Standard state Thermochemical

The three laws of thermodynamics provide the theoretical basis required to master nearly all the concepts that are relevant in discussions of molecular energetics. We shall not dwell on those laws, because they are mandatory in any general physical chemistry course [1,8], but we will ponder some of their outcomes. It is also necessary to agree on basic matters, such as units, nomenclature, standard states, thermochemical consistency, uncertainties, and the definition of the most common thermochemical quantities. 

Ideal gas absolute entropies of many compounds may be found in Daubert et al.,"" Daubert and Danner," JANAF Thermochemical Tables,TRC Thermodynamic Tables,and Stull et al. ° Otherwise, the estimation method of Benson et al. " is reasonably accurate, with average errors of 1-2 J/mol K. Elemental standard-state absolute entropies may be found in Cox et al." Values from this source for some common elements are listed in Table 2-389. ASjoqs may also be calculated from Eq. (2-52) if values for AHjoqs and AGJoqs are known. 

Standard-State Enthalpy Changes (AH°). To expedite calculations, thermochemical data are ordinarily presented in the form of standard-state enthalpy changes of the system AH°(T,P), with the requirement that materials start and end at the same temperature (T) and pressure (P) and in their standard states of aggregation, i.e.,... 

Most thermochemical data are reported for 25°C (more precisely, for 298.15 I<). Temperature is not part of the definition of standard states we can have a standard state at any temperature 298.15 K is simply the most common temperature used in tables of data. All reaction enthalpies used in this text are for 298.15 K unless another temperature is indicated. 

In order to have a consistent basis for comparing different reactions and to permit the tabulation of thermochemical data for various reaction systems, it is convenient to define enthalpy and Gibbs free energy changes for standard reaction conditions. These conditions involve the use of stoichiometric amounts of the various reactants (each in its standard state at some temperature T). The reaction proceeds by some unspecified path to end up with complete conversion of reactants to the various products (each in its standard state at the same temperature T). 

Thermochemical data from the compilation of Stull et at., 1969. Entropy values are based on a 1 M standard state. The asterisk denotes symmetry-corrected quantities. Symmetry numbers were chosen as follows 18 for the n-alkanes, cis-3-hexene, dibuthyl sulphide, diethyl ether, and diethyl amine 2n for the cycloalkanes and 2 for all of the remaining ring compounds 3 for the alkanols, alkanethiols and alkyl amines 9 for the methyl alkyl sulphides... 

The values included in thermochemical databases (see appendix B) are normally referred to the substances in their standard states. The standard state notion, which is a consequence of the mathematical formalism used to describe the thermodynamics of reaction and phase equilibria [1], greatly simplifies the calculation of thermochemical quantities for the infinite variety of real processes, that is, those where one or more substances are not in their standard states. This situation will be exemplified in several chapters of the present book, but several case studies are discussed here. 

It must be stressed that the temperature is not included in the definition of standard state. Nevertheless, all modern thermochemical databases list the values at 298.15 K, so this is now regarded as a reference temperature. As shown in appendix B, very few data compilations give values at any other temperature. 

The case of liquid solutions is more complicated because the conventions vary. These are always stated in introductory chapters of the thermochemical databases and deserve a careful reading. In most tables and in the present book, it is agreed that the standard state for the solvent is the pure solvent under the pressure of 1 bar (which corresponds to unit activity). For the solute, the standard state may refer to the substance in a hypothetical ideal solution at unit molality (the amount of substance of solute per kilogram of solvent) or at mole fraction x = 1. 

The problem can be tackledby considering reaction 2.2, where all reactants and products are the pure species in their standard states at 298.15 K, and evaluating Ar//°(2.2) from data, which are easily found in thermochemical compilations. These data are the standard enthalpies of formation of the substances involved. 

Figure 2.1 Thermochemical cycle, showing how to relate the enthalpy of the experimental reaction 2.1 with reaction 2.2, where reactants and products are in their standard states.

We have illustrated how standard enthalpy of formation values can be handled to yield data for practical conditions. The procedure always involves thermochemical cycles, relating the standard state processes with those observed in... 

THE SELECTION OF THERMOCHEMICAL DATA AND MORE ON STANDARD STATES... 

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. 

