Reference State Infinite Dilution

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 ... 

From Spedding et al. (189) except where otherwise stated values in brackets may not refer to infinite dilution. 

When speaking of solutions, we implicitly state that the H2O solvent has a different standard state of reference with respect to solutes (note that the term mixture is used when all components are treated in the same way see section 2.1). The standard state generally used for the solvent in aqueous solutions is that of pure solvent at P and T of interest (or P = 1 bar and T = 298.15 K). For solutes, the hypothetical one-molal solution referred to infinite dilution, at P and T of interest (or P = bar and T = 298.15 K) is generally used. This choice is dictated by practical considerations. 

Figure 8.8 Construction of standard state of hypothetical one-molal solution referred to infinite dilution. ...

At standard state, equation 8.211 obviously concerns standard state stable components—i.e., pure Fe metal at F = 25 °C, P = 1 bar, and a hypothetical one-molal Fe + solution referred to infinite dilution, at the same P and T conditions (cf section 8.4). The chemical potentials of components in reactions Fe2+(aqueous), ae-(aqueous)) SFC thosc of Standard State hence, by defini-tion, the activity of all components in reaction is 1—i.e.,... 

For water as solvent, pure liquid water is used as a standard state for the reference condition infinite dilution the activity of water is then defined as the mole fraction of pure water Xhjo-... 

As discussed, for the solute 1 it is rational to take as reference state an ideal solution obeying the Henry law. Therefore, we may define a virtual activity coefficient y having as reference the infinite diluted solution, as expressed by the equation ... 

For solutions of electrolytes, a standard state referred to infinite dilution is sometimes convenient at the pressures indicated above. 

The standard molar Gibbs energies of transfer of ions from water to nonaqueous solvents are dealt with in Section 4.3.2.1 and those for transfer into mixed aqueous-organic solvents in Section 6.1. Specifically, the standard molar Gibbs energies of transfer of hydrogen ions from water to solvents S, A G"(H, W S), are available in Table 4.2 for nonaqueous solvents, in Table 6.1 for equimolar mixtures of water with cosolvents, and in the compilations by Kalidas et al. [17] and by Marcus [18] for other compositions. The pH scale is a universal one, because it refers to the same standard state, infinite dilution of hydrogen ions in pure water, where its activity coefficient is unity. The acidity in other solvents, pH, is related to this universal one by Equation 8.8. 

It should be noted that all AH and AS values listed in the tables refer to the unit molal standard states (infinite dilution in pure H2O), or in the presence of supporting electrolyte, to a modified standard state (unit molal at infinite dilution in the supporting electrolyte) and therefore should be designated AH and AS . 

FIG. 2-29 Enthalpy-concentration diagram for aqueous sodium hydroxide at 1 atm. Reference states enthalpy of liquid water at 32 F and vapor pressure is zero partial molal enthalpy of infinitely dilute NaOH solution at 64 F and 1 atm is zero. [McCahe, Trans. Am. Inst. Chem. Eng., 31, 129(1935).]... 

In the reference state the activity coefficients are, by definition, unity. The reference state may be that in the limit of infinite dilution, but the more conventional reference state is C° = 1 M. With the -y s = 1,... 

The value obtained by Hamm et alm directly by the immersion method is strikingly different and much more positive than others reported. It is in the right direction with respect to a polycrystalline surface, even though it is an extrapolated value that does not correspond to an existing surface state. In other words, the pzc corresponds to the state of a bare surface in the double-layer region, whereas in reality at that potential the actual surface is oxidized. Thus, such a pzc realizes to some extent the concept of ideal reference state, as in the case of ions in infinitely dilute solution. 

All in aqueous solution at 25 C standard states are IM ideal aqueous solution with an infinitely dilute reference state, and for water the pure liquid. 

