Entropy associative

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 phenomenological definition for the change in entropy associated with the isothermal, reversible absorption of an element of heat dq is... 

Entropy of Formation The ideal gas standard entropy of formation (AS°298) of a chemical compound is the increment of entropy associated with the reaction of forming that compound in the ideal gas state from the constituent elements in their standard state definea as the existing phase at a temperature of 298.15 K and one atmosphere (101.325 kPa). Thus ... 

We can now answer the question under discussion. Since 29.1 e.u. is considerably smaller than the total difference (116.8 — 75.8) = 41.0 e.u., mentioned above, we conclude that the unitary term for the ion pair (Ag+ + I") is greater than for (Ag+ + Cl"). The contribution from the Ag+ ion and its co-sphere must be, within the experimental error, the same in the two cases. Finally then, we reach the conclusion that in water at 25°C the entropy associated with the iodide ion I" and its co-sphere is greater than that associated with the ion Cl" and its co-sphere in fact, the excess lies in the neighborhood of (41 — 29) = 12 e.u. 

In both processes the ions are supposed to be introduced into solutions where the interionic forces are negligible. When in (191) the COJ ion is formed, the solvent in the co-sphere of this ion loses a certain amount of entropy. Likewise, in (192) when the CO, ion is formed, the solvent in the co-sphere of the ion loses precisely the same amount of entropy. At the same time, the amount of entropy associated with the thermal energy of the COJ" ion in aqueous solution is, of course, the same in (192) as in (191). In the process (192) we shall be concerned with the unitary term for the two Li+ ions in contrast to (191) where two protons are added to two II20 molecules. 

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. 

Paramagnetic substances have a magnetic entropy associated with the random orientation of the spin of the unpaired electrons as shown in (a) below ... 

The activation parameters bring out several features. Note that the activation enthalpy and activation energy for kn, which represents a very rapid reaction, are quite small. Of course, a fast reaction can have a higher activation energy, if the value of AS is more positive, so as to compensate. The activation entropy associated with k is particularly large and negative, as is most often the case for a second-order reaction that occurs by a bimolecular step. In such cases, AS reflects the loss of entropy from the union of the two reaction partners into a single transition state. 

Papisov et al. (1974) performed calorimetric and potentiometric experiments to determine the thermodynamic parameters of the complex formation of PMAA and PAA with PEG. They investigated how temperature and the nature of the solvent affected the complex stability. They found that in aqueous media the enthalpy and entropy associated with the formation of the PMAA/PEG complex are positive while in an aqueous mixture of methanol both of the thermodynamic quantities become negative. The exact values are shown in Table II. The viscosities of aqueous solutions containing complexes of PMAA and PEG increase with decreasing temperature as a result of a breakdown of the complexes. 

Note that the pre-exponential factors indicate only small entropies of activation in the Eyring form of the rate equations. This is a significant observation which indicates that the decrease of entropy associated with the incorporation of a hydrogen molecule at or prior to the transition state must be compensated for by a dissociation or decrease of coordination number. 

In much the same fashion as the AH° was tabulated, the standard molar entropies (S°) of elements and compounds are tabulated. This is the entropy associated with 1 mol of a substance in its standard state. Unlike the enthalpies, the entropies of elements are not zero. For a reaction, it is possible to calculate the standard entropy change in the same fashion as the enthalpies of reaction ... 

The so-called site energy e also contains small contributions from the entropy associated with vibrations of the ions in their sites.)... 

As seen from Fig. 12, quantum chemical calculations indeed support the fact that the activation energy for the SiHj-H bond scission reaction corresponds to the bond dissociation energy or the heat of reaction, i.e., AH, % s 90 kcal/mol. In addition, at the transition state, the Si-H bond distance is calculated to be about 2.5 A, a clear indication of the loosness and the increase in entropy associated with the formation of the transition state. 

If excess specific heat, defined as that part of the specific heat that is due to the structural phase transition (cf Salje, 1988), is denoted by ACpexcess,trans> the excess entropy associated with transition within the upper and lower limits of Cp perturbation is given by... 

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. 

To a significant extent, the theoretical basis of modern communication theory arose from the work of Claude Shannon at Bell Labs. [80]. In these seminal works, the concept of the information entropy associated with an arbitrary signal arose. In 1981, Watanabe realised the close association between entropy minimization and pattern recognition [81]. An association between entropy minimization and the principle of simplicity is also recognized [82]. The basic mathematical form of signal... 

Data derived from pressure experiments on semi-conducting elements by Klement and Jayamaran (1966) and Minomura (1974) have also been useful in obtaining confirmation that the entropies associated with transitions in Si, Ge and Sn form a consistent pattern, supporting the concept that each crystallographic transformation tends to have a characteristic associated entropy change (Miodownik 1972a, 1972b). Similarly, extrapolations from pressure data on alloys can be used to obtain estimates of lattice stabilities at P = 0, which can then be compared with estimates obtained by other routes, such as SFE measurements. 

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... 

In some cases the adsorption is so weak that the entropy associated with the vibration replacing the translational motion perpendicular to the surface may not be negligible. The entropy associated with a vibration of frequency v is given by... 

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