Excess mixtures, thermodynamic

The excess molar thermodynamic function Z is defined as the difference in the property Zm for a real mixture and that for an ideal solution. That is,... 

The TNAN aqueous mixtures are characterized by the following conditions for the excess molar thermodynamic functions of mixing GE <0 and i//E > T- SE. ... 

To sum up, it can be estabhshed that in the case of adsorption from perfect mixtures, both adsorption excess and thermodynamical fimctions of adsorption are fully concentrated in the... 

The discussion and interpretation of the difference between n-alkanes and alcohols isotherms will be presented by considering the contributions to the excess partial Gibbs fi ee energy of the penetrants in the polymer phase. In this anal3 s, rather standard arguments fi om classical theories of mixture thermodynamics are used. 

An excess of crotonaldehyde or aUphatic, ahcyhc, and aromatic hydrocarbons and their derivatives is used as a solvent to produce compounds of molecular weights of 1000—5000 (25—28). After removal of unreacted components and solvent, the adduct referred to as polyester is decomposed in acidic media or by pyrolysis (29—36). Proper operation of acidic decomposition can give high yields of pure /n j ,/n7 j -2,4-hexadienoic acid, whereas the pyrolysis gives a mixture of isomers that must be converted to the pure trans,trans form. The thermal decomposition is carried out in the presence of alkaU or amine catalysts. A simultaneous codistillation of the sorbic acid as it forms and the component used as the solvent can simplify the process scheme. The catalyst remains in the reaction batch. Suitable solvents and entraining agents include most inert Hquids that bod at 200—300°C, eg, aUphatic hydrocarbons. When the polyester is spHt thermally at 170—180°C and the sorbic acid is distilled direcdy with the solvent, production and purification can be combined in a single step. The solvent can be reused after removal of the sorbic acid (34). The isomeric mixture can be converted to the thermodynamically more stable trans,trans form in the presence of iodine, alkaU, or sulfuric or hydrochloric acid (37,38). 

Nitrile ylides derived from the photolysis of 1-azirines have also been found to undergo a novel intramolecular 1,1-cycloaddition reaction (75JA3862). Irradiation of (65) gave a 1 1 mixture of azabicyclohexenes (67) and (68). On further irradiation (67) was quantitatively isomerized to (68). Photolysis of (65) in the presence of excess dimethyl acetylenedicar-boxylate resulted in the 1,3-dipolar trapping of the normal nitrile ylide. Under these conditions, the formation of azabicyclohexenes (67) and (68) was entirely suppressed. The photoreaction of the closely related methyl-substituted azirine (65b) gave azabicyclohexene (68b) as the primary photoproduct. The formation of the thermodynamically less favored endo isomer, i.e. (68b), corresponds to a complete inversion of stereochemistry about the TT-system in the cycloaddition process. 

R. C. Pemberton and C. J. Mash. "Thermodynamic Properties of Aqueous Non-Electrolyte Mixtures II. Vapour Pressures and Excess Gibbs Energies for Water-)- Ethanol at 303.15 to... 

Deoxy-a-D-ribosyl-l-phosphate 20, a key substrate in the preparation of 2 -deoxynucleosides, was stereoselectively prepared by crystallization-induced asymmetric transformation in the presence of an excess of ortho-phosphoric acid and tri( -butyl)amine under strictly anhydrous conditions (Scheme 2).7 Initial Sn2 displacement of Cl in ot-glycosyl chloride 16 by phosphoric acid resulted in a 1 1 a/p anomeric mixture of 17 and 18 due to the rapid anomerisation of the a-chloride in polar solvents. Under acidic conditions, in the presence of an excess of H3P04, an equilibration between the a and p anomers gradually changed in favour of the thermodynamically more stable a-counterpart. By selective crystallization of the mono tri( -butyl)ammonium salt of the a-phosphate from the mixture, the equilibrium could be shifted towards the desired a-D-ribosyl phosphate 18 (oc/p = 98.5 1.5), which was isolated as bis-cyclohexylammonium salt 19 and deprotected to furnish compound 20. 

Renon, H., Prauznits, J.M., 1968, Local Compositions in Thermodynamic Excess Functions for Liquid Mixtures, AIChE Journal, 14, 135. 

The view that the clay surface perturbs water molecules at distances well in excess of 10 A has been largely based on measurements of thermodynamic properties of the adsorbed water as a function of the water content of the clay-water mixture. There is an extensive literature on this subject which has been summarized by Low (6.). The properties examined are, among others, the apparent specific heat capacity, the partial specific volume, and the apparent specific expansibility (6.). These measurements were made on samples prepared by mixing predetermined amounts of water and smectite to achieve the desired number of adsorbed water layers. The number of water layers adsorbed on the clay is derived from the amount of water added to the clay and the surface area of the clay. 

LS measurements on binary liquid mixtures have been directed primarily as a means of obtaining fundamental thermodynamic information such as chemical potentials and the excess mixing functions. Although molecular weights could in fact be derived from some published data, this has largely not been done by the authors, since such an exercise on substances of known molecular weight would have been subsidiary to the main purpose of their studies. 

A rams, D. S., and J. M. Prausnitz, "Statistical Thermodynamics of Liquid Mixtures A New Expression for the Excess Gibbs Energy of Partly or Completely Miscible Systems," AIChE J., 1975, 21, 116. 

The product is an equilibrium mixture and an excess of 2-propanol must be used to obtain high yields. Ammonium formate or formic acid have also been used as the hydrogen donor and now the reaction to the alcohol is complete, because the thermodynamics are more favourable and because C02 leaves the reaction medium. 

Here x and x are isotopomer mole fractions in the binary mixture. Remembering x = 1 — x, differentiating to obtain partial molar free energies (and using the thermodynamic relations p,E(V) = AE(V) — x (dAE(V)/dx ) and xE (V) = AE(V) + x (dAE(V)/dx ) one finds expressions for the excess partial molar free energies, xE(V) and il (V). In the high dilution limit, an important case of practical interest, the excess chemical potential of the trace isotopomer, say the unprimed one, is... 

It should be noted here that a regioselective control may also be exerted by just controlling the experimental conditions. Thus, working under strictly kinetic conditions (low temperature, absence of oxygen and slow addition of the ketone to an excess of a solution of an aprotic base) the less substituted enolate of carvomenthone can also be selectively generated and may be then submitted to different kind of reactions. However, reversible reactions like the Michael addition would equilibrate the reaction mixture to the thermodynamically more stable enolate. 

Interesting information about the catalytic systems was obtained by studying the stereochemistry of the reaction of the catalyst precursor 1 with methacrylonitrile. The water molecule of complex 1 is readUy displaced by methacrylonitrile rendering complex [(t -C5Me5)Ir (/ )-Prophos (methacrylonitrile)] (SbFg)2 (9) as a mixture of the two possible epimers at metal, namely, R iJic and 5ir,/ c, in 34% diastereomeric excess in the former (Scheme 20). In acetone, at 50°C, the R r,Rc isomer slowly epimerizes to the thermodynamically preferred epimer. From the solution, pure samples of the latter can be isolated that have been employed as stoichiometric catalysts for the DCR between methacrylonitrile and nitrones IV and V. 

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