Dimerization reactions equilibrium

The failure of the above process to show a discrete or sharp critical concentration behavior can be obviated by having one or more of the initial equilibrium constants much smaller than K. For example, one may change the dimerization reaction equilibrium constant to, where is much less than K, the constant for all remaining polymerization steps. Now c, will be defined by the following expression ... 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

If the mixture includes organic acids, the equations of Hayden and O Connell yield equilibrium constants for all possible dimerization reactions. 

A more complete coverage of the literature on electronic spectra of radicals is presented in our paper submitted for publication in Fortschr. Chem. Forsch. (Topics in Current Chemistry), where theafi initio studies are also reviewed and the existing open-shell computational procedures discussed. Recently we performed semiempirical all-valence-electron calculations on ground-state properties and electronic spectra of small radicals (Zahradnik, R., and P. Carsky, Theoret, Chim. Acta, 27, 121 (1972) and Carsky, P., M. Machacek, and R. Zahradnik, Coll. Czech. Chem. Commun., in press) and on equilibrium constants of dimerization reactions of small radicals (Zahradnik, R., Z. Slanina, and P. (5arsky, to be published). 

Glucose-6-phosphate dehydrogenase is a dimer with a molecular mass of about 135 000. Up to eight electrophoretically separable isoenzymes for this enzyme are known. A specific feature of the above reaction is the formation of NADP Hr The reaction equilibrium is strongly shifted to the right, since the lactone formed is liable to hydrolysis, which is spontaneous or lactonase-assisted. 

The deprotonation of 2-pyridylmethylamine with dimethylzinc, Scheme 76, afforded methylzinc-2-pyridylmethy-lamide 116, which crystallizes as a trimer, but exists in solution in a dimer-trimer equilibrium. A dinuclear zinc complex bearing a diamino(tetrapyridyl) ligand 117, which must have been formed in a complex sequence of reactions, was isolated in low yield from a THF solution of 116. 

The three rate constants for Eq. (98) correspond to the acid-catalyzed, the acid-independent and the hydrolytic paths of the dimer-monomer equilibrium, respectively, and were evaluated independently (107). The results clearly demonstrate that the complexity of the kinetic processes is due to the interplay of the hydrolytic and the complex-formation steps and is not a consequence of electron transfer reactions. In fact, the first-order decomposition of the FeS03 complex is the only redox step which contributes to the overall kinetic profiles, because subsequent reactions with the sulfite ion radical and other intermediates are considerably faster. The presence of dioxygen did not affect the kinetic traces when a large excess of the metal ion is present, confirming that either the formation of the SO5 radical (Eq. (91)) is suppressed by reaction (101), or the reactions of Fe(II) with SO and HSO5 are preferred over those of HSO3 as was predicted by Warneck and Ziajka (86). Recently, first-order formation of iron(II) was confirmed in this system (108), which supports the first possibility cited, though the other alternative can also be feasible under certain circumstances. 

Magnesacyclopentane, -heptane and -decane all completely dimerize, while magnesacy-clohexane exists to a small extent as the monomer. The authors assert that the magnesacy-clohexane monomer is only observable because of the highly dilute solution that shifts the equilibrium toward the monomer . The enthalpy and entropy of the dimerization reaction for n = 5 were determined to be —48.0 3 kJmoG and 106.0 10.0 JmoG deg, respectively. The dimerization enthalpies for reactions when n = 6,9 are more exothermic than 65 kJmol This thermodynamic (and kinetic) proclivity to dimerization obviously is not shared by the corresponding carbocycles. 

Cuprous acetate monomer, complexed with the quinoline solvent, is in rapid equilibrium with dimer. The equilibrium constant is such that dimer formation is incomplete. Activation of the hydrogen occurs by a slow reaction between dimer complex and dissolved molecular hydrogen. Following activation of the hydrogen, the substrate quickly reacts with the hydrogen. Reaction (11) is believed rate controlling. Weller and Mills (5) attempted to establish whether the reaction went through a two-step oxidation and reduction of the Cu1 catalyst however, the conclusion was that the reaction depicted above best fits the observed facts. 

