Aqueous solution standard thermodynamic properties

As we have seen in the preceding chapter, the standard thermodynamic properties of species in aqueous solutions are functions of ionic strength when they have electric charges. Substituting equation 3.6-3 for species j and for H + in equation 4.4-9 yields the standard transformed Gibbs energy of formation of species j as a function of pH and ionic strength at 298.15 K ... 

A new thermodynamic model for the Cu(I,II)-HC1-H20 system was developed on the basis of the representative data on GuGl(s) solubility in aqueous solutions of HC1 in a concentration interval from 1 to 6 mol kg1 HG1 (Akinfiev, 2009). The model takes into account a number of aqueous Cu(I) species [Cu+, CuOH°, Cu(OH)2, CuC1°, CuClj, HCuCL ], aqueous Cu(II) species [Cu2 CuOH+, CuO°, HCuO , CuOJ- CuCl+, CuCL , GuGlg, CuClJ)] and a mixed Cu(I)/Cu(II) chloride aqueous complex, Cu2Cl . The thermodynamic approach used a modelling approach based on i) the standard thermodynamic properties of the listed above species ii) a model for the activity coefficients iii) use of HCh software (Shvarov, 1999). 

When the standard thermodynamic properties of species are unknown for two reactants in a biochemical equation, the Af Gy (7=0) and Af 7/y (/=0) of the more basic species of this reactant can be assigned values of zero, so Af Gi for that reactant can be calculated under the experimental conditions. These assigned values become conventions of the thermodynamic table, like Af G (H ) = 0 and Af 7/ (H+) = 0 at each temperature. As described in the preceding section, this was done for adenosine in dilute aqueous solution (3) in 1992, but the determination of the thermodynamic properties of adenosine in dilute aqueous (4) made it possible to drop this convention for the ATP series. 

This table contains standard state thermodynamic properties of positive and negative ions in aqueous solution. It includes en-thcdpy and Gibbs energy of formation, entropy, and heat capacity, and thus serves as a companion to the preceding table, Standard Thermodynamic Properties of Chemical Substances . The standard state is the hypothetical ideal solution with molality m = 1 mol/kg (mean ionic molality in the case of a species which is assumed to dissociate at infinite dilution). Further details on conventions may be found in Reference 1. 

The solubility product Ksp can be calculated for a given temperature, as in the case of a typical chemical reaction, using the tabulated standard thermodynamic properties of formation for the Gibbs energy and enthalpy and the molar heat capacity of the salt and the ions in aqueous solution (aq). 

The procedure for the calculation of salt solubilities in aqueous solutions can be extended to organic solvents or solvent mixtures, starting from the condition that the fugacity (chemical potential) of a precipitated salt in phase equilibrium is identical in water, an organic solvent or the aqueous solution (r ee Figure 8.16). This means that the already available standard thermodynamic properties in the aqueous phase given in Table 8.1 can be used to determine the salt solubility in organic solvents or solvent mixtures [10]. 

Figure 8.16 Starting point for the derivation of the required equations for the calculation of salt solubilities in organic solvents starting from the tabulated standard thermodynamic properties of the ions in an aqueous solution.

In Chapter 7, we learned how to combine thermodynamic properties of different substances to calculate the heat absorbed or released by a reaction. In Chapter 13, we learned how to combine thermodynamic properties of different substances to calculate equilibrium constants for reactions. Many chemical reactions occur in aqueous solution and involve ions. To be able to calculate heats of reaction or equilibrium constants for such reactions, we need values for the thermodynamic properties of the aqueous ions involved. In this section, we discuss the standard thermodynamic properties of ions in solution, particularly with respect to how their values are established and interpreted. 

In Chapter 14 (Solutions and Their Physical Properties), we have added a section to describe the standard thermodynamic properties of aqueous ions. We use the concepts of entropy and chemical potential in Chapter 13 to explain vapor pressure lowering and why gasoline and water don t mix. 

The values given in the following table for the heats and free energies of formation of inorganic compounds are derived from a) Bichowsky and Rossini, Thermochemistry of the Chemical Substances, Reinhold, New York, 1936 (h) Latimer, Oxidation States of the Elements and Their Potentials in Aqueous Solution, Prentice-Hall, New York, 1938 (c) the tables of the American Petroleum Institute Research Project 44 at the National Bureau of Standards and (d) the tables of Selected Values of Chemical Thermodynamic Properties of the National Bureau of Standards. The reader is referred to the preceding books and tables for additional details as to methods of calculation, standard states, and so on. 

Practically in every general chemistry textbook, one can find a table presenting the Standard (Reduction) Potentials in aqueous solution at 25 °C, sometimes in two parts, indicating the reaction condition acidic solution and basic solution. In most cases, there is another table titled Standard Chemical Thermodynamic Properties (or Selected Thermodynamic Values). The former table is referred to in a chapter devoted to Electrochemistry (or Oxidation - Reduction Reactions), while a reference to the latter one can be found in a chapter dealing with Chemical Thermodynamics (or Chemical Equilibria). It is seldom indicated that the two types of tables contain redundant information since the standard potential values of a cell reaction ( n) can be calculated from the standard molar free (Gibbs) energy change (AG" for the same reaction with a simple relationship... 

In order to discuss thermodynamic properties in dilute aqueous solutions at temperatures other than 298.15 K, it is necessary to have the standard enthalpies of the species involved. Over narrow ranges of temperature, calculations can be based on the assumption that Af// values are independent of temperature, but more accurate calculations can be made when Cpm(i) values are known. It is also necessary to take into account the temperature dependencies of the numerical coefficients in equations 3.6-4 to 3.6-6. Clarke and Glew (1980) calculated the Debye-Hiickel slopes for water between 0 and 150°C. They were primarily concerned with electrostatic deviations from ideality of the solvent osmotic... 

