Entropies individual

In this discussion, entropy factors have been ignored and in certain cases where the difference between lattice energy and hydration energy is small it is the entropy changes which determine whether a substance will or will not dissolve. Each case must be considered individually and the relevant data obtained (see Chapter 3), when irregular behaviour will often be found to have a logical explanation. 

As is suggested frequently , this term might well result from the restriction of the hydrogen bonding possibilities experienced by the water molecules in the first hydration shell. For each individual water molecule this is probably a relatively small effect, but due to the small size of the water molecules, a large number of them are entangled in the first hydration shell, so that the overall effect is appreciable. This theory is in perfect agreement with the observation that the entropy of hydration of a nonpolar molecule depends linearly on the number of water molecules in the first hydration shell ". ... 

In the volume elements describing individual subchains, the x, y, and z dimensions will be different, so Eq. (3.32) must be averaged over all possible values to obtain the average entropy change per subchain. This process is also easily accomplished by using a result from Chap. 1. Equation (1.62) gives the mean-square end-to-end distance of a subchain as n, 1q, and this quantity can also be written as x + y + z therefore... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Thus, an analysis of the lost work, made by calculation of the fraction that each individual lost-work term represents of the total lost work, is the same as an analysis of the rate of entropy generation, made by expressing each individual entropy-generation term as a fraclion of the sum of all entropy-generation terms. 

Equation (1) can be viewed in an over-simplistic manner and it might be assumed that it would be relatively easy to calculate the retention volume of a solute from the distribution coefficient, which, in turn, could be calculated from a knowledge of the standard enthalpy and standard entropy of distribution. Unfortunately, these properties of a distribution system are bulk properties. They represent, in a single measurement, the net effect of a large number of different types of molecular interactions which, individually, are almost impossible to separately identify and assess quantitatively. 

The Gibbs free energy is given in terms of the enthalpy and entropy, G — H — TS. The enthalpy and entropy for a macroscopic ensemble of particles may be calculated from properties of the individual molecules by means of statistical mechanics. 

Measure Entropy In the same way as the information dimension, Dp generalizes the fractal dimension. Dp, of an attractor. 4, by taking into account the relative frequency with which the individual e-boxes of a partition are visited by points on the attractor, so too the finite set entropy generalizes to a finite measure entropy,... 

Entropies The individual spac e and time measures introduced above may also be generalized to space-time blocks of size B x T ... 

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.

Thus, the self information of a sequence of N symbols from a discrete memoryless source is the sum of N independent random variables, namely the self informations of the individual symbols. An immediate consequence of this is that the entropy of the sequence, ff(Ujr), is the average value of a sum of random variables so that... 

The conclusion that can be reached from the Nernst heat theorem is that the total entropy of the products and the reactants in a chemical reaction must be the same at 0 Kelvin. But nothing in the statement requires that the entropy of the individual substances in the chemical reaction be zero, although a value of zero for all reactants and products is an easy way to achieve the result of equation (4.17). 

Although this is true in some sort of averaged sense, in that the net forward rate is less than the net backward rate for / < lmi , the length of the individual stems may fluctuate about lmin because of surface entropy effects. Using Eq. (3.99) in Eq. (3.96) shows that ... 

The entropies of individual ions in solution are determined by setting the entropy <>1 II in water equal to 0 and then defining the entropies of all other ions relative to this value hence a negative entropy is one that is lower than the entropy of H in water. All absolute entropies are positive, and no sign need he given all entropies of ions are relative to that ot H+ and are listed here with a sign (either + or —). 

C14-0135. S ° of graphite is 3 times larger than S ° of diamond. Explain why this is so. (You may need to review the structures and properties of graphite and diamond in Section 11-.) Buckminsterfullerene is a solid that consists of individual molecules with formula Cgo. Is the molar entropy of buckminsterfullerene larger or smaller than that of graphite How about the entropy per gram Explain. 

The Gibbs-Helmholtz equation also links the temperature coefficient of Galvani potential for individual electrodes to energy effects or entropy changes of the electrode reactions occurring at these electrodes. However, since these parameters cannot be determined experimentally for an isolated electrode reaction (this is possible only for the full current-producing reaction), this equation cannot be used to calculate this temperature coefficient. 

Fig. 9.38 (a) Measured upper panel) and calculated lower panel) NIS spectra of the HS open circle, dashed line) and the LS filled triangle, solid line) isomer (1 meV = 8.06 cm ) of [Fe (phen)2(NCS)2]. (b) Calculated contributions A5vib(i) of individual modes i to the vibrational entropy difference bars, left axis) and sum I /ASyib (i) of the contributions of modes 1 to i filled circle, right axis). The 15 modes of an idealized octahedron (six Fe-N stretching modes and nine N-Fe-N bending modes) are marked by the letters s and b, respectively. (Taken from [44])... 

By equating the individual terms, the dependence on the time interval of the coefficients in the quadratic expansion of the second entropy may be obtained. Consider the expansions... 

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