Elements, free energy convention

In the literature (e.g., Thauer et al. 1977 Hanselmann, 1991) you find the AfG°(aq) values at 25°C for all the species involved in reaction Eq. 1. Note that by convention, the free energies of formation of the elements in their naturally occurring most stable form, as well as of the proton in aqueous solution, are set to zero. From these values, calculate the standard free energy of reaction Eq. 1 ... 

The other solution species are formed from this "basis" by a series of chemical reactions, and their concentrations can be expressed through the use of equilibrium constants, in terms of the concentration of the chosen "basis". The resulting set of nonlinear simultaneous equations consists of as many unknowns as there are elements and can be solved by conventional niamerical methods. The "free energy minimization" method utilizes only free energy criteria for chemical equilibria making no distinction among the constituent species and is essentially a constraint non-linear minimization problem. A number of search methods have... 

If the standard free energies of the elements are set equal to zero, by convention, the standard free energy of 1 mole of water vapor becomes equal to the standard free energy of formation from its elements. 

By adopting the foregoing convention, therefore, it is possible to define the standard free energy of formation of a positive ion from the element M, as — z Em, where Em is the standard (oxidation) potential on the hydrogen scale. 

By convention (cf. 33k) the free energy of formation of every element in its standard state is taken as zero, and, as seen above, the same applies to the hydrogen ion. The standard free energy of formation of liquid water at 26 C is — 56.70 kcal. mole " (Table XXIV), and that of the iodide ion is derived from its standard potential (Table XXXIX) as 1 X 23,070 X ( — 0.536) cal., i.e., — 12.37 kcal. g. ion"" It follows, therefore, that... 

Learn the conventions used to define units of entropy, heat capacity, enthalpy, and Gibbs free energy of elements, solids, liquids, and ions, including the proton. 

Although the formation from the elements convention does not in turn require a convention that the free energy (or enthalpy, etc.) of the elements is zero, the convention adopted for the properties of the aqueous ions does. But even in this case, the convention is adopted to simplify things it is not necessary (see Chapter 17). 

The entropies so computed are termed Third Law, absolute, or conventional entropies, and designated S° or. These are not at all comparable to enthalpies and free energies of formation, AfH° and A/G°, which instead refer to reactions forming the compound from its elements. For example, AfH° and AfG° for an element such as 02(5) at 25°C are both necessarily zero, while the absolute entropy, S Igg, is 205.15 mol (see Table 7.1). 

The high temperature properties of the elements have discontinuities as mentioned above that make interpolation very inconvenient in some temperature ranges. Why not define free energies and enthalpies so as to leave the elements at 298 K Since they cancel out in all balanced reactions, it would make life simpler. Unfortunately there are two conventions for doing this at the present time. 

It is possible to effect some simplification in the equations defining the thermodynamic properties of the ions by introducing additional conventions (a convention can be defined somewhat facetiously as a convenient assumption that we know is not true). If, for example, we decide that the absolute free energies and enthalpies of all pure elements are to be set at zero, then the defining equation for free energies and enthalpies (equation 17.21) becomes the same as that for S, V, and Cp (equation 17.22). If in addition we define all properties of the hydrogen ion as zero, then the conventional ionic properties become the same as the corresponding absolute properties, and we could have stopped at equation (17.19). 

At standard state every element is assigned, by convention, a free energy of zero per mole. Thus H2(g), 02 g), Cgraphite(s). and so forth, all are assigned free energy values of zero kcal/mole. Also, to establish a baseline for ionic substances in solution, at a concentration of 1 mole/ liter in an ideal solution and at standard state conditions has been assigned a free energy of zero. 

To relate AG of the reactions, we need to know the free energy of formation for the substances involved in the reaction. Free-energy formation for a substance is defined as the free energy released or used to form one mole of the substance in its standard state and is denoted as G°, where f stands for formation, and additional subscripts such as T and t can be used to indicate whether temperature is in Kelvin or °C, respectively. By convention Gf is for stable configuration of elements in then-standard states. For example, Gf for C, HjO, Nj, and O2 is set at zero. Examples of free energies of formation for selected compounds involved in biogeochemical cycles of elements in wetlands (G°, kJ mok are shown in Table 2.1 (Lindsay, 1979 Madigan and Martinko, 2006). 

The work of Reiss and co-workers puts the question of the equilibrium distribution of liquid embryos in dilute supercooled vapors on sound conceptual ground. However, having to calculate embryo free energies by simulation rules out the use of such an approach in practical applications. To overcome this limitation, Weakliem and Reiss [67] developed a modified liquid drop theory that combines elements of the physically consistent cluster with the conventional capillarity approximation. These same authors have also developed a rate theory which allows the calculation of nucleation rates in supercooled vapors [68]. The dependence of the predicted rates on supersaturation agree with classical nucleation theory, but the temperature dependence shows systematic deviations, in accordance with scaling arguments [54]. 

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