Estimation, of entropies

We admit some cowardice. Most of our earlier estimates of entropy invoked symmetry numbers and/or were studies of bond cleavage reactions dominated by translational effects. We hesitate to compare isomers with the same carbon or heavy atom skeleton when effects of a few kJ mol-1 are crucial. 

First-order estimates of entropy are often based on the observation that heat capacities and thereby entropies of complex compounds often are well represented by summing in stoichiometric proportions the heat capacities or entropies of simpler chemical entities. Latimer [12] used entropies of elements and molecular groups to estimate the entropy of more complex compounds see Spencer for revised tabulated values [13]. Fyfe et al. [14] pointed out a correlation between entropy and molar volume and introduced a simple volume correction factor in their scheme for estimation of the entropy of complex oxides based on the entropy of binary oxides. The latter approach was further developed by Holland [15], who looked into the effect of volume on the vibrational entropy derived from the Einstein and Debye models. 

Dannenfelser, R. M., and S. H. Yalkowsky, Estimation of entropy of melting from molecular structure A non-group contribution method , Ind. Eng. Chem. Res., 35, 1483-1486 (1996). 

Yalkowsky, S. H., Estimation of entropies of fusion of organic compounds , Ind. Eng. Chem. Fundam., 18, 108-111... 

Yalkowsky, S. 1979. Estimation of Entropies of Fusion of Organic Compounds, lnd. Eng. Chem. 

The reactions with which we are mostly concerned in chemistry take place in solution rather than in the gas phase. The majority of them moreover involve reactants, products, or transition states carrying electric charges. In such cases the entropies of solvation are extremely large, and these entropies cannot be estimated at present. This immediately rules out any possibility of estimating absolute values of equilibrium or rate constants for reactions of this kind. If we are concerned with absolute calculations of rates and equilibria, we must confine ourselves either to gas-phase reactions, or to reactions of non-polar type. Even here we will usually be forced to make estimates of entropies that are of dubious significance chemical theory has not yet progressed to a point where problems of this kind can usefully be discussed. 

Yalkowsky, S.H. (1979) Estimation of entropies of fusion of organic compounds. Ind. Eng. Chem. Fundam. 18, 108-111. Yalkowsky, S.H., Mishra, D.S. (1990) Comment on Prediction of aqueous solubility of organic chemicals based on molecular structure. 2. Application to PNAs, PCBs, PCDDs, etc. Environ. Sci. Technol. 24(6), 927-929. 

Equation 4. Among the heavier elements in the B subgroup of the periodic table, thallium, lead, and bismuth are notable because their compounds resemble those of the elements with atomic numbers two lower thus the properties of Pb(II) compounds are similar to those of Hg(II) compounds, etc. (12). For this reason, we have chosen Pb(II) compounds as the principle bases for estimation of entropies of Hg(II) compounds with Equation 4. 

Lu, B., and Wong, C. F. (2005) Direct estimation of entropy loss due to reduced translational and rotational motions upon molecular binding. Biopolymers 79, 277-285. 

Two different approaches need to be considered. In the first one the thermodynamic parameters are calculated on the basis of spectroscopic and specific heat data of monomer and its polymer. The estimation of entropy from specific heat values is based on the assumption that at 0 °K the entropy of the perfect crystal equals zero. Since polymers are never perfectly crystalline this method is based on a rough approximation. 

The values are derived from ihermochemical data and estimates of entropy changes... 

The book is divided into four parts. Part One, which consists of six chapters, deals with basic principles and concepts of non-equilibrium thermodynamics along with discussion of experimental studies related to test and limitation of formalism. Chapter 2 deals with theoretical foundations involving theoretical estimation of entropy production for open system, identification of fluxes and forces and development of steady-state relations using Onsager reciprocity relation. Steady state in the linear range is characterized by minimum entropy production. Under these circumstances, fluctuations regress exactly as in thermodynamics equilibrium. 

Detailed treatment of ET between Ru and Co coordination complexes tethered by a tetrapro-line B has led to estimates of entropy as well as enthalpy of activation, a distinction shown to be crucial when it comes to extracting the magnitude from the Arrhenius prefactor. ... 

This leads to an estimated heat of formation value for ethanol of —56.20 kcal/mol, which is essentially identical with the value found in the NIST webbook [44]. The estimations of entropies and heat capacities... 

Estimates of entropy change of mixing can be made from APb, j. Information about APm, h is available from EOS theories discussed in Chapter 2. A cubic equation for TgS can be recognized from Equation (6.39). 

One major problem of free energy methods is the need for extensive sampling of the phase space, which can lead to a prohibitively large computational effort for the QM part. The unavailability of complete sampling also limits the estimation of entropy differences, whereas free energy differences can be determined routinely today since extensive sampling of only the relevant part where the two states differ... 

It shall be our purpose here to illustrate these facts in tables and graphs. For this purpose we shall rely heavily on a review paper by Westrum (1967) and Holley et al. (1968) particularly for references and data up to the middle sixties including the estimation of entropy values and a review of the high temperature data. Gschneidner et al. (1973) reviewed the literature for information making possible the tabulation of enthalpy and free energy values as a function of temperature. There will be no effort to document values taken from these three sources and only more recent values or those not reviewed by these authors shall be noted separately. 

Table 9.1 Estimation of Entropy and Enthalpy Departure Values for i-Butane...

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