Kinetics concentration dependence

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

The kinetics of initiation reactions of alkyllithium compounds often exhibit fractional kinetic order dependence on the total concentration of initiator as shown in Table 2. For example, the kinetics of the initiation reaction of //-butyUithium with styrene monomer in benzene exhibit a first-order dependence on styrene concentration and a one-sixth order dependence on //-butyUithium concentration as shown in equation 13, where is the rate constant for... 

The often fast binding step of the inhibitor I to the enzyme E, forming the enzyme inhibitor complex E-I, is followed by a rate-determining inactivation step to form a covalent bond. The evaluation of affinity labels is based on the fulfillment of the following criteria (/) irreversible, active site-directed inactivation of the enzyme upon the formation of a stable covalent linkage with the activated form of the inhibitor, (2) time- and concentration-dependent inactivation showing saturation kinetics, and (3) a binding stoichiometry of 1 1 of inhibitor to the enzyme s active site (34). 

Salt flux across a membrane is due to effects coupled to water transport, usually negligible, and diffusion across the membrane. Eq. (22-60) describes the basic diffusion equation for solute passage. It is independent of pressure, so as AP — AH 0, rejection 0. This important factor is due to the kinetic nature of the separation. Salt passage through the membrane is concentration dependent. Water passage is dependent on P — H. Therefore, when the membrane is operating near the osmotic pressure of the feed, the salt passage is not diluted by much permeate water. 

The Michaelis constant is equal to substrate concentration at which the rate of reaction is equal to one-half the maximum rate. The parameters and characterize the enzymatic reactions that are described by Michaelis-Menten kinetics. is dependent on total... 

First-order reaction (Section 11.4) A reaction whose rate-limiting step is unimolecular and whose kinetics therefore depend on the concentration of only one reactant. 

The simplest case to be analyzed is the process in which the rate of one of the adsorption or desorption steps is so slow that it becomes itself rate determining in overall transformation. The composition of the reaction mixture in the course of the reaction is then not determined by kinetic, but by thermodynamic factors, i.e. by equilibria of the fast steps, surface chemical reactions, and the other adsorption and desorption processes. Concentration dependencies of several types of consecutive and parallel (branched) catalytic reactions 52, 53) were calculated, corresponding to schemes (Ila) and (lib), assuming that they are controlled by the rate of adsorption of either of the reactants A and X, desorption of any of the products B, C, and Y, or by simultaneous desorption of compounds B and C. 

The shape of the kinetic curves depends on the catalyst type and polymerization conditions (ethylene pressure, temperature, concentration of inhibitors in reaction medium) (89, 97, 98). The types of the kinetic curves obtained. at ethylene polymerization under various conditions are presented in Fig. 1. 

Kresge et a/.498 have drawn attention to the fact that detritiation of [3H]-2,4,6-trihydroxy- and [3H]-2,4,6-trimethoxy-benzenes by concentrated aqueous perchloric acid gives correlations of log rate coefficient with — H0 with slopes of 0.80 and 1.14 respectively. Protonation to give the carbon conjugate acids is, however, governed by h0lA0 and h0l 9S, respectively, which suggests that the difference in kinetic acidity dependence is a property of the substrate and should not be interpreted as a major difference in mechanism. The kinetic difference can be eliminated by an appropriate comparison of kinetic and equilibrium acidity dependencies. In equation (230)... 

Each of these variables will be considered in this book. We start with concentrations, because they determine the form of the rate law when other variables are held constant. The concentration dependences reveal possibilities for the reaction scheme the sequence of elementary reactions showing the progression of steps and intermediates. Some authors, particularly biochemists, term this a kinetic mechanism, as distinct from the chemical mechanism. The latter describes the stereochemistry, electron flow (commonly represented by curved arrows on the Lewis structure), etc. 

