Sequential equilibrium

Note that K, K2, and are sequential equilibrium constants for the first, second, and third binding of ligands. The configurations of the ligands on the sites... 

An attempt to determine the sequential equilibrium constants, Ki, K2, etc., was reported by Vrancken et al.183). They initiated polymerization of a-methyl styrene by a stepwise addition of the monomer to a dilute solution of its dimeric dianions in tetrahyd-rofuran. After each addition the concentration of the residual, equilibrated monomer was determined, and its value was plotted vs. the total concentration of the supplied monomer. The resulting curve is shown in Fig. 4, and its shape allows, in principle, the determination of Ki, K2 and Kp = K3 = K4, etc. Although the approach is sound, this method gives only a reasonable estimate of Kt because the deviation of K2 from the Kp s value is too small to be determined. The maximum seen in Fig. 4 arises from an increase in the activity coefficient of the monomer caused by increasing volume fraction of the polymer - an effect discussed earlier. 

Environment and Life, RSC Publishing, p. i60 As this cytoplasmic (in cell) organic chemistry was reductive of necessity, because the ingredients were made of the oxides of carbon, it was inevitable that oxidizing compounds, which became oxygen, would be released. There followed in the environment an unavoidable and predictable sequence of the oxidation of minerals and non-metal elements in solution, limited by diffusion but generally following sequentially equilibrium constants, redox potentials. ... 

The proton transfer equilibrium that interconverts a carbonyl compound and its enol can be catalyzed by bases as well as by acids Figure 18 3 illustrates the roles of hydroxide ion and water m a base catalyzed enolization As m acid catalyzed enolization protons are transferred sequentially rather than m a single step First (step 1) the base abstracts a proton from the a carbon atom to yield an anion This anion is a resonance stabilized species Its negative charge is shared by the a carbon atom and the carbonyl oxygen... 

The second classification is the physical model. Examples are the rigorous modiiles found in chemical-process simulators. In sequential modular simulators, distillation and kinetic reactors are two important examples. Compared to relational models, physical models purport to represent the ac tual material, energy, equilibrium, and rate processes present in the unit. They rarely, however, include any equipment constraints as part of the model. Despite their complexity, adjustable parameters oearing some relation to theoiy (e.g., tray efficiency) are required such that the output is properly related to the input and specifications. These modds provide more accurate predictions of output based on input and specifications. However, the interactions between the model parameters and database parameters compromise the relationships between input and output. The nonlinearities of equipment performance are not included and, consequently, significant extrapolations result in large errors. Despite their greater complexity, they should be considered to be approximate as well. 

The holistic thermodynamic approach based on material (charge, concentration and electron) balances is a firm and valuable tool for a choice of the best a priori conditions of chemical analyses performed in electrolytic systems. Such an approach has been already presented in a series of papers issued in recent years, see [1-4] and references cited therein. In this communication, the approach will be exemplified with electrolytic systems, with special emphasis put on the complex systems where all particular types (acid-base, redox, complexation and precipitation) of chemical equilibria occur in parallel and/or sequentially. All attainable physicochemical knowledge can be involved in calculations and none simplifying assumptions are needed. All analytical prescriptions can be followed. The approach enables all possible (from thermodynamic viewpoint) reactions to be included and all effects resulting from activation barrier(s) and incomplete set of equilibrium data presumed can be tested. The problems involved are presented on some examples of analytical systems considered lately, concerning potentiometric titrations in complex titrand + titrant systems. All calculations were done with use of iterative computer programs MATLAB and DELPHI. 

The container was sealed with a serum cap and thermostatted at 25°C. 100 mg aliquots of the solute were added sequentially to the mixture by means of a hypodermic syringe. After each addition, the container was shaken, thermal equilibrium allowed to become established over a period of about 30 minutes and then a 5 pi sample of the solvent taken for GC analysis. Corrections were made for... 

