Temperature-dependent equilibrium

Liquid ammonia solutions of lithium polysulfides have been characterized by Dubois et al. [18]. The least reduced polysulfide was shown to be 8 (not found previously in aquo) lying in a strongly temperature-dependent equilibrium with the radical 83 . 

Dialkyl zinc compounds form phosphine complexes of formula RZnP(SiMe3)2 on addition of one equivalent of bis(trimethylsilyl)phosphine. Solution and solid-state studies showed that the complexes are dimeric or trimeric in solution or the solid state. Bis(trimethylsilyl)phosphido-methylzinc crystallizes as a trimeric molecule with a Zn3P3 core in the twist-boat conformation. Bis(trimethylsilyl)phosphido- -butylzinc, shows a similar central Zn3P3 fragment. The sterically more demanding trimethylsilylmethyl substituent forms a dimeric species of bis(trimethylsilyl) phosphido-trimethylsilylmethylzinc. Solution studies of bis(trimethylsilyl)phosphido- .vo-propyl-zinc demonstrate a temperature-dependent equilibrium of the dimeric and trimeric species and the crystalline state contains a 1 1 mixture of these two oligomers. A monomeric bis(trimethyl-silyl)phosphido-tris(trimethylsilyl)methylzinc has also been synthesized.313... 

The coefficient kK was found to decrease with the increasing temperature, which can be explained by the temperature-dependent equilibrium between dioxygen, phenoxyl radical, and the formed peroxyl radical [100],... 

The reaction of the -C(Hal)=N-function with azide ion or hydrazoic acid is known to give the tetrazole system. As part of a mechanistic study of the one-pot synthesis of an azadibenzoporphyrine in 84% isolated yield from reaction of a 1-bromobenzopyrromethene hydrobromide 74 with sodium azide at 140 °C, 74 was treated with azide at lower temperature (60 °C) in an attempt to isolate the proposed azide mechanistic intermediate 75 however, the fused tetrazole 76 was isolated in 47% yield (identified by X-ray analysis) (Equation 4) <1999MI530>. Upon heating a dimethyl formamide (DMF) solution of tetrazole 76 to 140°C for 1 h, the desired porphyrin was indeed obtained in 14% yield, consistent with the temperature-dependent equilibrium between tetrazole and azide that has been observed with some fused tetrazoles. 

Amino-2-deoxy aldoses. The behaviour of O-unprotected sugars is exemplified in D-gluco series after basic hydrolysis of the starting 2-benzamidoglycoside followed by buffering the medium with carbon dioxide and treatment with thiophosgene, an intermediate isothiocyanate was obtained.320 However, NMR revealed a temperature-dependent equilibrium of this isothiocyanate with a trans-fused OZT (Scheme 5). 

Table 2.3 Corrected equations for the calculation of temperature-dependent equilibrium constants based on publications of Reimschuessel and co-workers [21]...

Transesterification is the main reaction of PET polycondensation in both the melt phase and the solid state. It is the dominant reaction in the second and subsequent stages of PET production, but also occurs to a significant extent during esterification. As mentioned above, polycondensation is an equilibrium reaction and the reverse reaction is glycolysis. The temperature-dependent equilibrium constant of transesterification has already been discussed in Section 2.1. The polycondensation process in the melt phase involves a gas phase and a homogeneous liquid phase, while the SSP process involves a gas phase and two solid phases. The respective phase equilibria, which have to be considered for process modelling, will be discussed below in Section 3.1. 

The relative importance of the dissolved species will be dependent upon the type of process under consideration. For example, in the magnesium oxide process, magnesium is one of the dominant species while sodium is one of the dominant species in the regenerative sodium process. A general list of equilibria is presented in Table 1. Expressions of the following form have been developed for the temperature dependent equilibrium constants (y). 

K is the temperature dependent equilibrium constant T is the absolute temperature in degrees Kelvin and B, C, D, and E are constants. Numerical values of these constants are presented in Table 2. 

The most significant chemical equilibria present in flue gas scrubbing slurries are outlined. Expressions for temperature dependent equilibrium constants are presented that are suitable for the temperature ranges encountered in scrubbing applications. Expressions for activity coefficients of ions and ion-pairs are presented that are suitable for the ranges of ionii strengths encountered for this type of applications. 

Instead, the reaction proceeds to an equilibrium point, where both products and reactants remain. The equilibrium composition is dependent upon both the initial composition and final temperature. Fortunately, the equilibrium concentrations can be determined by a temperature dependent equilibrium constant, K, and the following equation. 

Amino-4,5-dihydro-5-hydroxy-l,2,4-triazine (82B) exhibits a temperature-dependent equilibrium with the open-chain hydrazide-hydrazone derivative 82A in CDCI3 solution, as shown by the H-NMR data (85LA78). 

For ancient seafloor sulfide deposits an alternative model has been discussed by Ohmoto et al. (1983), in which H2S and sulfides are buffered by precipitated anhydrite and where 5 " S-values reflect temperature dependent equilibrium fractionations between SO4 and H2S. 