The route from kinetic data to reaction mechanism entails several steps. The first step is to convert the concentration-time measurements to a differential rate equation that gives the rate as a function of one or more concentrations. Chapters 2 through 4 have dealt with this aspect of the problem. Once the concentration dependences are defined, one interprets the rate law to reveal the family of reactions that constitute the reaction scheme. This is the subject of this chapter. Finally, one seeks a chemical interpretation of the steps in the scheme, to understand each contributing step in as much detail as possible. The effects of the solvent and other constituents (Chapter 9) the effects of substituents, isotopic substitution, and others (Chapter 10) and the effects of pressure and temperature (Chapter 7) all aid in the resolution. 

The cure kinetics will depend on the initial isocyanate to hydroxy ratio and on the humidity. Assuming that the concentration of water in the coating is constant during cure, it is possible to define the following parameter which determines the effect of humidity on cure ... 

The oxidation by Mn(Iir) in a perchlorate medium follows two kinetic paths depending on the bromide concentration, viz. 

The PL-catechin conjugate showed greatly amplified concentration-dependent inhibition activity against bacterial collagenase (ChC) on the basis of the catechin unit, which is considered to be due to effective multivalent interaction between ChC and the catechin unit in the conjugate. The kinetic study suggests that this conjugate is a mixed-type inhibitor for ChC. Hyaluronidase is an enzyme which catalyzes hydrolysis of hyaluronic acid and is often involved in a number... 

For a classical diffusion process, Fickian is often the term used to describe the kinetics of transport. In polymer-penetrant systems where the diffusion is concentration-dependent, the term Fickian warrants clarification. The result of a sorption experiment is usually presented on a normalized time scale, i.e., by plotting M,/M versus tll2/L. This is called the reduced sorption curve. The features of the Fickian sorption process, based on Crank s extensive mathematical analysis of Eq. (3) with various functional dependencies of D(c0, are discussed in detail by Crank [5], The major characteristics are... 

It is also possible to use integral methods to determine the concentration dependence of the reaction rate expression and the kinetic parameters involved. In using such approaches one again requires a knowledge of the equilibrium constant for use with one of the integrated forms developed in Section 5.1.1. 

Adsorption kinetics of Zn on the untreated soil and the soils with the removal of organic matter and Fe oxides has been studied in detail by Hinz and Selim (1999) using a thin disk flow method. They reported that Zn sorption was highly concentration-dependent. When Zn concentration was... 

The original proposal of the approach, supported by a Monte Carlo simulation study [36], has been further validated with both pre-clinical [38, 39] and clinical studies [40]. It has been shown to be robust and accurate, and is not highly dependent on the models used to fit the data. The method can give poor estimates of absorption or bioavailability in two sets of circumstances (i) when the compound shows nonlinear pharmacokinetics, which may happen when the plasma protein binding is nonlinear, or when the compound has cardiovascular activity that changes blood flow in a concentration-dependent manner or (ii) when the rate of absorption is slow, and hence flip-flop kinetics are observed, i.e., when the apparent terminal half-life is governed by the rate of drug input. 

However, there is another operative timescale in solution. This is that timescale for reaction with other photolytically generated species or with added reactants. This reaction cannot take place faster than the diffusion-limited reaction rate which is concentration dependent (59). Typical diffusion-controlled reaction rate constants are 109-1010 dm3 mol"1 second-1. By comparison, a typical gas-kinetic rate con-... 

We wish to account for (i.e., interpret) the Arrhenius parameters A and EA, and the form of the concentration dependence as a product of the factors c (the order of reaction). We would also like to predict values of the various parameters, from as simple and general a basis as possible, without having to measure them for every case. The first of these two tasks is the easier one. The second is still not achieved despite more than a century of study of reaction kinetics the difficulty lies in quantum mechanical... 

In the absence of S2, the true Michaelis constant, Kml, is obtained. Consequently, the values of f and Vmax determined in a kinetics study depend upon the composition (csl and cS2) and total substrate concentration within the system. 

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