The second reason for a reaction not going to completion is that it proceeds to a state of material equilibrium in which both reactants and products exist. This is the case for all gas-phase reactions, because free energy minimizes in gas mixtures when some of each component is present. (See Problem 16 in Chapter 4.) In fact, even in the case of the spark-initiated H2-02 reaction discussed earlier, some H2 and 02 will remain after the reaction. Equilibrium is more evident with the gaseous molecule N02, a fraction of which exists as the dimer, N204, near ambient conditions. This fraction depends on the temperature and pressure and rapidly adjusts to changes in these variables, indicating that there is... 

A new type of photo-dimerization reaction for coumarin derivatives has also been described (Equation 16) <2002TL5161>. Irradiation of coumarin-3-carboxylic acid 180 in ethanol provided three different types of products the 4,4 -dimer of chroman-2-one 181, 3-(l -hydroxyethyl)-coumarin 182, and coumarin 183. The authors postulated that for the formation of 181, a ketyl radical is first formed, and the equilibrium between the 2-position and 4-position radical favors the latter. Dimerization of the 4-position radicals, followed by tautomerization and decarboxylation, provides dimer 181. 

Dimers RR and SS are termed homochiral dimers, whereas the mixed dimer RS is termed a heterochiral dimer. A fraction of pure enantiomer is always a mixture of the monomer and the corresponding homochiral dimer, but it does not contain any heterochiral dimer. It was shown, that the separation of the excess enantiomer of a non-racemic feed mixture is the combination of two effects [31], the difference in reaction equilibrium constants of the homo- and heterochiral dimerization reaction and the difference in the adsorptivity of the homo- and heterochiral dimers. 

With simultaneous phase and reaction equilibrium the system has only two dynamic degrees of freedom (five solutes - three chemical equilibria) and therefore corresponds again to a nonreactive system with two solutes. If the dimers are taken as reference components the following definition of the transformed concentration variables is found from Eq. (6)... 

For the dimerization reaction 2A A2, the equilibrium constant in the molL-1 scale is 105. What is the concentration in molL-1 of dimer in equilibrium with 10-3molL-1 monomer ... 

The monomeric radical anion is dimerized [reaction (41)1, and polymerization takes place on the ions or ion pairs. The equilibrium (46) is very rapidly established. Radical defects decay by combination thus naphthalenesodium is used quantitatively for practically instantaneous initiation. This method can therefore also be used to prepare polymer chains of uniform length. The regenerated naphthalene does not usually cause trouble. In some cases, the aromatic residue can be incorporated into the chains [190] (the metal cation is omitted for simplicity). 

If the decomposition reaction is carried out in a constant volume at 35°C, plot the pressure rise in the reactor as a function of time, for an initial charge of pure N2O5 at 0.4 atm. Assume that the dimerization reaction equilibrates immediately. The equilibrium constant of the NO2 dimerization reaction at 35°C is 3.68. Assume ideal behavior. 

The kinetics of the silicic acid condensation was investigated using the molybdate method introduced by Alexander [14]. Upon addition of a molybdate solution to a silicate solution, monomeric and dimeric silicic acid react to form the yellow molybdosilicate [SiMoi204o] [5]. The change in the absorption of this solution reflects the decrease in monomeric and dimeric silicic acid due to the condensation reaction. Because of the reaction equilibrium between silicic acid and the molybdate as well as between monomeric, dimeric, and oligomeric silicic acids, it is important to adhere to a well-defmed, constant, and reproducible time protocol for the formation of the molybdosilicate. 

An improvement of catalyst activity, especially for the oxidation of electron-poor, deactivated systems like p-toluic acid, can be reached by addition of other transition metal compounds to the Co/Mn/Br catalyst. The most prominent additive is zirconium(IV) acetate, which by itself is totally inactive. An addition of zirconi-um(IV) acetate (ca. 15 % of the amount of cobalt) can yield reaction rates which are higher than those observed using a tenfold amount of cobalt acetate. This amazing co-catalytic effect can be attributed to the common ability of zirconium to attain greater than sixfold coordination in solution, to the high stability of Zr toward reduction, and to the ability of zirconium or Hf to redistribute the dimer/ monomer equilibrium of dimerized cobalt acetates (Co 7Co, Co VCo " systems) by forming a weak complex with the catalytically more active monomeric Co species [17]. 

---