Structure entropy contribution

For the cyclopentyl cation (20) formation, the reaction is slightly endothermic, while for methylcyclohexyl cation (21), the reaction profile itself is slightly exothermic. However, relative to the most stable 2-heptyl cation, (the 1,5-bridged structure 16) this reaction is also slightly endothermic. Based on calculated AG values at 298K, both reaction profiles are exergonic due to a larger entropy contribution for the product side in each case. 

Since practically the same protoljrtic reaction takes place for all aromatic substances, it may be assumed that the reaction entropy is largely independent of the structure of the aromatic substance itself. If, however, several points of identical proton affinity are present, then AO will contain an entropy contribution which depends on z. This contribution is given by RT. Inz, so that one obtains the relation... 

The total heat released during cell discharge is the sum of the thermodynamic entropy contribution plus the irreversible contribution. This heat is released inside the battery at the reaction site on the surface of the electrode structures. Heat release is not a... 

Considerable information is available on the magnetic parameters associated with three different crystal structures of Fe which are b.c.c. and f.c.c. at ambient pressures and c.p.h. which is observed at high pressures. Table 6.5 gives the corresponding values of the maximum enthalpy and entropy contributions due to... 

Molecular structure enters into the rotational entropy component, and vibrational frequencies into the vibrational entropy component. The translational entropy component cancels in a (mass) balanced reaction, and the electronic component is most commonly zero. Note that the vibrational contribution to the entropy goes to oo as v goes to 0. This is a consequence of the linear harmonic oscillator approximation used to derive equation 7, and is inappropriate. Vibrational entropy contributions from frequencies below 300 cm should be treated with caution. 

There is another entropy contribution which should always be included in a kinetic model, and that is the configurational entropy of an adlayer. This entropy derives from the various ways that adsorbates may be distributed over the sites. At high temperatures the adlayer will be disordered because this gives a high configurational entropy. At low temperatures the energy determines the structure, which is then most often ordered with a low entropy. 

The resulting equilibrium concentrations of these point defects (vacancies and interstitials) are the consequence of a compromise between the ordering interaction energy and the entropy contribution of disorder (point defects, in this case). To be sure, the importance of Frenkel s basic work for the further development of solid state kinetics can hardly be overstated. From here on one knew that, in a crystal, the concentration of irregular structure elements (in thermal equilibrium) is a function of state. Therefore the conductivity of an ionic crystal, for example, which is caused by mobile, point defects, is a well defined physical property. However, contributions to the conductivity due to dislocations, grain boundaries, and other non-equilibrium defects can sometimes be quite significant. 

The exergonicity (AG°) is entirely enthalpy-driven, whilst a respectable negative entropy contribution testifies to the formation of a well ordered complex structure. The energetic signature is quite different from ordinary hydrophobic bonding in water which is commonly characterized by positive association entropies thereby reflecting the poor structural definition of the associate. 

Subscript designates ligancy of atom, i.e., number of atoms bonded to central atom. The entropy contribution must be corrected by the addition of any electronic entropy, R In qny where qn is the electronic partition function. The quantity R n a must also be subtracted from the total entropy to correct for symmetry. symmetry number of the final species. Values taken from S. W. Benson and J. H. Buss, J. Chem, Phys., 29 (1958). These quantities are not to be used for cyclic structures such as benzene compounds. Estimates of Cp and are good to about 2 cal/mole- K for most species but may be poorer for heavily substituted species such as neopentane. They may also be poorer for very simple H-containing species such as NH3 and CH4. 

Pitzer and Brewer ( ) suggest this approach for estimation if Nj[ Aj is similar, in terms of structure and properties, to M Aj. This approach should minimize error arising in neglect of non-mass-related entropy contributions. 

This ordering of the water structure makes a negative contribution to the entropy of solution and in certain cases leads to a negative value of AS° in. In fact, this unfavorable entropy contribution resulting from cage formation could be an important reason why nonpolar solutes are insoluble in water. 

Lyotropic sequences have also been Interpreted in terms of the "making" and breaking" of water structure and correlations have been sought with enthalpies of immersion of the solids in water. The first of these is merely paraphrasing the quest for a structure analysis in enthalpy-entropy contributions, the latter considers only the enthalplc part, ignoring the entropic side of the story. 

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