Equilibrium constant kinetic interpretation

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

The polymerization kinetics have been intensively discussed for the living radical polymerization of St with the nitroxides,but some confusion on the interpretation and understanding of the reaction mechanism and the rate analysis were present [223,225-229]. Recently, Fukuda et al. [230-232] provided a clear answer to the questions of kinetic analysis during the polymerization of St with the poly(St)-TEMPO adduct (Mn=2.5X 103,MW/Mn=1.13) at 125 °C. They determined the TEMPO concentration during the polymerization and estimated the equilibrium constant of the dissociation of the dormant chain end to the radicals. The adduct P-N is in equilibrium to the propagating radical P and the nitroxyl radical N (Eqs. 60 and 61), and their concentrations are represented by Eqs. (62) and (63) in the derivative form. With the steady-state equations with regard to P and N , Eqs. (64) and (65) are introduced, respectively ... 

Hersey and Robinson also foundthat many guest species that show kinetic behavior apparently explicable in terms of a single-step binding, give a discrepancy between the values of the equilibrium constant determined kinetically and those determined from equilibrium studies. It was found that the equilibrium constant, deterrmned spectrophotometrically, was usually greater than the ratio of the forward and backward rate-constants, determined kinetically. They therefore suggested that this discrepancy could be adequately explained if the two-step mechanism just described was used to interpret the results. A similar proposal has also been made by Hall and coworkers, who observed a large discrepancy between AV° values for the inclusion of 1-butanol and 1-pentanol by alpha cyclodextrin, calculated from equilibrium-density measurements and kinetic, ultrasonic-absorption data. 

The kinetic interpretation of the chemistry of oceanic waters (kinetics of inputs of primary constituents interactions between biologic and mixing cycles) leads to the development of steady state models, in which the relatively constant chemistry of seawater in the recent past (i.e., Phanerozoic cf. Rubey, 1951) represents a condition of kinetic equilibrium among the dominant processes. In a system at... 

The rate-controlling step is the elementary reaction that has the largest control factor (CF) of all the steps. The control factor for any rate constant in a sequence of reactions is the partial derivative of In V (where v is the overall velocity) with respect to In k in which all other rate constants (kj) and equilibrium constants (Kj) are held constant. Thus, CF = (5 In v/d In ki)K kg. This definition is useful in interpreting kinetic isotope effects. See Rate-Determining Step Kinetic Isotope Effects... 

As mentioned previously, unique kinetic results were obtained upon LFP of o-fluorophenyl azide,in that the singlet nitrene decays faster than the ketenimine is formed. This finding requires the presence of an intermediate, presumably ben-zazirine 40, between the singlet nitrene and ketenimine 42. The data could be interpreted by assuming that azirine 40 reverts easily to singlet nitrene according to the scheme below.The equilibrium constant is equal to the ratio of [40]/[39s] and was deduced to be 0.5 with AG 350 caFmol. Younger and Bell have also reported a system in which a benzazirine and ketenimine interconvert. 

In the interpretation of the kinetics, it was concluded that a mechanism involving adsorption equilibrium between methylcyclohexane in the gas phase and methylcyclohexane molecules adsorbed on platinum sites was not very likely. If Eq. (1) were interpreted on such a basis, then b would be an adsorption equilibrium constant. From the temperature dependence of b, one would calculate a heat of adsorption of 30 kcal./mole, which seems too high for adsorption of methylcyclohexane molecules as such. Furthermore, the small inhibition by aromatics casts doubt on such a picture, since the extent of adsorption of aromatics would be expected to be considerably greater than that of methylcyclohexane molecules at equilibrium, in view of the unsaturated nature of aromatics. 

