High entropy state

As a result of the above discussion what can be said about the meaning of entropy if our basic assumptions are correct It is evidently a measure of the mixed-up-ness of a system— a phrase used by Gibbs. It can also be said that high entropy states are those which have a high probability. The quantity Q is sometimes referred to as the thermodynamic probability , because the ratio for the... 

Systems tend to proceed from ordered low entropy or low probability) states to disordered high entropy or high probability) states. 

If a system, when left to itself, tends towards a state of greatest possible disorder, i.e., maximum entropy, then negative entropy (named negentropy by Brioullin) refers to a highly-ordered state of the system. With respect to the cosmos, this means that there are two opposing tendencies present in the universe ... 

Large entropy increments accompany the spin transitions. For Co3+ in an octahedral crystal field the high-spin state has a degeneracy of 15 (the product of orbital... 

Hilvert s group used the same hapten [26] with a different spacer to generate an antibody catalyst which has very different thermodynamic parameters. It has a high entropy of activation but an enthalpy lower than that of the wild-type enzyme (Table 1, Antibody 1F7, Appendix entry 13.2a) (Hilvert et al., 1988 Hilvert and Nared, 1988). Wilson has determined an X-ray crystal structure for the Fab fragment of this antibody in a binary complex with its TSA (Haynes et al., 1994) which shows that amino acid residues in the active site of the antibody catalyst faithfully complement the components of the conformationally ordered transition state analogue (Fig. 11) while a trapped water molecule is probably responsible for the adverse entropy of activation. Thus it appears that antibodies have emulated enzymes in finding contrasting solutions to the same catalytic problem. 

Substances in the solid state tend to have low entropy values. This is not surprising because the particles in a solid occupy approximately fixed positions. They can vibrate, but they cannot move from one place to another. Solids are therefore highly ordered. Gases, however, have very high entropy values. Gases contain particles that have... 

The point that solids have low entropies and gases have high entropies has already been made. An examination of the values in the table should convince you that this is indeed a valid generalization. Compare the pairs of values for the two states of H2O and also the two states of lithium. 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

The resistivities of the mixed crystals are shown in Fig. 6.22. It can be seen that (as indeed follows from the phase diagram, Fig. 6.20) the transition to the insulating state occurs with larger x for increasing temperature, probably because of the high entropy of the AF insulator above its Neel temperature. 

For those systems with AG° ss 0, it follows that AH0 % TAS°. Conversion from the low-spin to the high-spin state involves lengthening and weakening the metal-ligand bonds. This results in a high-spin state with higher enthalpy and also greater entropy. Such a reaction profile is shown in Fig. 5 for the Fe(HB(pz)3)2 complex. 

It is not possible to evaluate k directly, for it appears with the entropy of activation in the temperature-independent part of the rate constant. An estimate of k requires an extrathermodynamic assumption. In two cases of iron(II) spin equilibria examined by ultrasonic relaxation the temperature dependence of the rates was precisely determined. If the assumption is made that all of the entropy of activation is due to a small value of k, minimum values of 10-3 and 10-4 are obtained. Because there is an increase in entropy in the transition from the low-spin to the high-spin states, this assumption is equivalent to assuming that the transition state resembles the high-spin state. There is now evidence that this is not the case. Volumes of activation indicate that the transition state lies about midway between the two spin states. This is a more chemically reasonable and likely situation than the limiting assumption used to evaluate k. In this case the observed entropy of activation includes some chemical contributions which arise from increased solvation and decreased vibrational partition functions as the high-spin state is compressed to the transition state. Consequently, the minimum value of k is increased and is unlikely to be less than about 10 2. 

A disordered state of a system (state of high entropy) can be achieved in more ways (W) than an ordered state and is therefore more probable. The entropy of a state can be calculated from Boltzmann s formula, S = k In W. According to the third law of thermodynamics, the entropy of a pure, perfectly ordered crystalline substance at 0 K is zero. 

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