Zero-Point and Heat Content Energies

The same formula applies to linear molecules, except for — Hq, which is now 

Zero-point energies are obtained from vibrational spectra using experimental frequencies whenever available, while the inactive frequencies are extracted from data calculated by means of an appropriate force-held model. In the harmonic oscillator approximation, the zero-point energy is 

A detailed study [180] of acyclic alkanes has revealed that the following formula, in kcal/mol, is accurate 

Cycloalkanes constmcted from six-membered rings behave in essence like acyclic alkanes, provided that the suppression of internal rotations is adequately taken into account [180] by subtracting / T/2 = 0.296 kcal/mol (at 298.15 K) for each CC bond in the cycle. Most detailed calculations have dealt with six-membered cycloalkanes [36,181]. 

The important result is that the comparison of isomerides differing in the number of gauche interactions (e.g., 6 vs. 7, 8 vs. 9, or 10 vs. 11) reveals no dependence on the number of gauche interactions. 

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This chapter offers pertinent information facilitating the comparison between theory and experiment using thermochemical data, such as the standard enthalpies of formation, and spectroscopic information that serve our purpose. Special attention is given to zero-point and heat-content energies which are often not as readily available as desired. 

TABLE 9.1. Theoretical Zero-Point and Heat Content Energies of Cycloalkanes, at 298.15 K (kcal/mol)... 

This book is about atomic charges, chemical bonds, and bond energy additivity. However, nuclear magnetic resonance, inductive effects, zero-point and heat content energies, and other topics are an integral part of this study, to achieve... 

Here they are examined primarily because they greatly facilitate the comparison between thermochemical results and calculations made for molecules in their hypothetical vibrationless state at 0 K. While, of course, preference is given to verifications involving only genuine experimental data, well-established structure-dependent regularities of zero-point plus heat content energies considerably augments the number of molecules that can be tested. 

The results are reported in Table 13.1. The zero-point plus heat content energies, abbreviated as ZPE + A//, are those described in Chapter 9, Eq. (9.9). The shifts are from Refs. 166, 169, and 243. 

The energy of atomization at T = 298.15 K, namely AEa = AH° — RT (where A//° is the corresponding enthalpy), thus follows from AE by subtracting the zero-point and the gas-phase heat content Hj — Hq) and by adding the translational energy (jRT) of the carbon atoms formed during the atomization of graphite AH° = AE - ZPE... 

The specific enthalpy, denoted h, corresponds to the energy content of an air-water mixture. It is expressed in J/kg of dry air. Measurement of enthalpy is relative, i.e., the actual heat content is dependent on the datum or zero point chosen. The usual datum for dry air is 0 F (-17.78 C) and for water 32°F (0°C). 

The molar heat content, MH, of a molecule consists of the zero-point energy, the Boltzmann averaged thermal energies (see Figure 1), and sl PV term ... 

The enthalpy, or heat content, is expressed as Btu per pound of steam. This is, in effect, the potential energy contained in the steam measured above the conventionally accepted zero point (that of condensed steam at 32 F). Practically, it is not possible to release all the energy so that the end point of heat extraction in a condensing turbine is given by the temperature attainable in the condenser. The considerable amoimt of energy still contained in the steam at this point cannot be recovered and must be rejected to the cooling water. 

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