Estimation of thermodynamic data

In practice, we can see that we actually have very scant data on the standard enthalpies and standard entropies of compounds, found by reliable measurements, and that those data are not known for a large number of compounds. Hence, users have sought to estimate, with the greatest possible degree of accuracy, values for those data when they have not had values gleaned from calorimetrie experimentation or the examination of the adsorption spectmm. 

We have seen (section 4.2.7 4) the method for determining the bond energies on the basis of the limit of the continuous absorption spectrum. This limit, though, is often fairly difficult to observe directly. We shall see, however, that we can estimate the energy of dissociation by calculation, by determining the law which gives the position of the successive vibration bands. 

Let us look again at the approximate expression [4.25] for the absorption energy corresponding to a spectral line for the value v of the level parameter. We shall apply that relation for the first two lines in the spectral series characterized by the transitions v = 1—v = 2 and v = 2— v = 3. We obtain  

By solving the system composed of these two equations [4.50] and [4.51], we obtain an estimated value of the energy Eco and of the vibration frequency The energy of dissociation is then calculated by the relation  

In the evaluation of the enthalpy of formation, we can then treat the energy of dissociation and the bond energy as identical. 

The systematization of the results of measurement is a normal scientific activity which leads to methods for the interpolation and extrapolation of data. For example, the Periodic Table may be used to seek relations between a thermodynamic property for compounds in a Group of elements. In the estimation of the properties of aliphatic compounds it is common practice to consider members of a homologous series, and therefore to study the change in a property produced by an increment of one CHa group. For this purpose it is often convenient to use the appropriate hydrocarbon homologous series as a source of reference. However, a word of caution is necessary here because some of the recorded properties of hydrocarbons have themselves been obtained by incremental methods, 

Bondi has provided a somewhat similar book to that by Reid and Sherwood, but treats substances of higher molecular weight, up to and including polymers and glasses. 

Reid and T. K. Sherwood, The Properties of Gases and Liquids, McGraw-Hill, New York, 1966. 

36S Physical Property Estimation System , American Institute of Chemical Engineers, New York, 1965. 

Physical Properties of Molecular Crystals, Liquids and Glasses , J. Wiley and Sons, New York, 1968. 

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By these methods, one can obtain fairly reliable estimates of enthalpies of formation of many compounds. As the bond enthalpies used are average values, they cannot be expected to result in highly accurate results for enthalpies of formation. More complex procedures also have been developed that will provide greater accuracy [14]. Related methods for estimation of thermodynamic data are discussed in Appendix A. 

Benson, S. W. (1976). Thermodynamic Kinetics. Methods for the Estimation of Thermodynamic Data and Rate Parameters. Wiley, New York. 

Bond Energies and Approximate Methods for Estimation of Thermodynamic Data... 

Despite these difficulties of (piantitative interpretation, there are sufficient data on the most important steps in the proposed mechanism [Eq. (XIII. 13.2)] to indicate that at least (lualitatively it is a correct scheme. In Table XIII. 13 arc collected some estimates of thermodynamic data pertinent to the reaction scheme. The data on reactions 3 and 4 are included in Tables XI1.6 and XII.8, respectively. Volman and Graven loc, cit.) have estimated the activation energy of reaction 7 as 13.5 db 2 Kcal, which is very close to the heat of reaction estimated at 10 Kcal (Table XIII. 13). There are no quantitative data on the value of the frequency factor of 7, but from the low activation energy one might expect that it should show pressure dependence. ... 

Methods of estimation of thermodynamic data of organic substances are discussed in [5] and especially in [11]. 

In Chapter 3 of this textbook the estimation of thermodynamic data is described for compounds for which no experimental data are available. For the heat capacity of predominantly ionic, solid compounds at 298 K cationic and anionic group contributions can be added. Moreover a set of equations is given to estimate the constants in the equation ([C J J (NiC03, cr) = (88.701 + 38.91x10 (r/K) - 12.34x10 (77K) ) J K mor ). The variables are the sum of the cationic and anionic contributions, the melting temperature of the compound, and the number of atoms in the molecule. 

Computer programs THERGAS (estimation of thermodynamical data), KING AS (estimation of kinetic data), EXGAS (generation of combustion mechanisms). Combustion mechanisms of alkanes, alkenes, ethers, cyclanes and mixtures thereof are available upon request. 

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