In calculating the lattice energy of a crystal, we adopt an arbitrary reference condition (two isolated ions in the gaseous state and at infinite distance) to which we assign a zero potential. It is worth stressing that this condition is not equivalent to the standard state commonly adopted in thermochemical calculations, which is normally that of element at stable state at reference P, T. 

The relationships between the two different states and between the enthalpy of formation from the elements at standard state (H°) and the lattice energy (U) are easily understood by referring to the Born-Haber-Fayans thermochemical cycle. In this cycle, the formation of a crystalline compound from isolated atoms in the gaseous state is visualized as a stepwise process connecting the various transformations. Let us follow the condensation process of a crystal MX formed from a metal M and a gaseous molecule X2 ... 

Table 5.12 reports a compilation of thermochemical data for the various olivine components (compound Zn2Si04 is fictitious, because it is never observed in nature in the condition of pure component in the olivine form). Besides standard state enthalpy of formation from the elements (2) = 298.15 K = 1 bar pure component), the table also lists the values of bulk lattice energy and its constituents (coulombic, repulsive, dispersive). Note that enthalpy of formation from elements at standard state may be derived directly from bulk lattice energy, through the Bom-Haber-Fayans thermochemical cycle (see section 1.13). 

Table 5.12 Thermochemical data for various olivine end-members (7) = 298.15 K P, = 1 bar). Listed values in kJ/mole (from Ottonello, 1987). = standard state enthalpy of formation...

The values given in Table 3-5 were used for the enthalpies of the gases of atoms in their normal states (the reference states for the bond energies) relative to the standard states of the elements, to which the enthalpies of formation given in the Bureau of Standards compilation refer. Most of the values in Table 3-5 are taken from the Bureau of Standards compilation an important exception is the value for nitrogen, which has been shown by recent spectroscopic and thermochemical... 

Although the best source of AH is certainly experimental measurement, this is often unavailable for a species of interest. The standard-state heat of formation is sometimes available from theory. The wide availability of powerful computing platforms has made calculation of thermochemical properties from first-principles practical in many cases. 

The formulas that we have derived in this chapter to calculate thermochemical data are accurate and easy to apply. This approach can be used to fill in the gaps in species thermochemical data needed in reacting-flow calculations. Their accuracy is limited by the values of the molecular constants used in the calculations, that is, vibrational frequencies, moments of inertia, and the standard-state heat of formation. 

Equation (3.106) is the well-known starting point for thermochemical calculations as described in many elementary textbooks. Standard enthalpies of formation Af/f [Ad have been measured and tabulated (see, e.g., the NIST website http //webbook.nist.gov/ chemistry) for a vast number of chemical compounds Ah so (3.106) makes it rather easy to obtain A//lxn values under standard state conditions for virtually any chemical reaction of interest. 

In this article both unsensitized and mercury vapor sensitized reactions are discussed. The plan has been to proceed from the chemically simplest system, oxygen molecule, to the chemically most complex, ozone plus hydrogen peroxide. Unless otherwise stated, thermochemical values have been taken from compilations of the National Bureau of Standards (68) and are reported in kcal. for the reaction represented in mole amounts. Conversion factors for energy units, spectroscopic notation, and unless noted, spectroscopically based values have been taken from... 

No elements are listed in Table 8.2 because, by definition, the most stable form of any element in its standard state has AH°f = 0 kj. (That is, the enthalpy change for formation of an element from itself is zero.) Defining AH°f as zero for all elements thus establishes a kind of thermochemical "sea level," or reference point, from which all enthalpy changes are measured. 

Figure 1 Thermodynamic cycle for the enthalpy of formation of methane (CH4) from the standard states of carbon and hydrogen (graphite and H2). The quantities in italics are calculated in typical thermochemical quantum chemical predictions.

To correct the 0 K heat of formation to that at 298.15 K we add the increase in enthalpy of methanol on going from 0 to 298 K and subtract the corresponding increases for the elements in their standard states. The value for methanol is the difference of two quantities provided in the thermochemical summary at the end of the G2 calculation as implemented in Gaussian 94 and subsequent versions ... 

Example 10 illustrates how thermochemical data for aqueous ions may be obtained from measurements in electrochemical cells. The problem of measuring cell potentials in the standard state, which is a hypothetical state, will be discussed in section 10.12. The temperature variation of the voltage of such cells would provide AHJ of aqueous ions, through the use of Eq. (48). 

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