The procedure for calculating standard formation properties of species at zero ionic strength from measurements of apparent equilibrium constants is discussed in the next chapter. The future of the thermodynamics of species in aqueous solutions depends largely on the use of enzyme-catalyzed reactions. The reason that more complicated ions in aqueous solutions were not included in the NBS Tables (1992) is that it is difficult to determine equilibrium constants in systems where a number of reactions occur simultaneously. Since many enzymes catalyze clean-cut reactions, they make it possible to determine apparent equilibrium constants and heats of reaction between very complicated organic reactants that could not have been studied classically. 

Electrolytes pose a special problem in chemical thermodynamics because of their tendency to dissociate in water into ionic species. It proves to be less cumbersome at times to describe an electrolyte solution in thermodynamic-like terms if dissociation into ions is explicitly taken into account. The properties of ionic species in an aqueous solution cannot be thermodynamic properties because ionic species are strictly molecular concepts. Therefore the introduction of ionic components into the description of a solution is an etfrathermodynamic innovation that must be treated with care to avoid errors and inconsistencies in formal manipulations.20 By convention, the Standard State of an ionic solute is that of the solute at unit molality in a solution (at a designated temperature and pressure) in which no interionic forces are operative. This convention implies that an electrolyte solution in its Standard State is an ideal solution,21 as mentioned in Section 1.2. 

The Standard-State chemical potentials of substances in the gas, liquid, and .olul phases, as well as of solutes in aqueous solution, can be determined by a v.uiely of experimental methods, among them spectroscopic, colorimetric, mi 11 ib i lily, colligative-property, and electrochemical techniques.817 The accepted values of these fundamental thermodynamic properties are and should be undergoing constant revision under the critical eyes of specialists. It is not the puipose of this book lo discuss the practice of determining values of /i° for all < (impounds of interest in soils. This is best left lo. specialized works on... 

The compilations by Wagman et al. and Robie et al. are quite extensive, including many solids as well as ionic solutes in aqueous solution. Since a compound may be written as the product of a chemical reaction that involves only chemical elements as reactants, and since pP for an element is equal to zero, pP for a compound can be considered to be a special example of ArG° for a reaction that forms the compound from its constituent chemical elements. Thus pP values also are termed standard Gibbs energies of formation and given the symbol AfG°. In addition to p° (or AfG°) values, Wagman et al. and Robie et al. list H° and S° for many substances. These Standard-State thermodynamic properties are related to ArH° and ArS° in Eq. 1.42 15... 

The two primary reference works on inorganic thermochemistry in aqueous solution are the National Bureau of Standards tables (323) and Bard, Parsons, and Jordan s revision (30) (referred to herein as Standard Potentials) of Latimer s Oxidation Potentials (195). These two works have rather little to say about free radicals. Most inorganic free radicals are transient species in aqueous solution. Assignment of thermodynamic properties to these species requires, nevertheless, that they have sufficient lifetimes to be vibrationally at equilibrium with the solvent. Such equilibration occurs rapidly enough that, on the time scale at which these species are usually observed (nanoseconds to milliseconds), it is appropriate to discuss their thermodynamics. The field is still in its infancy of the various thermodynamic parameters, experiments have primarily yielded free energies and reduction potentials. Enthalpies, entropies, molar volumes, and their derivative functions are available if at all in only a very small subset. 

The standard formation properties of species are set by convention at zero for the elements in their reference forms at each temperature. The standard formation properties of in aqueous solution at zero ionic strength are also set at zero at each temperature. For other species the properties are determined by measuring equilibrium constants and heats of reaction. Standard transformed Gibbs energies of formation can be calculated from measurements of K, and so it is really these Maxwell relations that make it possible to calculate five transformed thermodynamic properties of a reactant. 

A eiei is the number of atoms of element i in the crystalline substance and (j m (298.I5 is the standard molar entropy of element i in its thermodynamic reference state. This equation makes it possible to calculate Af5 ° for a species when Sm ° has been determined by the third law method. Then Af G° for the species in dilute aqueous solution can be calculated using equation 15.3-2. Measurements of pATs, pA gS, and enthalpies of dissociation make it possible to calculate Af G° and Af//° for the other species of a reactant that are significant in the pH range of interest (usually pH 5 to 9). When this can be done, the species properties of solutes in aqueous solution are obtained with respect to the elements in their reference states, just like other species in the NBS Tables (3). 

That is, we set AG° y,(H+, aq) = 0. Then the thermodynamic properties of anions can be found by measuring the chemical potentials of ionic solutions containing H" " in combination with different anions, and then using Eq. (4.1.3b). The anionic chemical potentials so determined can be employed as secondary standards in solutions containing different cations, and this matching process is continued as needed. Extensive tabulations constructed in this manner are available. However, this convention becomes null and void in processes where H" ions are transported across the phase boundaries of the aqueous solutions. 

NBS D. D. Wagman et al., Selected Values of Chemical Thermodynamic Properties, U.S. National Bureau of Standards, Technical Notes 270-3 (1968), 270-4 (1969), 270-5 (1971). R R. A. Robie, B. S. Hemingway, and J. R. Fisher, Thermodynamic Properties of Minerals and Related Substances at 298.15 K and 1 Bar (ICf Pascals) Pressure and at Higher Temperatures, Geological Survey Bulletin No. 1452, Washington, DC, 1978. Bard et al. Bard, A. J., R. Parsons and D. L. Parkhurst, Standard Potentials in Aqueous Solution, Marcel Dekker, New York (1985). S Other sources (e.g., computed from data in Stability Constants). 

---