Thermochemistry standard states

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. 

Equation 7.31 was derived from a least squares fit to the data given in W.N. Hubbard, D. W. Scott, G. Waddington. Standard States Corrections for Combustions inaBomb at Constant Volume. In Experimental Thermochemistry, vol. 1 F. D. Rossini, Ed. Interscience New York, 1956 p. 93. 

In Fig. 1, various elements involved with the development of detailed chemical kinetic mechanisms are illustrated. Generally, the objective of this effort is to predict macroscopic phenomena, e.g., species concentration profiles and heat release in a chemical reactor, from the knowledge of fundamental chemical and physical parameters, together with a mathematical model of the process. Some of the fundamental chemical parameters of interest are the thermochemistry of species, i.e., standard state heats of formation (A//f(To)), and absolute entropies (S(Tq)), and temperature-dependent specific heats (Cp(7)), and the rate parameter constants A, n, and E, for the associated elementary reactions (see Eq. (1)). As noted above, evaluated compilations exist for the determination of these parameters. Fundamental physical parameters of interest may be the Lennard-Jones parameters (e/ic, c), dipole moments (fi), polarizabilities (a), and rotational relaxation numbers (z ,) that are necessary for the calculation of transport parameters such as the viscosity (fx) and the thermal conductivity (k) of the mixture and species diffusion coefficients (Dij). These data, together with their associated uncertainties, are then used in modeling the macroscopic behavior of the chemically reacting system. The model is then subjected to sensitivity analysis to identify its elements that are most important in influencing predictions. 

We see that Kp has an explicit temperature dependence. However, Kp is not pressure dependent. That is, from Eq. 9.43, Kp is seen to depend on the standard-state thermochemistry in other words, properties at the standard-state pressure p = p° alone. 

THERMOCHEMISTRY. That aspect of chemistry which deals with die heat changes which accompany chemical reactions and processes, the heal produced by them, and die influence of temperature and odier thermal quantities upon them. Tt is closely related to chemical thermodynamics. The heat of formation of a compound is the heat absorbed when it is formed from its elements in their standard states. An exothermic reaction evolves heat and endothermic reaction requires heat for initiation. 

Superoxide (02 ) and the peroxyl radical (H02) have been intensively studied, and a good account of their thermochemistry is presented in Standard Potentials (pp. 60-63). They are related by the pKa of H02, which is 4.8 0.1 (51). The reduction potential of the 02/02 couple has been determined by a variety of methods, including, for example, the equilibria with various quinone-semiquinone systems. The value cited, — 0.33 V, is taken with respect to a standard state of 1 atm 02 pressure. When expressed relative to the 1 Mstandard state of 02, the potential is —0.16 V. Standard NBS data permit calculation of AfG° = 4.4 kJ/mol and 31.8 kJ/mol for H02 and 02, respectively. Some related potentials include 0.12 V for (H+, 02)/H02,1.44 V for (H+, H02)/H202, and 0.75 V for H02/H02 . 

It is evident that it is not necessary to determine the heat of a particular reaction by experiment. If the heat of formation of every compound involved in the reaction is known, the heat of the reaction can be calculated. Values of heats of formation of compounds from elements in their standard states are given in the chemical handbooks and other reference books. The standard reference book is F. R. Bichowsky and F. D. Rossini, The Thermochemistry of Chemical Substances Reinhold Publishing Corp., New York, 1936. 

The enthalpy change for a chemical reaction in which all reactants and products are in their standard states and at a specified temperature is called the standard enthalpy (written AFf°) for that reaction. The standard enthalpy is the central tool in thermochemistry because it provides a systematic means for comparing the energy changes due to bond rearrangements in different reactions. Standard enthalpies can be calculated from tables of reference data. For this purpose, we need one additional concept. The standard enthalpy of formation AH° of a compound is defined to be the enthalpy change for the reaction that produces 1 mol of the compound from its elements in their stable states, all at 25°C and 1 atm pressure. For example, the standard enthalpy of formation of liquid water is the enthalpy change for the reaction... 

In the meantime, Benson had developed an additive approach to the thermochemistry of molecules, based on the idea that thermodynamic properties like A H29i can, at least to a certain extent, be regarded as the sum of A fH29i values ascribed to constituent parts of the molecule, such as the C-C bond or the -CH2 - group. These constituent values he called bond additivity values or group additivity values. We shall see the distinction below. Although the objective of these calculations is the standard state enthalpy of formation, superscript ° will not be used in the notation because calculated AfH29S values are approximate by definition. 

Note that arbitrarily assigning zero AHf for each element in its most stable form at the standard state does not affect our calculations in any way. Remember, in thermochemistry we are interested only in enthalpy changes, because they can be determined experimentally whereas the absolute enthalpy values cannot. The choice of a zero reference level for enthalpy makes calculations easier to handle. Again referring to the terrestrial altitude analogy, we find that Mt. Everest is 8708 ft higher than Mt. McKinley. This difference in altitude is unaffected by the decision to set sea level at 0 ft or at 1000 ft. 

