, y " and on molarity scale, yf are related by ... 

The numerical value of the osmotic coefficient depends on the selection of the reference state of the solutes, whereas the number for the osmotic pressure does not depend on that reference state. 

In solution thermodynamics the standard or reference states of the components of the solution are important. Although the standard state in principle can be chosen freely, the standard state is in practice not taken by chance, but does in most cases reflect the type of model one wants to fit to experimental data. The choice of... 

Solvatochromism refers to changes in the electronic state of the solute (specifically, the solute s electronic state transition energy) caused by the solvent. 

So far, we have used the pure liquid compound as reference state for describing the thermodynamics of transfer processes between different media (Chapter 3). When treating reactions of several different chemical species in one medium (e.g., water) it is, however, much more convenient to use the infinite dilution state in that medium as the reference state for the solutes. Hence, for acid-base reactions in aqueous solutions, in analogy to Eq. 3-34, we may express the chemical potential of the solute i as ... 

B) As a second example, suppose that the original reference state of the /cth component, considered as a solute, is the pure substance and that mole fractions are used as the composition variable. It is then desired to make the infinitely dilute solution the reference state and to use the molality for the composition variable. Here, again, we express the chemical potential of the fcth component in the two equivalent ways ... 

C) In this example let the original reference state of the kth component, considered as a solute, be the infinitely dilute solution, and let the molalities be used to express the composition. Let the new reference state of the fcth component, again considered as a solute, be the infinitely dilute solution, but with the molarities being used as the composition variable. Then we have... 

The reference state of the electrolyte can now be defined in terms of thii equation. We use the infinitely dilute solution of the component in the solvent and let the mean activity coefficient go to unity as the molality or mean molality goes to zero. This definition fixes the standard state of the solute on the basis of Equation (8.184). We find later in this section that it is neither profitable nor convenient to express the chemical potential of the component in terms of its molality and activity. Moreover, we are not able to separate the individual quantities, and /i . Consequently, we arbitrarily define the standard chemical potential of the component by... 

We define the reference state of the component to be the infinitely dilute solution of the component in the second component, so that Aapproaches... 

In order to evaluate each of the derivatives, such quantities as (V" — V-), (S l — Sj), and (dfi t/x t)T P need to be evaluated. The difference in the partial molar volumes of a component between the two phases presents no problem the dependence of the molar volume of a phase on the mole fraction must be known from experiment or from an equation of state for a gas phase. In order to determine the difference in the partial molar entropies, not only must the dependence of the molar entropy of a phase on the mole fraction be known, but also the difference in the molar entropy of the component in the two standard states must be known or calculable. If the two standard states are the same, there is no problem. If the two standard states are the pure component in the two phases at the temperature and pressure at which the derivative is to be evaluated, the difference can be calculated by methods similar to that discussed in Sections 10.10 and 10.12. In the case of vapor-liquid equilibria in which the reference state of a solute is taken as the infinitely dilute solution, the difference between the molar entropy of the solute in its two standard states may be determined from the temperature dependence of the Henry s law constant. Finally, the expression used for fii in evaluating (dx Jdx l)TtP must be appropriate for the particular phase of interest. This phase is dictated by the particular choice of the mole fraction variables. 

When the reference state of the first component is chosen as the pure component and that of each of the other two components as the infinitely dilute solution of the component in the first component, each of the excess chemical potentials become zero in the limit and Equation (10.214) can be written as... 

Here Ap [p = 1, excess chemical potential of the second component in the binary system composed of the second and third components at the composition equal to q. The reference state of the second component may be either the pure component or the infinitely dilute solution of the second component in the third component. In the limit of p=l, q/p becomes l/(k+ 1), where k = x2/x3 and, with the proper choice of components or... 

Two reference states, one for each phase, must be defined. As we decrease the mole fraction of the third component, we approach the two-liquid-phase binary system composed of the first and second components. We thus define the reference states of the third component as the infinitely dilute solutions of the component in the two liquid phases that are at equilibrium in the 1-2 binary system. Thus, the value of A/i x), x 3] approaches zero as x 3 approaches zero, and x j approaches its value in the 1-2 system, and the value of A/if [x i, x3] also approaches zero, and x] approaches its value in the 1-2 system. In the limit Equation (10.251) becomes... 

In general, the enthalpy of a solution containing r moles H20/mole solute is for reference states of pure solute and solvent at 25°C and 1 atm... 

