Rotation, internal heat capacity

At present the derivation of this equation from the fully quantum-mechanical theory relies upon a heuristic extension of the semiclassical treatment for rigid rotors in which the rotational heat capacity and rotational collision number are replaced by the total internal heat capacity and the internal collision number respectively. This (approximate) extension seems to be justified by a result of van den Oord Korving (1988). 

Here, and are the contributions of translational and rotational degrees of freedom to the thermal conductivity of the dilute gas evaluated from the six-site model, im.exp experimental internal heat capacity at constant volume, whereas is the equipartition value obtained by assuming the benzene molecule is rigid, that is, — 3/2)R, where R is the universal gas constant. It turns out that... 

Internal rotation and heat capacity of a few polymers at low tempera-... 

Empirically, liquid heat capacities are often observed to change linearly with temperature. They have a smaller increase with temperature than solids, and are additive with regard to their constituent groups. In case of atomic backbone repeating units, such as Se (74), O (75), or S (76), the group contribution of the heat capacity decreases with temperature. This occurs most likely because of increasing changes of vibrational modes of motion to internal rotations whose heat capacity contributions decrease with temperature from R to R/2. Table 3 shows... 

A considerable variety of experimental methods has been applied to the problem of determining numerical values for barriers hindering internal rotation. One of the oldest and most successful has been the comparison of calculated and observed thermodynamic quantities such as heat capacity and entropy.27 Statistical mechanics provides the theoretical framework for the calculation of thermodynamic quantities of gaseous molecules when the mass, principal moments of inertia, and vibration frequencies are known, at least for molecules showing no internal rotation. The theory has been extended to many cases in which hindered internal rotation is... 

Figure 10.10 Internal rotation contribution to the heat capacity of CH3-CCI3 as a function of temperature. Reprinted from K. S. Pitzer. Thermodynamics, McGraw-Hill, Inc., New York, 1995, p. 374. Reproduced with permission of the McGraw-Hill Companies.

Table A4.6 gives the internal rotation contributions to the heat capacity, enthalpy and Gibbs free energy as a function of the rotational barrier V. It is convenient to tabulate the contributions in terms of VjRTagainst 1/rf, where f is the partition function for free rotation [see equation (10.141)]. For details of the calculation, see Section 10.7c.

The molar heat capacities of gases composed of molecules (as distinct from atoms) are Higher than those of monatomic gases because the molecules can store energy as rotational kinetic energy as well as translational kinetic energy. We saw in Section 6.7 that the rotational motion of linear molecules contributes another RT to the molar internal energy ... 

Pitzer, K.S., Guttman, L., Westrum, Jr., E.F. (1946) The heat capacity, heats of fusion and vaporization, vapor pressure, entropy, vibration frequencies and barrier to internal rotation of styrene. J. Am. Chem. Soc. 68, 2209-2212. 

W. Weltner, Jr., andK. S. Pitzer, Methyl alcohol The entropy, heat capacity and polymerization equilibria in the vapor, and potential barrier to internal rotation. J. Am. Chem. Soc. 73, 2606 2610 (1951). 

RADICALC Bozzelli, J. W. and Ritter, E. R. Chemical and Physical Processes in Combustion, p. 453. The Combustion Institute, Pittsburgh, PA, 1993. A computer code to calculate entropy and heat capacity contributions to transition states and radical species from changes in vibrational frequencies, barriers, moments of inertia, and internal rotations. 

The ionization potentials of some of the bipyridines have been investigated. Solubility data for 2,2 -bipyridine in aqueous solution, in aqueous solvent mixtures, and in various aqueous salt solutions have been obtained, whereas the heat of solution, heat capacities, and related data for 2,2 - and 4,4 -bipyridines in water have been measured. The enthalpies of solution of 2,2 -bipyridine in water and aqueous solvent mixtures have also been obtained. Dielectric relaxation studies of 2,2 -bipyri-dine in carbon tetrachloride have been reported in connection with hindered internal rotation. Partition coefficients for 2,2 -bipyridine between water and various organic solvents have been measured. ... 

The rotational contribution to the heat capacity Ck>mt is calculated from Eq. 8.127 or 8.128. The internal contribution to the heat capacity C, int contains all the contributions except from translation. The total heat capacity Cp is usually available as a polynomial fit to temperature. Therefore, in using Eq. 8.124, it is convenient to calculate C jnt as... 

The thermodynamic properties of a substance in the state of ideal gas are calculated as the sums of contributions from translation and rotation of a molecule as a whole, vibrations and internal rotation in the molecule, and electronic excitation. For example, for entropy and heat capacity the following equations hold ... 

Aston, J.G., Wills, P.E., Zolki, T.P (1955) The heat capacities from 10.9 K., heats of transition, fusion and vaporization, vapor pressures and entropy of pentafluorochloroethane, the barrier hindering internal rotation. J. Am. Chem. Soc. 77, 3939-3341. 

A computer code to calculate entropy and heat capacity contributions to transition states and radical species from changes in vibrational frequencies, barriers, moments of inertia, and internal rotations. 

Other estimated values that have been reported include 200 cm ( ) and 37 cm (5 ). The inactive torsional frequency is treated as a hindered Internal rotation. We use an estimated potential barrier of 8.0 kcal mol ( ) to calculate heat capacity contributions for hindered rotation from the table of Pitzer and Brewer (9). Contributions below 201 K could not be obtained by... 

The partial molar heat capacity can be considered to be composed of intrinsic and hydration contributions. The intrinsic component contains contributions from covalent and non-covalent interactions. It has been shown that about 85% of the total heat capacity of the native state of a protein in solution is due to the covalent structure [72]. Changes in the heat capacity upon unfolding are therefore primarily interpreted as due to changes in the hydration. A physical picture of energy fluctuations means changing the conformation between ordered and less ordered structures. This can be achieved by hindered internal rotations, low frequency... 

The contribution to the internal energy (measured relative to the zero-point energy) and to the heat capacity of the vibrational motion is also negligible (Table 9.4) whereas that from translational and rotational motion is classical. Thus... 

Frankosky M, Astron JG (1965) The heat capacity and entropy of hexamethylbenzene from 13 to 340 K. An estimate of the internal rotation barrier. J. Phys. Chem. 69 3126... 

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