Rotational entropies

Translational entropy Rotational entropy Vibrational entropy Electronic entropy Total... 

The 20/1 y/5 ratio, when both carbons are unactivated methylenes, is also displayed by alkoxy radicals 75>. The slower 1,6-hydrogen transfer presumably reflects some of the strain in a 7-membered ring. It must also involve a more negative entropy. Rotations about three C—C bonds are frozen in the transition state, whereas only two C—C rotations need be frozen for y-hydrogen abstraction. 

For diatomic molecules the configurational entropy remains the same but the vibrational term has to be modified and now a rotational term, also proportional to N, has to be included. For physlsorptlon the intramolecular vibration is usually not significantly perturbed. Hence, this contribution to S Ivibr) may be disregarded. To identify the entropy with the excess entropy, rotation-free molecules must be taken as the reference. 

It is given from table 1, that an activation free energies, activation enthalpies, activation entropies and pre-exponential factors are satisfactory compared with experimental ones. Complex activation entropy is increasing, but that factor is not contradicted with well-known ideas. Changing is occurred with increasing of vibration part of active complex entropy. Rotation part of active complex entropy is changed lightly (table 2). 

Translational Enthalpy Rotational Enthalpy Vibrational Enthalpy gas constant (RT) Translational Entropy Rotational Entropy Vibrational Entropy ... 

Statistical Thermodynamics of Adsorbates. First, from a thermodynamic or statistical mechanical point of view, the internal energy and entropy of a molecule should be different in the adsorbed state from that in the gaseous state. This is quite apart from the energy of the adsorption bond itself or the entropy associated with confining a molecule to the interfacial region. It is clear, for example, that the adsorbed molecule may lose part or all of its freedom to rotate. 

It is of interest in the present context (and is useful later) to outline the statistical mechanical basis for calculating the energy and entropy that are associated with rotation [66]. According to the Boltzmann principle, the time average energy of a molecule is given by... 

Equation XVI-21 provides for the general case of a molecule having n independent ways of rotation and a moment of inertia 7 that, for an asymmetric molecule, is the (geometric) mean of the principal moments. The quantity a is the symmetry number, or the number of indistinguishable positions into which the molecule can be turned by rotations. The rotational energy and entropy are [66,67]... 

Molecular moments of inertia are about 10 g/cm thus 7 values for benzene, N2, and NH3 are 18, 1.4, and 0.28, respectively, in those units. For the case of benzene gas, a = 6 and n = 3, and 5rot is about 21 cal K mol at 25°C. On adsorption, all of this entropy would be lost if the benzene were unable to rotate, and part of it if, say, rotation about only one axis were possible (as might be the situation if the benzene was subject only to the constraint of lying flat... 

Calculate the rotational contribution to the entropy of adsorption of benzene on carbon at 35°C, assuming that the adsorbed benzene has one degree of rotational freedom. 

Calculate the rotational contribution to the entropy of adsorption of ammonia on silica at -30°C, assuming (n) that the adsorbed ammonia retains one degree of rotational freedom and (b) that it retains none. In case (n) assume that the nitrogen is bonded to the surface. 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

Fig. 3-11 shows that, foi watei, entropy and heat capacity ai e summations in which two terms dominate, the translational energy of motion of molecules treated as ideal gas paiticles. and rotational, energy of spin about axes having nonzero rnorncuts of inertia terms (see Prublerris). 

Molecular enthalpies and entropies can be broken down into the contributions from translational, vibrational, and rotational motions as well as the electronic energies. These values are often printed out along with the results of vibrational frequency calculations. Once the vibrational frequencies are known, a relatively trivial amount of computer time is needed to compute these. The values that are printed out are usually based on ideal gas assumptions. 

Vibrational frequencies Rotational enthalpy and entropy Vibrational enthalpy and entropy Translational enthalpy and entropy... 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

Unimolecular reactions that take place by way of cyclic transition states typically have negative entropies of activation because of the loss of rotational degrees of freedom associated with the highly ordered transition state. For example, thermal isomerization of allyl vinyl ether to 4-pentenal has AS = —8eu. ... 

FIGURE 16.4 Formation of the ES complex results in a loss of entropy. Prior to binding, E and S are free to undergo translational and rotational motion. By comparison, the ES complex is a more highly ordered, low-entropy complex. 

The above treatment has made some assumptions, such as harmonic frequencies and sufficiently small energy spacing between the rotational levels. If a more elaborate treatment is required, the summation for the partition functions must be carried out explicitly. Many molecules also have internal rotations with quite small barriers, hi the above they are assumed to be described by simple harmonic vibrations, which may be a poor approximation. Calculating the energy levels for a hindered rotor is somewhat complicated, and is rarely done. If the barrier is very low, the motion may be treated as a free rotor, in which case it contributes a constant factor of RT to the enthalpy and R/2 to the entropy. 

Regarding Case 1, it is known that the rotator phases of -paraffins are three dimensionally ordered solids with molecules in aW-trans conformation, their specific volumes, Vh, and specific entropies, Sh, are closer to corresponding values and for the orthorhombic phases than they are to those for the melt and Sm In contrast,... 

Conversely, the high-pressure hexagonal phase is one of high entropy for which the reverse inequality is true. In lower -paraffins, the occurrence of the rotator phase at atmospheric pressure is due to the fact that the orthorhombic-hexagonal (or rotator) transition temperature, is lower than the temperature of fusion of... 

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