To compare activities of solutes in different solvents, a single reference state for the solute must be chosen. Although from some points of view it is awkward, water is a logical choice for a single reference solvent in which the behavior of solutes in other solvents can be compared. To make comparisons of solute activities among solvents, it is convenient to consider separately the effect of dilution within a given solvent and the difference in the usual reference states of a solute at infinite dilution in different solvents. The activity coefficient yt of a species i in a solvent may be considered the product of two terms... 

Several choices are available in defining the standard state of the solute. If the solute is a liquid which is miscible with the solvent (as, for example, in a benzene-toluene mixture), then the standard state is again the pure liquid. Several different standard states have been used for solutions of solutes of limited solubility. In developing a relationship between drug activity and thermodynamic activity, the pure substance has been used as the standard state. The activity of the dmg in solution was then taken to be the ratio of its concentration to its saturation solubility. The use of a pure substance as the standard state is of course of limited value since a different state is used for each compound. A more feasible approach is to use the infinitely dilute solution of the compound as the reference state. Since the activity equals the concentration in such solutions, however, it is not equal to unity as it should be for a standard state. This difficulty is overcome by defining the standard state as a hypothetical solution of unit concentration possessing, at the same time, the properties of an infinitely dilute solution. Some workers have chosen to... 

As discussed above, the absolute activity of the solid depends on the chosen reference or standard state, and the usual practice is to take the supercooled liquid state of the pure solute at the temperature of solution as the standard state of unit activity. At temperatures lower than the melting point, the liquid state of the solute is less stable than its solid state, making the activity of the corresponding solid less than one. 

A choice must be made for the reference state for the solute either the pure liquid (possibly supercooled), or the solute at infinite dilution in the solvent. The latter differs from the conventional solute standard state only in the use of the mole fraction scale rather than molality units. The activity coefficient of a symmetrical salt MX is either... 

A system of equations for electrolytes based on the reference states expressed in Equations 3 and 4 was developed in detail for singly-charged ions by Pitzer and Simonson (. Although they considered both types of reference states for the solute, most of their working equations are for the pure liquid reference state. This reference state was used by Pitzer and Li (32) for a study of the NaCl-H20 system extending to 550 C. For the present research limited to 350 C, however, it seemed better to use the infinitely dilute reference state, and the equations below are derived on that basis. The short-range... 

Another reference-state for the solute / may be its pure liquid fugacity, fj. This state is a virtual one, because in practice x, 1. If the actual liquid mixture has as reference an ideal solution obeying the Lewis-Randall rule, we may define the reference-state f- as the limit of component fugacity at jc, 1 ... 

The energy properties refers to stationary, time-independent, states of the solute molecules. This implies a complete equilibration between the degrees of freedom, electronic and nuclear, of the solute and of the solvent. For the last two categories, on the contrary, we have to consider not only an equilibrated solute-solvent system but also the dynaunics of its response to a time dependent perturbation. 

Fig. 4.3.1. Diagrammatic representations of solvent effects on the transition energies of polar solutes in polar solvents. A refers to a reference solvent, 5 to a less solvating solvent and C to a more solvating solvent, (a) Case where the dipole moment of the Franck-Condon excited state of the solute is larger than that of the ground state. (b) Case where the Franck-Condon excited state dipole moment is less than that of the ground state.

However, the influence of long-range interactions has to be taken into account by a term describing the Debye-Hiickel theory. For this term, in the general case the density and the dielectric constant of the mixed solvent have to be determined (see Eq. (7.49)). As the reference state of the electrolyte components refers to the infinitely diluted solution in pure water, the Debye-Hiickel term must be corrected by the so-called Born term, which takes into account the difference between the dielectric constants of water and the solvent mixture [14] ... 

Critically revised data of various electrolyte solution properties help scientists and engineers to overcome the time-consuming procedure of searching for reliable data for technical applications. Special knowledge-based databases undertake the interpolation, estimation, or simulation of data by theory-founded procedures differing fundamentally from those for nonelectrolytes. The reason for the difference is the essentially different reference states of electrolyte solutions which are the infinitely dilute solutions with at least three interacting components, namely solvent molecules, cations, and anions. In contrast, databases for nonelectrolytes always use the pure substances as the references. 

Dissolution and condensation may be compared provided that the standard state of the solute is represented by (a) in the vapour state pressure 1 atm temperature T reference state ideal behaviour (b) in the liquid phase single solute in hypothetical liquid state at temperature T reference state infinitely diluted solution [21]. In these conditions the concentration unit is fugacity unit (atmosphere) in the vpaour phase and the mole fraction in the liquid phase. The phase equilibrium constant, K, is then replaced by another constant x given by the equation ... 

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