Free energy interpretation

Equation (42) provides a thermodynamically valid way to determine y for an interface involving a solid. The thermodynamic approach makes it clear that curvature has an effect on activity for any curved surface. The surface free energy interpretation of y is more plausible for solids than the surface tension interpretation, which is so useful for liquid surfaces. Either interpretation is valid in both cases, and there are situations in which both are useful. From solubility studies on a particle of known size, y5 can be determined by the method of Example 6.2. 

Solvent effects on chemical equilibria and reactions have been an important issue in physical organic chemistry. Several empirical relationships have been proposed to characterize systematically the various types of properties in protic and aprotic solvents. One of the simplest models is the continuum reaction field characterized by the dielectric constant, e, of the solvent, which is still widely used. Taft and coworkers [30] presented more sophisticated solvent parameters that can take solute-solvent hydrogen bonding and polarity into account. Although this parameter has been successfully applied to rationalize experimentally observed solvent effects, it seems still far from satisfactory to interpret solvent effects on the basis of microscopic infomation of the solute-solvent interaction and solvation free energy. 

When two or more substituents are present on a cyclohexane ring, the interactions between the substituents must be included in the analysis. The dimethylcyclohexanes provide an example in which a straightforward interpretation is in complete agreement with the experimental data. For 1,2-, 1,3-, and 1,4-dimethylcyclohexane, the free-energy change of the equilibrium for the cis trans isomerization is given below. ... 

Similar free-energy diagrams, which can be interpreted in exactly the same way, have been constructed for sulphides , carbides and nitrides (Figs. 7.56 to 7.58). 

The results obtained by measuring the affinity to oxygen in the presence of various monohydric alcohols (methanol, ethanol, 2-propanol, 1-propanol) 140-144> were interpreted in terms of the Monod-Wyman-Changeux model145), by which the change of the standard free-energy difference between R and T state in the absence of oxygen, due to the addition of alcohol, can be determined, i.e. 

We now discuss the effects of finite chain length. The difficulties arise from the definition of a bulk free energy term, when the very nature of the chains constrains the crystal thickness to be finite. There are two different approaches to this problem the first to be considered is due to Hoffman et al. [31] and is a simple modification of the infinite chain case, but is somewhat lacking in theoretical justification the second, due to Buckley and Kovacs [23], aims to correct this deficiency and suggests that the interpretation of experimental data given by Hoffman s approach is misleading. 

Since the free energy of a molecule in the liquid phase is not markedly different from that of the same species volatilized, the variation in the intrinsic reactivity associated with the controlling step in a solid—liquid process is not expected to be very different from that of the solid—gas reaction. Interpretation of kinetic data for solid—liquid reactions must, however, always consider the possibility that mass transfer in the homogeneous phase of reactants to or products from, the reaction interface is rate-limiting [108,109], Kinetic aspects of solid—liquid reactions have been discussed by Taplin [110]. 

The value of AG at a particular stage of the reaction is the difference in the molar Gibbs free energies of the products and the reactants at the partial pressures or concentrations that they have at that stage, weighted by the stoichiometric coefficients interpreted as amounts in moles ... 

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

A note on good practice Equation 5 was derived on the basis of the "molar convention for writing the reaction Gibbs free energy that means that the n must be interpreted as a pure number. That convention keeps the units straight FE° has the units joules per mole, so does RT, so the ratio FE°/RT is a pure number and, with n a pure number, the right hand side is a pure number too (as it must be, if it is to be equal to a logarithm). 

The application of the overpotential t] can be considered to be equivalent to the displacement of the potential energy curves by the amount 7]F with respect to each other. The high field is now applied across the double layer between the electrode and the ions at the plane of closest approach. It is apparent from Fig. 12 that the energy of activation in the favoured direction will be diminished by etrjF while that in the reverse direction will be increased by (1 — ac)r]F where the simplest interpretation of a is in terms of the slopes of the potential energy curves (a = mi/ mi+m )) at the points of intersection electrode processes indeed are the classical example of linear free energy relations. 

The salt is a colorless crystalline solid which is virtually insoluble in all common organic solvents. It reacts slowly with chloroform and carbon tetrachloride to give thallium(I) chloride 25), gives a characteristic red coloration with carbon disulfide, and undergoes the Diels-Alder reaction with maleic anhydride 110). It is rapidly decomposed by acids, but is stable to water this latter fact has been interpreted (55) in terms of the small free energy change for the reaction... 

Note that the particle shape is affected by the interaction between the active phase and the support and by the surface free energy. The former tends to lead to spreading of a particle, whereas the latter tends to form spherical particles (Scholten et al., 1985). When particles are partially poisoned (Fig. 3.48.b), chemisorption data can be interpreted wrongly the average particle size is overestimated. The same applies to particles encapsulated in the support. 

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