AfG for aqueous ions

In Section 6.9, we saw that the standard free energies of formation of aqueous ions can often be determined from E° values. Worked example 7.9 provides an illustration of the use of reduction potential data in a calculation of a standard Gibbs energy of solution of an ionic salt. 

Calculate the value of Aso G (298K) for NaBr giveu that AfG (NaBr,s) is -349.0kJ mol. (F = 96485 Cmol 

To find AfG°(Na, aq) and AfG°(Br ,aq), we need (from Appendix 11) the standard reduction potentials for the processes  

Now determine AfG° for each aqueous ion, remembering that the standard reduction potential refers to the reverse of the formation of Na (aq)  

Calculate the value of A G (298K) for NaCI given that 

Worked example 8.9 Determination of soi6° for an ionic salt 

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For aqueous solutions of electrolytes, a concise method of tabulating such entropy data is in terms of the individual ions, because entropies for the ions can be combined to give information for a wide variety of salts. The initial assembling of the ionic entropies generally is carried out by a reverse application of Equation (7.26) that is, Af6m of a salt is calculated from known values of AfG and AfFT for that salt. After a suitable convention has been adopted, the entropy of formation of the... 

The SIT ion-interaction parameters, AfG° /RT values, and the values of equilibrium constants for aqueous and solid phases determined in this review are listed in Table IX-2, Table IX-5, and Table IX-6, respectively. The model where ion interactions are described using the two-term equation proposed by [1980CIA], s = si + S2logio/m is not veiy satisfactory at very low ionic strengths, where s can attain unrealistic values. However, activities calculated from this version of the model are correct even under those conditions, since in the expression for log, s appears only in a term s-m, (see Equation (B.4)), which does not diverge when m -> 0. In any case, all the solubility studies discussed in Sections IX.1.3.3.3 and IX.1.3.3.5 involve ionic strengths where the 8 values are still reasonable. The uncertainties may be somewhat larger than those listed as a result of the assumption for some species that the values of AjG° /RT at 16 and 30°C are the same as those at 25°C. 

Values of AfH°, AfG°, S°, and for a selection of aqueous ions are given in Table 14.2. Notice that the thermodynamic properties of H" (aq) are all equal to zero. These values are established by convention. 

The values of AfH° and AfG° for an aqueous ion are based on a formation reaction in which the aqueous ion is formed from its elements, each in its standard state. Formation reactions for H (aq), Na" (aq), and Cl (aq) are given below, along with the corresponding AfH° values. Notice that the formation reaction for an aqueous ion also involves the production or consumption of electrons. 

TABLE D.2 Thermodynamic Properties of Substances at 298.15 K. Substances are at 1 bar pressure. For aqueous solutions, solutes are at unit activity (roughly 1 M). Data for ions in aqueous solution are relative to values of zero for AfH°, AfG°, and S° for H + ... 

To conclude the derived values of log,o K° and their associated uncertainties are based only on the aqueous phase model and the experimental data, and not on the selected values or uncertainties of the AfG° IRT values of Th" or other auxiliary species used in the modelhng. This holds trae for all the other cases where values of equilibrium constants are determined directly from the experimental data. NONLIN-SIT is a comprehensive program that uses ion interaction parameters and chemical potentials of all of the species expected in a given system, but it may be regarded as a method to optimise equilibrium constants, even if it operates v/o AfG°/Rr values. 

For this reaction, using the convention that A H°, S, and AfG° are zero for the aqueous H+ ion and the fact that AfH° and AfG° are zero for the elements, we can write the following expressions for standard molar reaction quantities ... 

We have now acquired all the tools with which to perform one of the most practical calculations of chemical thermodynamics determining the equilibrium constant for a reaction from tabulated data. Example 13-10, which demonstrates this application, uses thermodynamic properties of ions in aqueous solution as well as of compounds. An important idea to note about the thermodynamic properties of ions is that they are relative to H" (aq), which, by convention, is assigned values of zero for AfH°, AfG°, and S°. This means that entropies listed for ions are not absolute entropies, as they are for compounds. Negative values of S° simply denote an entropy less than that of H (aq). 

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