Entropy contribution

Some representative plots of entropies of adsorption are shown in Fig. XVII-23, in general, T AS2 is comparable to Ah2, so that the entropy contribution to the free energy of adsorption is important. Notice in Figs. XVII-23 i and b how nearly the entropy plot is a mirror image of the enthalpy plot. As a consequence, the maxima and minima in the separate plots tend to cancel to give a smoothly varying free energy plot, that is, adsorption isotherm. 

B2.4.2). The slope of the line gives AH, and the intercept at 1/J= 0 is related to A imimolecular reaction, such as many cases of exchange, might be expected to have a very small entropy change on gomg to the transition state. However, several systems have shown significant entropy contributions—entropy can make up more than 10% of the barrier. It is therefore important to measure the rates over as wide a range of temperatures as possible to obtain reliable thennodynamic data on the transition state. 

Subtracting the entropy contributions of the pure components from gives the entropy of mixing according to the present model ... 

The total heat released is the sum of the entropy contribution plus the irreversible contribution. This heat is released inside the battery at the reaction site. Heat release is not a problem for low rate appHcations however, high rate batteries must make provisions for heat dissipation. Failure to accommodate heat can lead to thermal mnaway and other catastrophic situations. 

The high enthalpy contribution results from its larger mass and size providing stronger interactions with the stationary phase molecules, and its increased entropy contribution arises from it being a terminal atom, thus prior to interaction with the stationary phase, it has greater freedom. 

I.D. The data has been curve fitted to a linear function and thus the enthalpy and entropy contributions are extracted as the slope and intercept of each curve. 

Although AGrxn depends on both enthalpy and entropy, there are many reactions for which the entropy contribution is small, and can be neglected. Thus, if AHjxn = AErxn, wc cuu estimate equilibrium constants for such reactions by the following equation ... 

Reaction rate constants, k,x , are also related to free energies. As before, if entropy contributions can be neglected, the rate constant can be obtained directly from the activation energy, AE, by ... 

The assumption that the energy can be written as a sum of terms implies that the partition function can be written as a product of terms. As the enthalpy and entropy contributions involve taking the logarithm of q, the product thus transforms into sums of enthalpy and entropy contributions. 

We note that is positive and goes through a maximum as a increases. If the positive holes were localised on the cations, they would give an entropy contribution exactly equal to. The positive holes have, however, considerable mobility (see below), and are perhaps best treated as an ideal gas consisting of particles of effective mass m. In this case ... 

Table III presents integral excess entropies of formation for some solid and liquid solutions obtained by means of equilibrium techniques. Except for the alloys marked by a letter b, the excess entropy can be taken as a measure of the effect of the change of the vibrational spectrum in the formation of the solution. The entropy change associated with the electrons, although a real effect as shown by Rayne s54 measurements of the electronic specific heat of a-brasses, is too small to be of importance in these numbers. Attention is directed to the very appreciable magnitude of the vibrational entropy contribution in many of these alloys, and to the fact that whether the alloy is solid or liquid is not of primary importance. It is difficult to relate even the sign of the excess entropy to the properties of the individual constituents.

If the energy of formation of a vacancy is U (which should include all entropy contributions other than the configurational entropy), the change in the free energy F at constant temperature is given by... 

Extrapolations are always subject to error, but fortunately the contribution to the entropy resulting from the extrapolation is a small part of the total. In glucose, for example, S g = 219.2 0.4 J-K -moF1, but the entropy contribution at 10 K obtained from the Debye extrapolation is only 0.28 J-K 1-mol 1. Well-designed cryogenic calorimeters are able to produce Cp measurements of high accuracy hence, the Third Law entropy obtained from the Cp measurements can also be of high accuracy. 

In contrast to the situation observed in the trivalent lanthanide and actinide sulfates, the enthalpies and entropies of complexation for the 1 1 complexes are not constant across this series of tetravalent actinide sulfates. In order to compare these results, the thermodynamic parameters for the reaction between the tetravalent actinide ions and HSOIJ were corrected for the ionization of HSOi as was done above in the discussion of the trivalent complexes. The corrected results are tabulated in Table V. The enthalpies are found to vary from +9.8 to+41.7 kj/m and the entropies from +101 to +213 J/m°K. Both the enthalpy and entropy increase from ll1 "1" to Pu1 with the ThSOfj parameters being similar to those of NpS0 +. Complex stability is derived from a very favorable entropy contribution implying (not surprisingly) that these complexes are inner sphere in nature. 

Cyclic monomers with five- and six-membered ring atoms exist in strainless puckered conformations their heats of polymerization are either negative or have small positive values due to the repulsion of eclipsed hydrogen atoms. Because the nthalpy and entropy contributions are comparable, the free energies of polymerization are either positive or may become positive at high temperatures. 

We again assume that the pre-exponential factor and the entropy contributions do not depend on temperature. This assumption is not strictly correct but, as we shall see in Chapter 3, the latter dependence is much weaker than that of the energy in the exponential terms. The normalized activation energy is also shown in Fig. 2.11 as a function of mole fraction. Notice that the activation energy is not just that of the rate-limiting step. It also depends on the adsorption enthalpies of the steps prior to the rate-limiting step and the coverages. 

If xi contains an entropy contribution, the form of the chemical potential is unaltered but its resolution into entropy and heat contributions must be carried out according to operations like those applied above to the free energy of mixing. 

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