A number of studies of H-atom transfer from hydrogen halides to free radicals, R + HX - RH + X, have been done by FPTRMS in which R was detected by photoionization, and its decay was monitored as a function of [HX] under pseudo-first-order conditions. When the rate coefficient is combined with determinations of the rate coefficient of the reverse reaction to obtain the equilibrium constant, the enthalpy of formation of the radical can be deduced. If the kinetics are accurately measured in isolation, this is a direct kinetic method which can be used to confirm (or otherwise) thermodynamic data obtained by classical, indirect kinetic methods which depend on correct mechanistic interpretation. In a number of instances free radical enthalpies of formation by these two different approaches have not been in good agreement. It is not the purpose of this short survey to discuss the differences, but rather to briefly indicate the extent to which the FPTRMS method has contributed to the kinetics of these reactions and to free radical thermochemistry. 

These are now probably the most widely used methods in kinetic and mechanistic studies, and include a wide range of spectral frequencies radio frequencies (NMR, ESR), IR and UV-vis. Appropriate instrumentation which is easily adapted for kinetics is readily available in most research laboratories it is usually easy to use, and the output easily interpreted. Spectrophotometric methods are also widely used for the determination of equilibrium constants [25]. However, before deciding upon a spectrophotometric technique, the following experimental aspects must be considered carefully. 

An additional factor that complicates interpretation of SPR data occurs when the partitioning species is multivalent. In solution the two sites on a bivalent antibody bind in an equivalent and independent manner. Upon binding to immobilised antigen the two sites can interact simultaneously and hence bind with greatly increased apparent affinity to what is expected from their solution behaviour. The reliance upon pseudo first order kinetic expressions based upon 1 1 stoichiometry for multivalent species such as antibodies can lead to quite erroneous estimates of equilibrium constants when using this approach [3]. 

Here we describe studies of the interaction of interleukin-6 (IL-6) with a soluble form of its cell surface receptor (sIL-6R). A procedure utilising a competition approach is presented which allows the determination of the equilibrium constant in solution thus avoiding any potential problems associated with deviation in kinetic characteristics upon surface immobilisation. In addition, binding characteristics of stable monomeric and dimeric forms of IL-6 are presented to demonstrate both the drastic influence of solute multivalency on kinetic and equilibrium properties and the importance of auxiliary techniques such as analytical ultracentrifugation for the interpretation of SPR data. 

The less protonated species are relatively insignificant. Crutchfield" " usedan expression which did not include the first term in (3) and consequently achieved best fit with different values of the rate coefficients to those reported by Goh et al. . The equilibrium constants, K, K2, for peroxodiphosphoric acid have been estimated as 2.0 and 0.3 by consideration of the corresponding values for hypo-phosphoric and pyrophosphoric acids. The values of the rate coefficients and the mechanistic interpretation of the kinetics are thus somewhat uncertain. Some data in terms of (3) has been published (Table 20). The activation energies for the overall process vary" from 18.3 (pH 0) to 28 kcal.mole (pH 3). 

The physical interpretation of this result is that deactivation is much faster than reaction. Hence, on average, many activations and deactivations will take place before reaction is likely to occur, leading to a pre-equilibrium between A and A. The equilibrium constant for this pre-equilibrium is ki/k-i, and so the rate expression implies in essence that the reaction takes place from an equilibrium concentration of A with a rate constant k2- Because the equilibrium concentration of A is proportional to [A] and independent of [M], the kinetics are truly first order and the rate constant is independent of the bath gas concentration [M]. 

The transition state theory gives us a framework to relate the kinetics of a reaction with the thermodynamic properties of the activated complex (Brezonik, 1990). In kinetics, one attempts to interpret the stoichiometric reaction in terms of elementary reaction steps and their free energies, to assess breaking and formation of new bonds, and to evaluate the characteristics of activated complexes. If, in a series of related reactions, we know the rate-determining ele-mentaiy reaction steps, a relationship between the rate constant of the reaction, k (or of the free energies of activation, AG ), and the equilibrium constant of the reaction step, K (or the free energy, AG°), can often be obtained. For two related reactions. 

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