Homogeneity postulate

A similar homogeneity postulate can be written for the singular part of the free energy,... 

Another consequence that follows from the homogeneity postulate for the free energy is the fact that exponents of corresponding quantities above and below Tc are identical, a = a, y = y, v = v. ... 

Catalytic hydrogenation is mostly used to convert C—C triple bonds into C C double bonds and alkenes into alkanes or to replace allylic or benzylic hetero atoms by hydrogen (H. Kropf, 1980). Simple theory postulates cis- or syn-addition of hydrogen to the C—C triple or double bond with heterogeneous (R. L. Augustine, 1965, 1968, 1976 P. N. Rylander, 1979) and homogeneous (A. J. Birch, 1976) catalysts. Sulfur functions can be removed with reducing metals, e. g. with Raney nickel (G. R. Pettit, 1962 A). Heteroaromatic systems may be reduced with the aid of ruthenium on carbon. 

Likewise, quantum mechanical calculation succeeds in giving a theoretical explanation of some facts that the resonance theory could not explain, for example, why bis(pyridine-2)monomethine cyanine and bis(pyridine-4)monomethine cyanine possess the same lowest energy transition contrary to the 2,2 - and 2,4 -quinoline monomethine dyes, together with a molecular coefficient extinction lower than that of the 4,4 -quinoline dye (11). Calculation shows also that there is no theoretical reason for observing a relationship between and pK in a large series of dyes with different nuclei as it has been postulated, even if limited observations and calculations in short homogeneous series could lead to this conclusion (105). 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

To explain the observed magnitude of E and other kinetic features of reaction, a homogeneous bimolecular interaction between neighbouring CIO4 ions in the crystal structure was postulated and application of the activated complex theory to this model gave good agreement with the experimental observations. 

Garratt and Thompson [J. Chem. Soc., 1934, 524, 1817, 1822] have studied the photochemical and thermal decomposition of nickel tetra-carbonyl. Later work by Day, Pearson and Basolo [J. Am. Chem. Soc., 90 (6933), 1968] confirmed that the rate law postulated by Garratt and Thompson was obeyed for the homogeneous process. The mechanism postulated by both groups is ... 

In this context we postulated that the shift reaction might proceed catalytically according to a hypothetical cycle such as Scheme I. There are four key steps in Scheme I a) nucleophilic attack of hydroxide or water on coordinated CO to give a hydroxycarbonyl complex, b) decarboxylation to give the metal hydride, c) reductive elimination of H2 from the hydride and d) coordination of new CO. In addition, there are several potentially crucial protonation/deprotonation equilibria involving metal hydrides or the hydroxycarbonyl. The mechanistic details have been worked out (but only incompletely) for a couple of the alkaline solution WGSR homogeneous catalysts. In these cases,... 

The postulated transition state of the tt—a bond conversion occurs when the plane of the rotating benzene molecule is approximately at 45° to the catalyst surface. The electronic hybridization changes involved in this process (Fig. 4) are similar to those proposed by Melander 22) for homogeneous substitution reactions and show how resonance interactions may achieve a lowering in the activation energy. This aspect has previously been discussed in terms of the Lennard-Jones theory where the activation energy is lowered more effectively by resonance effects... 

Nucleophilic astatination of halobenzenes CgHjX (X = Cl, Br, I) in homogeneous mixtures with -C4H9NH2, (C2H5)2NH, and (C2Hj>3N at 210° C has led to the formation of astatobenzene with radiochemical yields of 75-90% 143, 144). A two-step process has been postulated [Eqs. (10) and (11)], with the latter reaction [Eq. (11)] as the ratedetermining step ... 

The SHB concept was expanded to chiral phosphine catalysts by de Rege et al., who reacted the trifluoromethanesulfonate (triflate) counter anion of the cationic complex [Rh(COD)((R,Rj-MeDuPhos)] with the surface hydroxyl groups of the silaceous mesoporous material MCM-41 [122]. The complex was loaded to a level of 1.03 wt% Rh. A decrease in support surface area and pore volume is consistent with the complex being located within the support pores. The counterion is very important in this process if the anion of the homogeneous catalyst precursor is altered to BArp no adsorption of the catalyst is observed. It is postulated that the mechanism of triflate binding is hydrogen bonding with the support, and that the... 

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