Definition of kinetic constants

Interaction of Glycosidases with D-Glycals and Related Compounds (See Text for Definition of Kinetic Constants)... 

Competitive, 249, 123, 146, 190 [partial, 249, 124 progress curve equations for, 249, 176, 180 for three-substrate systems, 249, 133, 136] competitive-uncompetitive, 249, 138 concave-up hyperbolic, 249, 143 dead-end, 249, 124 [for bireactant kinetic mechanism determination, 249, 130-133 definition of kinetic constants, 249, 220-221 effects on enzyme progress curves, nonlinear regression analysis, 249, 71-72 inhibition constant evaluation, 249, 134-135 kinetic analysis with, 249, 123-143 one-substrate systems, 249, 124-126 unireactant systems, theory,... 

With the foregoing definition of kinetic constants, Eq. (4.38) can be reformulated into the kinetic form, and thus written by using the kinetic parameters only ... 

Definition of kinetic constants in terms of rate constants... 

If the interconversion of central complexes is taken into account (rate constants kg and fcio are present), the definition of kinetic constants in terms of rate constants becomes more complex (Plapp, 1973) ... 

Definition of Kinetic Constants in Terms of Rate Constants Ordered Ter Bi mechanism... 

In order to transform Eq. (16.9) from the rate constant form into a kinetic constant form, we shall divide the numerator and denominator with kik ik +ky), which is equal to CoefAB in Eq. (9.8) (Chapter 9) then, we shall transform the groups of rate constants into kinetic constants by using the appropriate definitions of kinetic constants from Eq. (9.9) (Chapter 9). The resulting rate equation for the A-Q exchange is... 

This Monte Carlo algorithm is able to reproduce both the equilibrium and kinetic properties of a generic surfactant solution in spite of the elementary definition of kinetic constants used. Of course, to get a more detailed description of micellization kinetics, a general theory to derive the kinetic constants as function of the surfactant molecular... 

To reduce the number of parameters in the kinetic equations that are to be determined from experimental data, we used the following considerations. The values klt k2, and k4 that enter into the definition of the constant L, (236), are of analogous nature they indicate the fraction of the number of impacts of gas molecules upon a surface site resulting in the reaction. So the corresponding preexponential factors should be approximately the same (if these elementary reactions are adiabatic). Then, since k1, k2, and k4 are of the same order of magnitude, their activation energies should be almost identical. It follows that L can be considered temperature independent. 

This approach provokes strong objections. First, the basic definition of rate constant becomes blurry. Indeed, none of the coefficients in the mass action law in the whole kinetic scheme can be considered as an independent physical... 

Definition of Rate Constants in Terms of Kinetic Constants... 

A noteworthy difference between the GP and Langmuir adsorption equations is the definition of the constants in each respective equation. The GP equation is derived from mass action thermodynamics so the equation constants are mass action constants. The Langmuir equation is most commonly derived from either a kinetic [62, 63] or statistical thermodynamic basis [62, 64]. As a result the constants in the Langmuir equation are functions of either rate constants or partition functions, respectively. 

Various experimental observations, obtained by studies of diverse nature, indirectly suggest that micellar pseudophase is not homogeneous in terms of micropolarity, water concentration, dielectric constant, and ionic strength (for ionic micelles). " This fact has not been considered in the classical pseudophase kinetic model hrst suggested by Berezin et al. " and Martinek et al. It is therefore logical for Davies et al. to suggest that the micellar pseudophase should be divided up into an arbitrary number of pseudophases, each with a different mean partition coefficient for the reactant or reactants and each with a different mean rate constant. This generalization of the classical (Berezin s) pseudophase model is referred to as the multiple micellar pseudophase (MMPP) model and leads to a kinetic equation similar to Equation 3.61 or Equation 3.11 with modified definitions of kinetic parameters such as kM (= (kMW]y,)KRKs) = E(kM iA Mr)KR iKs i with i = 1, 2, 3,. .., q Kr = S Kr, with i = 1, 2, 3,. .., q and Kg = X K i with i = 1,2, 3,..., q, where q represents an arbitrary number of micelle pseudophases. 

