Thermodynamic consequences

If A Gx values are sufficiently lower (greater by absolute value) than AG of the rest of the components of free energy change, the process can proceed at all the values of molecular weights from the point of view of thermodynamics. Consequently, the application AG in the definite conditions is unadvisable. 

But Langmuir s isotherm for the solute entails the generalized form of Raoult s law (Eq. 13) as a necessary thermodynamic consequence. This can best be seen from the Gibbs-Duhem equation,... 

The value of kl/k2 may then be obtained from the following relation, which is a thermodynamic consequence of the equilibrium 20 ... 

Thus far, we have focused upon the thermodynamic consequences of the fi-electron configuration. Many everyday observations in transition-metal chemistry have more to do with the relative rates of reactions rather than the position of a thermodynamic equilibrium. So now we consider some of the kinetic manifestations of partially filled d orbitals. 

Thermodynamic aspects of the interaction of metal ions with macrocyclic ligands have been well studied. In many instances such studies have involved a comparison of the behaviour of cyclic ligand systems with that of their open-chain analogues. In this manner, information concerning the thermodynamic consequences arising from the cyclic nature of the macrocyclic ligand has been obtained. Frequently these studies have been restricted to stability constant (log K) measurements and, for such studies, a variety of techniques has been employed (Izatt etal., 1985). 

For a given solid material, a progressive reduction of particle size corresponds to increases in the surface/volume ratio and the escaping tendency of the molecules until the nature of the surface dominates the properties of the material. Two related thermodynamic consequences of this effect are an increase of solubility in any solvent and an increase of vapor pressure as the size of the particle is reduced. For a spherical particle of radius r, thermodynamic arguments lead to the Thomson-Freundlich equation [19] ... 

For molecules and molecular ions, such as the cations of 8-methyl-N5-deazapterin and 8-methyl-pterin, the charge distribution (which is represented in MD simulations by a set of discrete atomic charges) will be dependent on the chosen quantum chemical model. Differences in the charge distributions of these cations may influence both the relative binding and solvation thermodynamics. Consequently, we studied the relative solvation thermodynamics of similar DHFR-binding molecular ions.30 Atomic charges... 

Fig. 6 presents the data for citric acid complexes and an extraction of ions, plotted as recommended by Fidelis etSiekerski (23),Peppard (24) and Sinha (25), who introduced different names for the deviations from a smooth log/ = f(Z) variation which occur for a quarter, a half and three-quarters of a filled f subshell. Fig. 6 effectively illustrates this accidents for the 4 f 3-4, 4 f7,4 fIdeviations from a smooth variation) is believed to be a thermodynamic consequence of the nephelauxetic effect. 

Thermodynamic Consequences of Multiple States Changes in Phase Equilibria Directly Attributable to Interaction with External Magnetic Fields... 

Statistical mechanics is, obviously, a course unto itself in the standard chemistry/physics curriculum, and no attempt will be made here to introduce concepts in a formal and rigorous fashion. Instead, some prior exposure to the field is assumed, or at least to its thermodynamical consequences, and the fundamental equations describing the relationships between key thermodynamic variables are presented without derivation. From a computational-chemistry standpoint, many simplifying assumptions make most of the details fairly easy to follow, so readers who have had minimal experience in this area should not be adversely affected. 

The thermodynamic state is therefore considered equivalent to specification of the complete set of independent intensive properties 7 1 R2, Rn. The fact that state can be specified without reference to extensive properties is a direct consequence of the macroscopic character of the thermodynamic system, for once this character is established, we can safely assume that system size does not matter except as a trivial overall scale factor. For example, it is of no thermodynamic consequence whether we choose a cup-full or a bucket-full as sample size for a thermodynamic investigation of the normal boiling-point state of water, because thermodynamic properties of the two systems are trivially related. 

In accordance with the thermodynamic consequences of the extreme activation energies associated with the formation of anhydrous silica... 

Stuerga, D.A.C. and Gaillard, R, Microwave athermal effects in chemistry a myth s autopsy 2. Orienting effects and thermodynamic consequences of electric field, J. Microw. Power Electromagn. Energy, 1996, 31, 101. 

Gelfand CA, Plum GE, Grollman AP, Johnson F, Breslauer KJ (1998) Thermodynamic consequences of an abasic lesion in duplex DNA are strongly dependent on base sequence. Biochemistry 37 7321-7327... 

This is a reversal of the argument of Chap. II, Sec. 6, where we used Joule s law as an experimental fact to prove that the gas scale of temperature was identical with the thermodynamic temperature. Here instead we assume the temperature T in Eq. (1.1) to be the thermodynamic temperature, and then Joule s law follows as a thermodynamic consequence of the equation of state. 

Figure 2 shows the strong dependence of temperature on the plateau pressure. The higher the temperature, the higher is the plateau pressure. This is an important thermodynamic consequence of the heat of reaction Ah associated with Eq. 1. The hydriding reaction (->) is exothermic and the dehydriding reaction ( -) is endothermic. The plateau pressure Pp is related to the absolute temperature T by the Van t Hoff equation... 

In treating the thermodynamic consequences of ion-pair formation (Section 3.8.4), it was shown that the association constant for the equilibrium between free ions and ion pairs is given by... 

It should be emphasized that the method is not limited to H bonding solutions. It is useful, for instance, in studying the thermodynamic consequences of mixing molecules of very different molecular size, as is done in polymer solutions. 

More recent polymer soluticm theories (41. 42) recognize the importance of the free volume dissimilarity of the solute and polymer. This effect, first introduced in theories of solution by Prigogine and collaborators (43), has important thermodynamic consequences. Flory and collaborators (42) now suggest that (In A Xioncotnb be composed of two terms, an equation of state and a contact interaction contribution, The newly defined parameter, denoted x, becomes... 

The major part of this article will be devoted to a particular class of reaction systems—namely, monomolecular systems. A reaction system of (n) molecular species is called monomolecular if the coupling between each pair of species is by first order reactions only. These linear systems are satisfactory representations for many rate processes over the entire range of reaction and are linear approximations for most systems in a sufficiently small range. They play a role in the chemical kinetics of complex systems somewhat analogous to the role played by the equation of state of a perfect gas in classical thermodynamics. Consequently, an understanding of their behavior is a prerequisite for the study of more general systems. 

THERMODYNAMIC CONSEQUENCES OF STRAIN/ORDER PARAMETER COUPLING... 

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