Interconversion rate constant

The second and third relaxation processes were coupled, where the observed rate constants differed by a factor of 3 to 7 and the rate constant for each relaxation process varied linearly with the DNA concentration.112 This dependence is consistent with the mechanism shown in Scheme 2, where 1 binds to 2 different sites in DNA and an interconversion between the sites is mediated in a bimolecular reaction with a second DNA molecule. For such coupled kinetics, the sum and the product of the two relaxation rate constants are related to the individual rate constants shown in Scheme 2. Such an analysis led to the values for the dissociation rate constants from each binding site, one of the interconversion rate constants and the association rate constant for the site with slowest binding dynamics (Table 2).112 The dissociation rate constant from one of the sites was similar to the values that were determined assuming a 1 1 binding stoichiometry (Table 1). 

The lability inherent in the planar, tetrahedral equilibria which nearly all involve Ni(II) requires that nmr line broadeningor photochemical perturbation methods be used for their kinetic resolution. First-order interconversion rate constants for... 

The tunneling intramolecular rearrangement of 2-norbornyl cation was considered by Yannoni et al. [1982] and Myhre et al. [1985], The NMR spectra show that the structure is symmetric at temperatures as low as 4.2 K, so that the interconversion rate constant between the two asymmetric structures is greater than 109s-1 ... 

When the process pN- n-> pv in the mobile phase or stationary phase can be represented by first-order or pseudo-first-order interconversion kinetics and as a reversible binding event, the resolution of the interconverting species can be evaluated319 by treating the column as a chemical reactor with properties specified by the corresponding Damkohler number Da and the corresponding interconversion rate constants derived. Thus,... 

The proton chemical environments are quite different for the keto and enol tautomers, and the interconversion rate constants ki and k i between these forms are small enough... 

Despite the similarity of cis to trans interconversion rates, secondary amide peptide bonds and imidic peptide bonds differ greatly in their capacity to form the cis isomeric state. This means that the decreased cis population of secondary amide peptide bonds results from higher rates for CTIs. In the case of the Ala-Tyr dipeptide a 250-fold difference for the interconversion rate constants was observed (kc t = 0.6 s-1, kt c = 2.4 x 10-3 s-1, 298 K) [21]. Generally, chain elongation causes destabilization of the cis conformation when located apart from charged termini, and thus leads to a decreased cis population as well as a lowered barrier to rotation in cis to trans direction. 

Several studies have been reported on the determination of the mean-force potential between aqueous ion pairs at ambient conditions, " yet little is known about the speciation in aqueous solutions at near-critical and supercritical conditions " which are typically encountered in technological processes where supercritical water is either the reaction medium or the energy carrier. In this section we analyze the association, equilibrium, and the kinetic (interconversion) rate constants for an infinitely dilute aqueous Na /CI" solution as described by a water-electrolyte model at several supercritical state conditions. In Section 3.3.1 we briefly describe the statistical mechanical formalism for the determination of the thermodynamic constants and the molecular dynamic determination via constraint dynamics. In Section 3.3.2 we discuss the actual kinetics of the inteicon-version between two ion pair configurations leading to the definition of the corresponding equilibrium constant. Finally, in Section 3.3.3 we discuss the outcome of the comparison between the association constants from simulation and... 

The quantitative solution of the problem, i.e. simultaneous determination of both the sequence of surface chemical steps and the ratios of the rate constants of adsorption-desorption processes to the rate constants of surface reactions from experimental kinetic data, is extraordinarily difficult. The attempt made by Smith and Prater 82) in a study of cyclohexane-cyclohexene-benzene interconversion, using elegant mathematic procedures based on the previous theoretical treatment 28), has met with only partial success. Nevertheless, their work is an example of how a sophisticated approach to the quantitative solution of a coupled heterogeneous catalytic system should be employed if the system is studied as a whole. 

