Calculation of the Isobaric Heat Capacities of the Liquid and Solid Phase of Organic Compounds at and around 298.15 K Based on Their “True” Molecular Volume

Abstract

A universally applicable method for the prediction of the isobaric heat capacities of the liquid and solid phase of molecules at 298.15 K is presented, derived from their “true” volume. The molecules’ “true” volume in A3 is calculated on the basis of their geometry-optimized structure and the Van-der-Waals radii of their constituting atoms by means of a fast numerical algorithm. Good linear correlations of the “true” volume of a large number of compounds encompassing all classes and sizes with their experimental liquid and solid heat capacities over a large range have been found, although noticeably distorted by intermolecular hydrogen-bond effects. To account for these effects, the total amount of 1303 compounds with known experimental liquid heat capacities has been subdivided into three subsets consisting of 1102 hydroxy-group-free compounds, 164 monoalcohols/monoacids, and 36 polyalcohols/polyacids. The standard deviations for Cp(liq,298) were 20.7 J/mol/K for the OH-free compunds, 22.91 J/mol/K for the monoalcohols/monoacids and 16.03 J/mol/K for the polyols/polyacids. Analogously, 797 compounds with known solid heat capacities have been separated into a subset of 555 OH-free compounds, 123 monoalcohols/monoacids and 119 polyols/polyacids. The standard deviations for Cp(sol,298) were calculated to 23.14 J/mol/K for the first, 21.62 J/mol/K for the second, and 19.75 J/mol/K for the last subset. A discussion of structural and intermolecular effects influencing the heat capacities as well as of some special classes, in particular hydrocarbons, ionic liquids, siloxanes and metallocenes, has been given. In addition, the present method has successfully been extended to enable the prediction of the temperature dependence of the solid and liquid heat capacities in the range between 250 and 350 K.

Calculation of the Isobaric Heat Capacities of the Liquid and Solid Phase of Organic Compounds at 298.15K by Means of the Group-Additivity Method

“…It turned out that the definition of the OH group on saturated carbon as in ordinary alcohols by the simple atom type "O" and its neighbours "HC" was inadequate for heat-capacity calculations, in contrast to the calculations of all the other descriptors mentioned in our earlier papers [6][7][8][9]. As a consequence, an additional procedure had to be integrated in the general GA algorithm outlined in [1], which redefined the atom type "O" into "O(prim)", "O(sec)", or "O(tert)", depending on the number of carbon atoms attached to the C atom neighbouring the O atom, according to the definition of primary, secondary, and tertiary alcohols, as shown in Table 2. (Consequently, the definition of their neighbourhood "HC" was no longer relevant and was thus not examined.)…”

“…(Consequently, the definition of their neighbourhood "HC" was no longer relevant and was thus not examined.) This redefinition procedure is only invoked if the redefined atom types appear in the group-parameters table, as a consequence of the algorithmic procedure determining that it is the content of the group-parameter tables that defines which group parameters are to be evaluated for the corresponding descriptors calculations (as explained in subsection 2.2 of [1]), and since none of the other descriptors in [6][7][8][9] requires this redefinition, this procedure is only called up for the evaluation of the group parameters of present Table 3 and Table 7 and the subsequent heat-capacity predictions. The remaining hydroxy groups attached to unsaturated carbon found in carboxylic acids and phenols are notated separately by the atom type "O" and the neighbourhood "HC(pi)", as defined in [6].…”

“…Most experimental measurements of thermodynamic properties, such as vaporization, sublimation, solvation, or fusion enthalpies, are usually carried out at temperatures that differ from the standard temperature, which has generally been accepted as being 298.15 K. These temperature differences lead to experimental values for the temperature-dependent properties that prevent a direct comparison of the results between various compounds or between scientific teams examining the same molecule, a deficiency which, however, can be corrected, provided that the heat capacity of the molecules under examination is known. Instead of measuring this property for a specific molecule, the large amount of experimental heat-capacity data for all kinds of compounds, such as inorganic and organic salts, liquid crystals, or ionic liquids, enabled its prediction by means of a large number of mathematical methods, a comprehensive overview of which has been given in a recent publication by the present author [1]. The majority of these prediction methods are based on the group-additivity (GA) approach, whereby the group notations vary from complete polyatomic ions as, e.g., applied by Gardas and Coutinho [2] to single atoms and their immediate neighbour atoms and ligands, as described by Benson and Buss [3].…”

“…A common deficiency of the GA and all the other approaches cited in [1] is that none of them enables the prediction of any specific descriptor for each and any molecular structure in the chemical realm. In the case of the heat capacities of the solid and liquid phase of molecules, however, this deficiency has been overcome in that their prediction values are determined via the "true" molecular volume (V m ) outlined in detail in [1]. Nevertheless, this approach has encountered several other shortcomings which could not all be addressed specifically, as it is based on one single number, the molecular volume.…”

“…The three most important deficiencies are 1) the general influence of the hydroxy group of alcohols and carboxylic acids, 2) the specific effects of primary, secondary, and tertiary alcohols and 3) the impact of saturated cyclic rings vs. open-chained systems on the heat capacities. Accordingly, a first attempt of a linear correlation calculation in [1], which included the molecular volume and the experimental liquid heat capacity C p (liq) of the complete set of compounds, for which both data were available, and which neglected the mentioned shortcomings, yielded a rather large standard deviation of 27.84 J/mol/K and a mean absolute percentage deviation (MAPD) of 8.23%. The neglect of the hydroxy-group effect on C p (liq) was immediately manifest in that the predicted values for all those compounds carrying at least one OH group were systematically well below the experimental ones by up to ca.…”