Minero et al. avoided exchange model formalism in the definition of exchange constants and used simple ratios between transfer constants because simple measurements of counterion activities showed that two kinds of counterions can independently associate with or dissociate from micelles even when they have the same charge. This model contains a fairly large number of assumptions, and experimentally usable kinetic equations could be obtained after several approximations. The quality of a model is not strictly proved by the fact that it is able to fit the data, especially if the model involves many approximations and assumptions that cannot be validated with convincing evidence. 

By definition, the kinetic constant ki is the average reaction rate per unit volume divided by the concentration of 5i,... 

Figure 10 shows that Tj is a unique function of the Thiele modulus. When the modulus ( ) is small (- SdSl), the effectiveness factor is unity, which means that there is no effect of mass transport on the rate of the catalytic reaction. When ( ) is greater than about 1, the effectiveness factor is less than unity and the reaction rate is influenced by mass transport in the pores. When the modulus is large (- 10), the effectiveness factor is inversely proportional to the modulus, and the reaction rate (eq. 19) is proportional to k ( ), which, from the definition of ( ), implies that the rate and the observed reaction rate constant are proportional to (1 /R)(f9This result shows that both the rate constant, ie, a measure of the intrinsic activity of the catalyst, and the effective diffusion coefficient, ie, a measure of the resistance to transport of the reactant offered by the pore stmcture, influence the rate. It is not appropriate to say that the reaction is diffusion controlled it depends on both the diffusion and the chemical kinetics. In contrast, as shown by equation 3, a reaction in solution can be diffusion controlled, depending on D but not on k. 

The quantities n, V, and (3 /m) T are thus the first five (velocity) moments of the distribution function. In the above equation, k is the Boltzmann constant the definition of temperature relates the kinetic energy associated with the random motion of the particles to kT for each degree of freedom. If an equation of state is derived using this equilibrium distribution function, by determining the pressure in the gas (see Section 1.11), then this kinetic theory definition of the temperature is seen to be the absolute temperature that appears in the ideal gas law. 

Symbols used are defined at the end of this paper. The definitions of other pseudo-kinetic rate constants can be found in earlier papers (6,7). 

Although the concepts of specific acid and specific base catalysis were useful in the analysis of some early kinetic data, it soon became apparent that any species that could effect a proton transfer with the substrate could exert a catalytic influence on the reaction rate. Consequently, it became desirable to employ the more general Br0nsted-Lowry definition of acids and bases and to write the reaction rate constant as... 

On the experimental side, evidence was accumulating that there is more than one kind of reducing species, based on the anomalies of rate constant ratios and yields of products (Hayon and Weiss, 1958 Baxendale and Hughes, 1958 Barr and Allen, 1959). The second reducing species, because of its uncertain nature, was sometimes denoted by H. The definite chemical identification of H with the hydrated electron was made by Czapski and Schwarz (1962) in an experiment concerning the kinetic salt effect on reaction rates. They considered four... 

Kinetic theory indicates that equation (32) should apply to this mechanism. Since the extent of protonation as well as the rate constant will vary with the acidity, the sum of protonated and unprotonated substrate concentrations, (Cs + Csh+), must be used. The observed reaction rate will be pseudo-first-order, rate constant k, since the acid medium is in vast excess compared to the substrate. The medium-independent rate constant is k(), and the activity coefficient of the transition state, /, has to be included to allow equation of concentrations and activities.145 We can use the antilogarithmic definition of h0 in equation (33) and the definition of Ksh+ in equation (34) ... 

The overall effect of the preceding chemical reaction on the voltammetric response of a reversible electrode reaction is determined by the thermodynamic parameter K and the dimensionless kinetic parameter . The equilibrium constant K controls mainly the amonnt of the electroactive reactant R produced prior to the voltammetric experiment. K also controls the prodnction of R during the experiment when the preceding chemical reaction is sufficiently fast to permit the chemical equilibrium to be achieved on a time scale of the potential pulses. The dimensionless kinetic parameter is a measure for the production of R in the course of the voltammetric experiment. The dimensionless chemical kinetic parameter can be also understood as a quantitative measure for the rate of reestablishing the chemical equilibrium (2.29) that is misbalanced by proceeding of the electrode reaction. From the definition of follows that the kinetic affect of the preceding chemical reaction depends on the rate of the chemical reaction and duration of the potential pulses. 

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