Free energies and enthalpies of formation from the elements

Free energies and enthalpies of formation from the elements 

Consider the following reactions, in each of which one mole of a compound is formed from its component elements  

From measured values of the equilibrium constants the values of may be calculated by use of equation (4 18). If the temperature to which this calculation refers is, say, 1000 K, the result is denoted A/GJodo called the standard free mcrgy of formation of the par- 

The value of AG for this reaction will have the same value whether it occurs directly as written, or as a process involving several steps. This is because G is a function of state, and its change in any process 

From this example it will now be clear that AC ., and therefore also the equilibrium constant, may be calculated for any conceivable reaction provided that the free energies of formation of the various compounds are already known. This property of additivity applies also, of course, to internal energies, entropies, etc., and in the case of the enthalpies it is known as Hess s law. 

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TABLE A13.1 Gibbs free energy and enthalpy of formation from the elements at 25 C and 1 bar total pressure of some uranium aqueous species and solids of geochemical interest... 

TABLE A13.8 Gibbs free energies and enthalpies of formation from the elements of some geochemically important aqueous species and solids of plutonium at 25T and 1 bar total pressure... 

The quantities AGf° and AHf° refer to free energies and enthalpies of formation from the elements with consumption or production of gaseous electrons if necessary. Standard states of elementary hydrogen and oxygen are one atmosphere fugacity. The standard state of the... 

Rubber Company Handbook (Weast, 1987) is one of the more commonly available sources. More complete sources, including some with data for a range of temperatures, are listed in the references at the end of the chapter. Note that many tabulations still represent these energy functions in calories and that it may be necessary to make the conversion to Joules (1 cal = 4.1840J). Because of the definition of the energy of formation, elements in their standard state (carbon as graphite, chlorine as CI2 gas at one bar, bromine as Br2 liquid, etc.) have free energies and enthalpies of formation equal to zero. If needed, the absolute entropies of substances (from which AS may be evaluated) are also available in standard sources. 

In Other words, the free energy and enthalpy of formation of a compound at T and P are calculated from the difference between the absolute G and H values of that compound at T and P and its constituent elements at T and Pr (one bar). The right-hand sides of both these equations are calculated from the known properties of the substance and its elements at 298 K and 1 bar, plus the equations for the change in these properties with T as described below. 

The standard partial molal volumes (V ), heat capacities (C >), and entropies (S ) of aqueous /i-polymers, together with their standard partial molal enthalpies AHj) and Gibbs free energies of formation from the elements AGf), are linear functions of the number of moles of carbon atoms in the alkyl chains (figure 8.28). 

Calculations are best carried out in units of hartrees, then converted to kcal mol 1 if desired (conversion constant 627.51 kcal mol /hartree) to avoid needless confusion over slightly differing literature values of C and H atomization energies and of the corresponding enthalpies of formation of the free atoms from the elements in their standard states. One can do this because the C and H atomization energies and enthalpies of formation cancel in the full calculation. 

Recall that we defined standard enthalpies of formation, AHf, as the enthalpy change when a substance is formed from its elements under defined standard conditions. oGo (Section 5.7) We can define standard free energies of formation, AGf, in a similar way AGf for a substance is the free-energy change for its formation from its elements under standard conditions. As is summarized in Table 19.2, standard state means 1 atm pressure for gases, the pure solid for solids, and the pure liquid for liquids. For substances in solution, the standard state is normally a concentration of 1 M. (In very accurate work it may be necessary to make certain corrections, but we need not worry about these.)... 

In practice, G and H for a substance are defined relative to the G and H for the constituent elements. These relative values are known as free energy of formation and enthalpy of formation for standard conditions and referred to as AG° and AH°. Values for these functions may be obtained from standard tables of thermodynamic data, usually for the reference temperature of 298.2 K. The Chemical... 

Calcite solubility product constants range over 0.3 log units. The major tabulated differences are in the free energies of calcite and of the calcium ion. The most reliable measurement and evaluation of calcite solubility is that of Plummer and Busenberg (31). They found log Ksp = -8.48(+ 0.02) at 298.15 K which agrees excellently with the CODATA value of -8.47. The main source of error can be traced to a 2 kJ/mol difference between the CODATA and USGS values for the enthalpy of formation of calcite from the elements. The recent CODATA revisions of the calcium ion and calcite values take into account many different properties including the Plummer and Busenberg solubility value (31). Hence, they are the most reliable values for this system. 

