The infinite dilution standard state

So far we have just assumed that the standard state for our mixing components is the pure phase, just as it was in Chapter 3. This presents no problem 

Standard states are necessary because G, A, H, and their partial derivatives, as well as the activity (functionally) related to a difference in Gibbs energies), can only express the energy difference between a state of interest and some other state. The standard state is used to answer the question, the difference from what other state Once this state is defined, it of course also has values of V° and C°p, which don t really require standard states, because their absolute values are (or can be) known. 

In summary, then, for dissolved substances we use the ideal one molal standard state for Gibbs energy, and the infinite dilution standard state for enthalpy, volume and heat capacity. What about entropy  

It happens that for H (and V, Cp), the value at infinite dilution is equal to the value in an ideal one molal solution (and anywhere else on the Henryan tangent), so if G, H, and S refer to an ideal one molal solution, then G — G° and H — H° are both zero, and S — S° is zero only if S° also refers to an ideal one molal solution. Because entropy is calculated from other measurements (e.g., S = (H — G)/T) rather than being measured directly, this fact is perhaps not as useful as the others we have been discussing. 

Because partial molar volume, enthalpy, and heat capacity are the same anywhere on the Henry s law tangent, including both the state of infinite dilution and the ideal one molal solution, either of these states can serve as the standard state for these properties. We have chosen to say that the infinitely dilute solution is the standard state, but many treatments prefer to say that the standard state for these properties, as well as for the Gibbs energy and entropy, is the ideal one molal solution. For some reason, these treatments (e.g., Klotz, 1964, p. 361) then define the reference state for enthalpy, volume and heat capacity 

---

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. 

All data in Table IV-1 and Table lV-2 refer to a temperature of 298.15 K, the standard state pressure of 0.1 MPa and, for aqueous species and reactions, to the infinite dilution standard state (/ = 0). 

At this point you should note that we have not used the infinite dilution standard state for aqueous solutes, as we will for other properties in Chapter 10. Having m- 0 in Equation (8.24) would obviously be inconvenient. 

The next step is to perform a simultaneous regression of NaCl(aq) apparent molal volumes from 25-350 C. Over this wide range of temperature, however, and particularly above 300 C, standard-state properties based on the infinitely dilute reference state exhibit a very complex behavior (7,8), which is related to various peculiarities of the solvent. Thus in their representation of NaCl(aq) volumetric properties, Rogers and Pitzer (7) adopted a reference composition of a hydrated fused salt, NaCl IOH2O, to minimize the P and T dependence of the reference state volume and to adequately fit volumetric ta to 300°C and 1 kb. In this study the (supercooled) fused salt is used as the reference state. The equation for the apparent molal volume on this basis can be easily derived from that for the excess Gibbs energy of Pitzer and Simonson (, and is given by ... 

Of more interest are solubility calculations in the ternary system NaCl-KCl-H20. The equations for the excess Gibbs energy and activity coefficients in a mixture of a solvent and two salts with a common ion, MX and NX, and with cation fraction F of M are given by Pitzer and Simonson (5). Their equation for the activity coefficient of the solute MX in the ternary mixture MX-NX-H2O based on a pure fused salt standard state can be converted to one based on the infinitely dilute reference state. This is given by ... 

Since the value of an activity coefficient depends on the standard state, an activity coefficient based on (10.2.21) will differ numerically from one that is based on a pure-component standard state. To emphasize that difference, we make a notational distinction between the two we use y for an activity coefficient in a pure-component standard state and use y for an activity coefficient in the solute-free infinite-dilution standard state. Then for y, the generic definition of the activity coefficient (5.4.5) gives... 

Infinite dilution standard state whereby the standard slate value of fugacily or activity of a component at the temperature and pressure of the solution is given by the ratio of the fugacily or activity to the mole fiacUon" under conditions of infinite dilution... 

If the solute i Is such that an infinite dilution standard state is necessary, then, from relation (3.3.79), we get... 

The estimation of Ki or i2 for cases where an infinite dilution standard state for the solute(s) is employed, can be made from equation (4.1.1) as fallows ... 

II The increment in the free energy, AF, in the reaction of forming the given substance in its standard state from its elements in their standard states. The standard states are for a gas, fugacity (approximately equal to the pressure) of 1 atm for a pure liquid or solid, the substance at a pressure of 1 atm for a substance in aqueous solution, the hyj)othetical solution of unit molahty, which has all the properties of the infinitely dilute solution except the property of concentration. 

Relative partial molar enthalpies can be used to calculate AH for various processes involving the mixing of solute, solvent, and solution. For example, Table 7.2 gives values for L and L2 for aqueous sulfuric acid solutions7 as a function of molality at 298.15 K. Also tabulated is A, the ratio of moles H2O to moles H2S(V We note from the table that L — L2 — 0 in the infinitely dilute solution. Thus, a Raoult s law standard state has been chosen for H20 and a Henry s law standard state is used for H2SO4. The value L2 = 95,281 Tmol-1 is the extrapolated relative partial molar enthalpy of pure H2SO4. It is the value for 77f- 77°. 

We showed in Section 7.3a that AMH - 0 for the change from the infinitely dilute solution to the standard state. 

AtH°4 takes the infinitely dilute solution to the Henry s law standard state. We have shown earlier that AH = 0 for this process. 

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. 

If the fused salt does not exist at the temperature of interest, one normally uses the infinitely dilute solute standard state. While these equations can easily be converted to that basis, the results are not immediately useful for two reasons ... 

Integrating Equation (17.31) from the infinitely dilute solution to some finite concentration, we obtain, with the assumption of a Raoult s-law standard state for the solvent and a Henry s-law standard state for the solute,... 

To apply Equation (19.31) to experimental data, we must specify our choice of standard states, because the values of and of ahci depend on this choice. We shall use the hypothetical unit molality ratio standard state obtained by extrapolation from the infinitely dilute solution. By convention, m° is taken equal to 1 mol kg ... 

As the enthalpy of the dissolved sodium chloride in its standard state according to Henry s law is that of the infinitely dilute solution, A// , for the reaction in Equation (20.74) is... 

Conceptually, although these standard states are not infinite dilution states, they reflect, through the linear extrapolation, the properties of the infinitely dilute solutions (61 Mil). 

As we described earlier, the calorimetric determination of log K allows one to also get ArH for reaction (15.37). The values reported by Izatt and his colleagues were obtained in an aqueous solution with an ionic strength of 0.1. Izatt reports that enough measurements were made in more dilute solutions to show that the enthalpy of dilution to the infinitely dilute solution (the standard state) is small and can be ignored. Hence, we will assume that the ArH values reported are the standard state ATH° values. Thus we have available, ArG°, obtained from equation (15.42), and ArS ° obtained from equation (15.43). 

In equations (18.91) and (18.92), C° 2 and V are the partial molar heat capacity and partial molar volume of the surfactant in the infinitely dilute solution (standard state values). 

The physical state of each substance is indicated in the column headed State as crystalline solid (c), liquid (liq), gaseous (g), or amorphous (amorp). Solutions in water are listed as aqueous (aq). Solutions in water are designated as aqueous, and the concentration of the solution is expressed in terms of the number of moles of solvent associated with 1 mol of the solute. If no concentration is indicated, the solution is assumed to be dilute. The standard state for a solute in aqueous solution is taken as the hypothetical ideal solution of unit molality (indicated as std state, m = 1). In this state the partial molal enthalpy and the heat capacity of the solute are the same as in the infinitely dilute real solution (aq. m). 

---