Opposing reactions. The reversible interconversion of d.y-[Cr(cn)2(OH)2 + to trans is characterized by an equilibrium constant of 0.16 and a forward rate constant of 3.30 X 10 4 s"1.In an experiment starting with the pure cis isomer, how long does it take to form half the equilibrium concentration of trans Starting with pure trans, how long does it take for half the equilibrium concentration of trans to form ... 

Consider the interconversion of two chiral molecules to yield ultimately the racemic mixture. This is simply the situation of opposing first-order reactions of A and P, treated in Chapter 3, for the special case of an equilibrium constant of unity. Recall that for such an equilibrating system ke = kf + kr because of that, knc is one-half the experimental rate constant. 

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [Mpropagation reaction rate constants. The steady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that... 

The most significant results obtained for complexes of iron(II) are collected in Table 3. The data derive from laser Raman temperature-jump measurements, ultrasonic relaxation, and the application of the photoperturbation technique. Where the results of two or three methods are available, a gratifying agreement is found. The rate constants span the narrow range between 4 x 10 and 2 X 10 s which shows that the spin-state interconversion process for iron(II) complexes is less rapid than for complexes of iron(III) and cobalt(II). 

Table 3. Rate constants and activation parameters for the LS HS and HS LS unimolecular spin-state interconversions in iron(II) complexes...

Step 1. An enzymatic reaction is considered as a cyclic process that displays all the interconversions among the various enzyme forms involved. For each step in the reaction a rate constant is defined in terms of the product of the actual rate constant for that step and the concentration of free substrate involved in the step. Hence, the cyclic form of the reaction scheme given in Equations 17.6, 17.7, and 17.8 is represented by... 

If the rate constants for interconversion between M and ML are infinitesimally small (on the effective timescale of the experimental conditions), the complex does not contribute significantly to the supply of metal to the biosurface. The equilibrium equation (50) behaves as if frozen. In a biouptake process, the complex ML then does not contribute to the supply of metal towards the biosurface, and all the expressions given in Section 2 apply, with the only noteworthy point that the value of c"M to be used differs from the total metal concentration. In this case, the complexed metal is not bioavailable on the timescale considered, as metal in the complex species is absent from any process affecting the uptake. 

Similar to irreversible reactions, biochemical interconversions with only one substrate and product are mathematically simple to evaluate however, the majority of enzymes correspond to bi- or multisubstrate reactions. In this case, the overall rate equations can be derived using similar techniques as described above. However, there is a large variety of ways to bind and dissociate multiple substrates and products from an enzyme, resulting in a combinatorial number of possible rate equations, additionally complicated by a rather diverse notation employed within the literature. We also note that the derivation of explicit overall rate equation for multisubstrate reactions by means of the steady-state approximation is a tedious procedure, involving lengthy (and sometimes unintelligible) expressions in terms of elementary rate constants. See Ref. [139] for a more detailed discussion. Nonetheless, as the functional form of typical rate equations will be of importance for the parameterization of metabolic networks in Section VIII, we briefly touch upon the most common mechanisms. 

The broad and nearly universal applicability of the cinchonan carbamate CSPs for chiral acid separations is further corroborated by successful enantiomer separations of acidic solutes having axial and planar chirality, respectively. For example, Tobler et al. [124] could separate the enantiomers of atropisomeric axially chiral 2 -dodecyloxy-6-nitrobiphenyl-2-carboxylic acid on an C-9-(tert-butylcarbamoyl)quinine-based CSP in the PO mode with a-value of 1.8 and Rs of 9.1. This compound is stereolabile and hence at elevated temperatures the two enantiomers were interconverted during the separation process on-column revealing characteristic plateau regions between the separated enantiomer peaks. A stopped-flow method was utilized to determine the kinetic rate constants and apparent rotational energy barriers for the interconversion process in the presence of the CSP. Apparent activation energies (i.e., energy barriers for interconversion) were found to be 93.0 and 94.6 kJ mol for the (-)- and (-l-)-enantiomers, respectively. 

Simplifications ease the extraction of accurate values for the rate constants. For example, the keto, enol interconversion may sometimes be ignored, and k 2 > Xc, and Xtj > k are justifiable assumptions. ... 

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