In solution, vitamin D (both D2 and D3) isomerizes to previtamin D and forms a temperature-dependent equilibrium mixture [520], which leads to quantification problems. Previtamin D is difficult to quantify because of interference from co-eluted contaminants. The reversibility of the isomerization is very slow, therefore the percentage of previtamin can be considered constant during the entire analysis. The quantification of the potential vitamin D can be performed using an external standard that has undergone saponification procedure as the sample [521]. Vitamin D2 and D3 can be used as an internal standard to quantify the other one. Indeed, the isomerization rates of vitamins D2 and D3 are virtually the same thereby the previtamin D/vitamin D ratio will be the same for both vitamers at any temperature. The isomerization problem can be resolved by... 

This law means that the intensity becomes smaller as the temperature is raised. Deviations from linearity could indicate a temperature-dependent equilibrium between a triplet and a singlet. Conversely, a linear Curie plot is taken as evidence for a triplet ground state far below the singlet, but such observations require that the carbene be stable to a certain extent at elevated temperature. 

Magnesium anthracene Ci4HioMg(THF)3 (118) can be prepared in high yield from the reaction of metallic magnesium and anthracene in THE (equation 12) . Kinetic measurements showed that a reversible temperature-dependent equilibrium exists between anthracene, magnesium and 118, the latter being favored at lower temperatures. This equilibrium opened a way to the preparation of elemental magnesium in a finely dispersed. 

In methanol, the extinction of the absorption at 241 nm is less than 40 % of the value in isopentane with little change on lowering the temperature. In isopentane, the extinction drops significantly to the value found in methanol when the temperature is lowered. The data on the temperature-dependent CD in methanol can be interpreted on the basis of a temperature-dependent equilibrium between two chiral species. The change of the rotatory strength appears to be AG° = —2.0 KJ mol-1. This phenomenon is interpreted by the assumption that the cis-conformer about the C(6)-C(7) bond is favored in methanol and, at lower temperatures, in isopentane. 

In solution, lepidopterene 113 (L) is in temperature dependent equilibrium with its cycloreversion product 114 (A). The equilibrium ratio [L]/[A] at room temperature in toluene is 630, and the regeneration of L from A proceeds by an intramolecular Diels-Alder reaction which is associated with an activation energy of 17kcal/mol [131]. Monosubstituted lepidopterenes 116 can give rise to two different cycloreversion products, 115 (A-l) and 117 (A-2). When R is methyl, formyl, benzoyl, and cyano, the cycloreversion involves mainly the A-l isomer, and the [L]/[A] equilibrium ratios at 25°C in toluene are 37,000, 1500, 33, and 22, respectively [73]. Presumably, the formation of the A-l isomer is favored for steric reasons over that of A-2. 

A clean, high-yielding asymmetric Baylis-HiUman reaction has been reported employing Oppolzer s sultam,63ab it couples acrylates witii a variety of aldehydes at 0 °C, with >99% ee in all cases described.630 Another new, practical variant of the reaction employs a phosphine catalyst,64 and here the temperature effect is critical the rate increases in either direction from room temperature, with a dramatic improvement observed at 0 °C. This unusual observation is explained in tenns of a temperature-dependent equilibrium between efficient and inefficient intermediates. 

Kensch, O., Restle, T., Wohrl, B. M., Goody, R. S., and Steinhoff, H. J. (2000). Temperature-dependent equilibrium between the open and closed conformation of the p66 subunit of HIV-1 reverse transcriptase revealed by site-directed spin labelling. / Mol. Biol. 301, 1029-1039. 

The kinetic information can be used as well to deduce if a compound is bound homogeneously or not. The kinetics of flutax and paclitaxel dissociation from (3-tublin are monophasic, which indicates a single rate limiting step, consistent with most of the compound bound to the same site. However, dissociation of Epothilone A from the binding site shows biphasic behaviour, which would be consistent with the compound distributed between the external and the luminal site, with a temperature-dependant equilibrium (Table 2) which favours the outer site at higher temperatures. 

Here and Kq2 are the temperature-dependent equilibrium constants for reactions G3 and G2 respectively. 

Temperature-dependent equilibrium constants for carbonate are shown in table 13.1 (Larson and Buswell, 1942). Equations 13.4 and 13.5 can result in more alkaline waters due to the generation of OH- this is typical of what may be found in lakes and streams due to high carbonates in the drainage basin. The percolation of H2O through soils results in the enrichment of CO2 from plant and microbial decay processes forming H2CO3 which can... 

In addition to the two ODE for the extents of reactions, reaction kinetics are required. The reaction rate expressions describe reversible kinetics with a temperature-dependent equilibrium constant. The temperature dependence of the reaction rate constant is assumed to obey Arrhenius law. However, for the proposed methodology this is of minor importance since isothermal cell operation is assumed. 

Although a temperature-dependent equilibrium determines the orthopara ratio, in a sample of H2, sudden temperature changes will not cause a rapid shift in this ratio unless the ortho-para conversion is catalyzed also. Obviously, methods to break and then remake the II—H bond offer a path to equilibrium. The passage of electric discharge through the sample results in such bond breaking and redistribution likewise, addition of a small amount of atomic hydrogen (abbreviated H ) results in similar action ... 

The studies on this system, to date, have not indicated the existence of a temperature-dependent equilibrium similar to the one in which the polymerization of caprolactam results. Here essentially quantitative conversion was obtained independent of the polymerization temperature used. The final degree of polymerization, however, depends strongly on the temperature of polymerization it increased when the polymerization temperature was increased. This may be explained by the increased mobility of the polymer molecules as a result of a temperature increase. 

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