For a solution of a non-volatile substance (e.g. a solid) in a liquid the vapour pressure of the solute can be neglected. The reference state for such a substance is usually its very dilute solution—in the limiting case an infinitely dilute solution—which has identical properties with an ideal solution and is thus useful, especially for introducing activity coefficients (see Sections 1.1.4 and 1.3). The standard chemical potential of such a solute is defined as... 

Here /g,hq and y ,ss are the activity coefficients of component B in the liquid and solid solutions at infinite dilution with pure solid and liquid taken as reference states. A fus A" is the standard molar entropy of fusion of component A at its fusion temperature Tfus A and AfusGg is the standard molar Gibbs energy of fusion of component B with the same crystal structure as component A at the melting temperature of component A. 

When the solution is dilute enough to approximate the activity coefficients to 1 (reference state solute at infinite dilution), activities can then be replaced by molar fractions (dimensionless quantities), but in solution they are generally replaced by molar concentrations ... 

In order to combine equation (14) with the Debye-Huckel formula, which accounts for the long-range force contribution, it is necessary to normalize to the infinite dilution reference state for the ions ... 

For this reason, the infinitely dilute solution frequently is called the reference state for the partial molar enthalpy of both solvent and solute. 

Absolute values of partial molar enthalpies cannot be determined, just as absolute values of enthalpies cannot be determined. Thus, it is necessary to choose some state as a reference and to express the partial molar enthalpy relative to that reference state. The most convenient choice for the reference state usually is the infinitely dilute solution. Without committing ourselves to this choice exclusively, we will nevertheless use it in most of our problems. 

As an example, consider phenol as the solute and water and toluene as two solvents. The parameters for phenol are A = 5.7, A = -12.9, A = -18.3, and A5 = 0.0091, whereas Aq is unspecified, but a negative quantity. With the solvent parameters from Tables 2.1 and 2.3, the standard Gibbs energy of solvation of phenol in water becomes Aq + 3.39, and in toluene Ao -1- 4.11 kJ mol". It is seen that As i,Gb is lower in water than in toluene, so that the transfer of phenol from water to toluene entails an increase in AjoItGb. The consequence of this is that phenol prefers water over toluene, since work would be required to make this transfer. It should be remembered that the standard Gibbs energies of solvation refer to the state of infinite dilution of the solute (solute-solute... 

The specific ion interaction approach is simple to use and gives a fairly good estimate of activity factors. By using size/charge correlations, it seems possible to estimate unknown ion interaction coefficients. The specific ion interaction model has therefore been adopted as a standard procedure in the NEA Thermochemical Data Base review for the extrapolation and correction of equilibrium data to the infinite dilution standard state. For more details on methods for calculating activity coefficients and the ionic medium/ ionic strength dependence of equilibrium constants, the reader is referred to Ref. 40, Chapter IX. 

The activity coefficients are referred to some chosen standard state, in which they are taken as unity (e.g., in aqueous solution to the state of infinite dilution). 

The reference state is the pure solvent at the same temperature ( solvent = I) At infinite dilution /solvent I The reference state is a hypothetical state at x, = 1 or... 

Although the standard state pertaining to these equilibria is often referred to as a state of infinite dilution, we stress that there are different standard states for solutes. They are defined as follows (61 Mil). 

In the field of environmental organic chemistry, the most common reference states used include (1) the pure liquid state, when we are concerned with phase transfer processes (2) the infinite dilution state, when we are dealing with reactions of... 

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 ... 

Note that we use the prime superscript to denote the infinite dilution reference state (as opposed to the pure liquid state), and that we omit any subscript to indicate that we are dealing with aqueous solutions. Also note that because we have chosen the aqueous solution as reference state, y, will in many cases not be substantially different from 1. Exceptions are the charged species at high ionic strength as, for example, encountered in seawater (see below). 

In Chapter 8, where we treated acid-base equilibria, we have seen that when dealing with reactions in dilute aqueous solutions, the appropriate choice of reference state for solutes is the infinite dilution state in water. The chemical potential of a compound i can then be expressed as ... 

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