Rotation, entropy associated with

In this reaction kinetics analysis the following assumptions were employed The surface entropies of oxygenated species were hnked together, assuming that these species exhibit similar mobility on the surface. Accordingly, the surface entropies of oxygenated species were described in terms of a factor that multiplied the local surface entropies of these species, where the local entropy,. S ioc, for a species is dehned as the vibrational and rotational entropy associated with the species in the gas phase. 

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. 

The fact that both heats of formation and equilibrium pressures of the hydrates of spherical molecules correctly follow from one model must mean that the L-J-D theory gives a good account of the entropy associated with the motions of these solutes in the cavities of a clathrate. That the heat of formation of ethane hydrate is predicted correctly, whereas the theoretical value of its vapor pressure is too low, is a further indication that the latter discrepancy must be ascribed to hindered rotation of the ethane molecules in their cavities. 

A negative change in entropy associated with the decreased freedom of motion of water molecules in the vicinity of a nonpolar group. As pointed out by Jencks one should not be too literal when interpreting this behavior, because the system is dynamic, and not frozen. The term flickering cluster implies some reduction in libration and rotation without complete loss. 

For immobile adsorption there may still be rotational freedom which may be estimated from the appropriate form of (5) but there will always be the combinatory term in the entropy associated with the number of ways of distributing the molecules over the surface. If the fraction of... 

Introduction.—Most theoretical v> ork on the relation between intermolecular forces and the thermodynamic properties of liquids and liquid mixtures has been limited to potential fields which are independent of the orientation of the particles. This condition, however, is only strictly satisfied by monoatomic substances. For a great many molecular substances directional intermolecular forces are likely to be important and will have a significant effect on the thermodynamic properties of liquids both because of the additional cohesive energy and because of the loss of entropy associated with hindrance to free rotation. Although many of the observed properties of liquids have been attributed to directional forces in a qualitative manner, there has been little in the way of general quantitative theory. 

The results of this analysis showed that the loss of entropy associated with each internal rotation AG on receptor binding is equivalent to a reduction in the free energy of binding by average of 3 kJ/mol. 

From an entropic viewpoint, imposition of even a fairly mild restriction on the vibrational amplitude reduces the entropy associated with that vibration essentially to zero, and little significant additional loss is possible on further restriction. Although a bond with a i/ of 1000 cm has a substantial vibrational amplitude owing to its zero point energy, it has only 0.1 eu of entropy because only a small number of quantum states are effectively occupied. Further restriction on the magnitude of this vibrational amplitude will further reduce this small residual entropy but will not significantly increase the much larger difference in entropy between these restricted states and that of a free rotation. 

Nonconformity with the third law also arises when a substance can exist in more than one state of such low energy that the distribution among these states is not influenced by the falling temperature down to the lowest attainable T. These states are frequently due to interactions of electronic or nuclear magnetic dipoles. An extrapolation to zero using the Debye law would reduce the system to a state of zero vibrational entropy, but the rotational entropy due to nuclear spin or the entropy associated with random orientation of magnetic dipoles in... 

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... 

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. ... 

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