To provide as complete a model of the thermochemistry of zirconium as possible, the reviewers adopted the following approach each experiment is evaluated, reviewed, and, if necessary and possible, the results are recalculated to be consistent with other experimental conclusions and the SIT model (Appendix A). Uncertainties are assigned at this point, subjectively, if necessary. These results, with their associated uncertainties, are accepted if there is no clear reason to reject them and such data are reported in Chapter V. Accepted results are used in the determination of the relevant thermodynamic parameter or to confirm a parameter derived by other methods. Uncertainties assigned at the review stage and associated with the extrapolation to the 7=0 standard state are propagated (Appendix C), to the extent possible, throughout the procedure and the final recommended results with the associated uncertainties are given in Chapter III. In some cases, uncertainties are derived from a sensitivity analysis of the... 

Step 1 is the decomposition of reactants into elements in their standard states. But this is just the opposite of the formation reaction of the reactants, so the enthalpy change of the process is -AHf°(reactants). Similarly, Step 2, the formation of the products from elements in their standard states, has an enthalpy change of AHf°(products). Remember, however, that the formation reaction is defined for the generation of one mole of the compound. Consequently, to use tabulated heats of formation we must multiply by the stoichiometric coefficients from the balanced equation to account for the number of moles of reactants consumed or products generated. Taking these factors into account leads to one of the more useful equations in thermochemistry. 

In thermochemistry we often used 25°C as the "standard" temperature—although temperature is not actually part of the definition of the standard state Section 5.6]. 

This equation differs from the calculation of AH° from standard enthalpies of formation (AHj), although it is equivalent to it. We return to the issue of obtaining AHj in theoretical methods later. At first sight, the notion of the enthalpy of a substance (Ha, Hb, He, and Ho) might be confusing there is after all no such thing as an absolute enthalpy. The quantities Ha, Hb, He, and Ho are relative enthalpies, but they are enthalpies of substances relative to the so-called quantum chemical standard state. The quantum chemical standard state consists of infinitely separated electrons and nuclei of a substance. For example, the quantum chemical enthalpy of the water molecule is the enthalpy relative to an O nucleus, two protons, and ten electrons, all infinitely separated. The quantum chemical standard state is the zero of the potential energy in the usual quantum chemical Hamiltonian. To make a parallel with experimental thermochemistry, the AHj of a substance is its molar enthalpy relative to the enthalpy of its elements in their standard states. 

Chemistry is concerned with the study of molecular structures, equilibria between these structures and the rates with which some stractures are transformed into others. The study of molecular structures corresponds to study of the species that exist at the minima of multidimensional PESs, and which are, in principle, accessible through spectroscopic measurements and X-ray diffraction. The equihbria between these structures are related to the difference in energy between their respective minima, and can be studied by thermochemistry, by assuming an appropriate standard state. The rate of chemical reactions is a manifestation of the energy barriers existing between these minima, barriers that are not directly observable. The transformation between molecular structures implies varying times for the study of chemical reactions, and is the sphere of chemical kinetics. The journey from one minimum to another on the PES is one of the objectives of the study of molecular dynamics, which is included within the domain of chemical kinetics. It is also possible to classify nuclear decay as a special type of unimolecular transformation, and as such, nuclear chemistry can be included as an area of chemical kinetics. Thus, the scope of chemical kinetics spans the area from nuclear processes up to the behaviour of large molecules. 

The reaction rate constant for each elementary reaction in the mechanism must be specified, usually in Arrhenius form. Experimental rate constants are available for many of the elementary reactions, and clearly these are the most desirable. However, often such experimental rate constants will be lacking for the majority of the reactions. Standard techniques have been developed for estimating these rate constants.A fundamental input for these estimation techniques is information on the thermochemistry and geometry of reactant, product, and transition-state species. Such thermochemical information is often obtainable from electronic structure calculations, such as those discussed above. 

Although this chapter concentrates on organosilicon compounds, a few purely inorganic compounds are also included (the hydrides and halides), since these provide inevitable reference points. It is worth mentioning at this point that the chapter title Thermochemistry is used with its traditional meaning here to signify heats (or enthalpies) of reaction, rather than in the looser sense of chemistry under the action of heat as employed by some workers in the field of organosilicon chemistry. Unless otherwise stated, all standard heats of reaction and heats of formation refer to the gas phase at 298.2 K. 

The heat associated with a chemical reaction depends on the pressure and temperature at which the reaction is carried out. All thermochemical data presented here are for reactions carried out under standard conditions, which are a temperatnre of 298 K (24.85°C) and an applied pressure of one bar. The quantity of heat released in a reaction depends on the amount of material undergoing reaction. The chemical formulas that appear in a reaction each represent 1 mole (see article on Mole Concept ) of material for example, the symbol CH4 stands for 1 mole of methane having a mass of 16 grams (0.56 ounces), and the 2 02(g) tells us that 2 moles of oxygen are required. Thermochemistry also depends on the physical state of the reactants and products. For example, the heat liberated in equation (1) is 890... 

---