A low-pressure process has been developed by ICl operating at about 50 atm (700 psi) using a new active copper-based catalyst at 240°C. The synthesis reaction occurs over a bed of heterogeneous catalyst arranged in either sequential adiabatic beds or placed within heat transfer tubes. The reaction is limited by equilibrium, and methanol concentration at the converter s exit rarely exceeds 7%. The converter effluent is cooled to 40°C to condense product methanol, and the unreacted gases are recycled. Crude methanol from the separator contains water and low levels of by-products, which are removed using a two-column distillation system. Figure 5-5 shows the ICl methanol synthesis process. 

In conclusion, it seems more likely that the folds go into the crystal sequentially as it is being formed, rather than forming through equilibrium considerations — this idea is used as a basis for kinetic theories. 

In addition to the synthetic applications related to the stereoselective or stereospecific syntheses of various systems, especially natural products, described in the previous subsection, a number of general synthetic uses of the reversible [2,3]-sigmatropic rearrangement of allylic sulfoxides are presented below. Several investigators110-113 have employed the allylic sulfenate-to-sulfoxide equilibrium in combination with the syn elimination of the latter as a method for the synthesis of conjugated dienes. For example, Reich and coworkers110,111 have reported a detailed study on the conversion of allylic alcohols to 1,3-dienes by sequential sulfenate sulfoxide rearrangement and syn elimination of the sulfoxide. This method of mild and efficient 1,4-dehydration of allylic alcohols has also been shown to proceed with overall cis stereochemistry in cyclic systems, as illustrated by equation 25. The reaction of trans-46 proceeds almost instantaneously at room temperature, while that of the cis-alcohol is much slower. This method has been subsequently applied for the synthesis of several natural products, such as the stereoselective transformation of the allylic alcohol 48 into the sex pheromone of the Red Bollworm Moth (49)112 and the conversion of isocodeine (50) into 6-demethoxythebaine (51)113. 

These phosphinous amide anions are presumably responsible for the formation of the by-products AT-phosphino phosphinous amides 11 and mono-phosphazenes derived from diphosphanes 12 in the sequential treatment of primary amines with n-BuLi and chlorophosphanes for preparing NH phosphinous amides [75,88] (Scheme 14). Compounds 11 and 12 are presumably derived from anions 9 and 10, respectively, generated by deprotonation of the newly formed phosphinous amide with the lithiated amine R NHLi. In solution, 9 can establish a metallotropic equilibrium with 10. 

Transport systems can be described in a functional sense according to the number of molecules moved and the direction of movement (Figure 41-10) or according to whether movement is toward or away from equilibrium. A uniport system moves one type of molecule bidirectionally. In cotransport systems, the transfer of one solute depends upon the stoichiometric simultaneous or sequential transfer of another solute. A symport moves these solutes in the same direction. Examples are the proton-sugar transporter in bacteria and the Na+ -sugar transporters (for glucose and certain other sugars) and Na -amino acid transporters in mammalian cells. Antiport systems move two molecules in opposite directions (eg, Na in and Ca out). 

Figure 2.12 Reaction pathway for a bi-bi rapid equilibrium, random sequential ternary complex reaction mechanism.

The aromatic hydrogenation reactions are reversible and at normal hydrotreating conditions, the equilibrium limits to achieve complete conversion. Low temperatures and higher pressures favor the aromatic saturation. The carbon atoms of a multi-ring system are hydrogenated in sequential steps, each one being equilibrium limited, as well. 

A series of bis(phenoxide) aluminum alkoxides have also been reported as lactone ROP initiators. Complexes (264)-(266) all initiate the well-controlled ROP of CL, NVL.806,807 and L-LA.808 Block copolymers have been prepared by sequential monomer addition, and resumption experiments (addition of a second aliquot of monomer to a living chain) support a living mechanism. The polymerizations are characterized by narrow polydispersities (1.20) and molecular weights close to calculated values. However, other researchers using closely related (267) have reported Mw/Mn values of 1.50 and proposed that an equilibrium between dimeric and monomeric initiator molecules was responsible for an efficiency of 0.36.809 In addition, the polymerization of LA using (268) only achieved a conversion of 15% after 5 days at 80 °C (Mn = 21,070, Mn calc 2,010, Mw/Mn = 1.46).810... 

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