The present author has the impression from the literature on the stability of diazomethane relative to diazirine that two different physico-chemical phenomena were called (thermal) stability in some of the publications, namely the thermodynamic stability, as defined by the free energy of formation AGf and the free enthalpy of formation A//f for the (hypothetical) formation of a compound from the elements in a gas phase reaction under standardized conditions (298 K, 1 mol). AGf and A//f are related to one another by the free entropy A5f in the Gibbs-Helmholtz equation AGf = A/ff-TASf. The absolute values of AGf, A/ff and ASf do not give definite information on the stability of a compound, as this word is used in the everyday language of a chemist, because it is related to an unrealistic chemical process, namely the formation from the elements. If A/ff is known, however, for a given compound and for a real product of one of its reactions, the difference in magnitude of the two free enthalpies tells us whether this reaction is likely to take place, but we cannot depict at all, at least in principle, the half-life of such a reaction. 

The enthalpy, entropy, and Gibbs free energy of formation of EuSe from the elements under standard conditions, AH298= -93.8 0.8 kcal/mol, AS298= -3.20 1.2 cal-mol -K" and 298= -92.8 1.2 kcal/mol, were calculated from available literature data and the authors own thermodynamic data for EuSe, McMasters et al. [9]. The enthalpy of formation calculated from the atomization energy of Gordienko etal. [10] is 14 kcal/mol larger [9]. 

High-temperature vaporization behaviors that yield high-temperature thermodynamic data such as activity and enthalpy are necessary for uses as nuclear reactor and fusion materials. High-temperature activity measurements make it possible to determine the Gibbs free energy of formation of compounds from the elements. Accurate high-temperature thermodynamic data serve to establish temperature-composition phase diagrams, i.e., limits for the formation of binary phases. 

Just as we can define a standard enthalpy of formation (AH°f) and a standard free energy of formation (AG°f), we can define an analogous standard entropy of formation (AS°f) as being the entropy change for formation of a substance in its standard state from its constituent elements in their standard states. Use the standard molar entropies given in Appendix B to calculate AS°f for the following substances ... 

We represent A///° and A/G° as the standard enthalpy and Gibbs free energy changes for the reaction in which the chemical substance is formed from the elements in their stable form, as they occur in nature at T = 298.15 K.rr For ions in solution, the values tabulated are relative to the standard enthalpy and Gibbs free energy of formation of the H+ ion being set equal to zero.ss... 

This table lists standard enthalpies of formation AH°, standard third-law entropies S°, standard free energies of formation AG°, and molar heat capacities at constant pressure, Cp, for a variety of substances, all at 25 C (298.15 K) and 1 atm. The table proceeds from the left side to the right side of the periodic table. Binary compounds are listed under the element that occurs to the left in the periodic table, except that binary oxides and hydrides are listed with the other element. Thus, KCl is listed with potassium and its compounds, but CIO2 is listed with chlorine and its compounds. 

The desired unsaturated hydrocarbons only appear to be stable in relation to the saturated structures from which they are derived at relatively elevated temperatures. This fact is illustrated by Fig. 21, which shows the variation of the free enthalpy of formation AGj as a function of temperature, related to a carbon atom, nf a number of characteristic hydrocarbon compounds. In this graph, and at a given temperature, a substance is unstable in relation to all the compounds or elements (C + H2), whose representative point remains below its own, since formation from these compounds or elements requires an input energy the substance is stable in the opposite case. Accordingly, hydrocarbons are unstable at all temperatures in relation to their elements, except for methane, which is stable at the low and medium temperatures. 

Table 7.2, for halite (NaCl) is more complicated and more typical of natural compounds. As with 02(g) and all other substances, the entropy S°t here is the absolute value for the forms of NaCl listed at the top of the Table—pure crystals for temperatures up to 1073.8 K, and liquid NaCl at higher temperatures. Now, however, the free energy, enthalpy, and log Kf for formation of NaCl from its elements are all non-zero because they refer to the reaction... 

Free enthalpy characterizes maximum useful work, which is performed between atoms and molecules on the account of potential energy of only electrons. In this coimection it may be assumed that the free enthalpy of elements per se is equal to zero. Then the values of median (molar) free enthalpy and of any compounds may be characterized as energy of its formation in the amoimt of 1 mole. In order to compare free enthalpy of the formation of different compounds, it is necessary to measure the energy of their formation from individual elements under some identical conditions. 

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