Rate-determining/limiting step approximation

The reaction of Si02 with SiC [1229] approximately obeyed the zero-order rate equation with E = 548—405 kJ mole 1 between 1543 and 1703 K. The proposed mechanism involved volatilized SiO and CO and the rate-limiting step was identified as product desorption from the SiC surface. The interaction of U02 + SiC above 1650 K [1230] obeyed the contracting area rate equation [eqn. (7), n = 2] with E = 525 and 350 kJ mole 1 for the evolution of CO and SiO, respectively. Kinetic control is identified as gas phase diffusion from the reaction site but E values were largely determined by equilibrium thermodynamics rather than by diffusion coefficients. 

It is important to realize that the assumption of a rate-determining step limits the scope of our description. As with the steady state approximation, it is not possible to describe transients in the quasi-equilibrium model. In addition, the rate-determining step in the mechanism might shift to a different step if the reaction conditions change, e.g. if the partial pressure of a gas changes markedly. For a surface science study of the reaction A -i- B in an ultrahigh vacuum chamber with a single crystal as the catalyst, the partial pressures of A and B may be so small that the rates of adsorption become smaller than the rate of the surface reaction. 

It is worth noting that Murr and Donnelly (1970a,b) have demonstrated that the secondary a-deuterium KIE is only approximately 75% of the theoretical maximum kinetic isotope effect when the ionization (ki) step of the reaction (Scheme 1) is fully rate determining, i.e. when the reaction occurs via a limiting SN1 mechanism (Shiner, 1970b Westaway, 1987c). 

Equations 2.26 and 2.27 carmot be solved analytically except for a series of limiting cases considered by Bartlett and Pratt [147,192]. Since fine control of film thickness and organization can be achieved with LbL self-assembled enzyme polyelectrolyte multilayers, these different cases of the kinetic case-diagram for amperometric enzyme electrodes could be tested [147]. For the enzyme multilayer with entrapped mediator in the mediator-limited kinetics (enzyme-mediator reaction rate-determining step), two kinetic cases deserve consideration in this system in both cases I and II, there is no substrate dependence since the kinetics are mediator limited and the current is potential dependent, since the mediator concentration is potential dependent. Since diffusion is fast as compared to enzyme kinetics, mediator and substrate are both approximately at their bulk concentrations throughout the film in case I. The current is first order in both mediator and enzyme concentration and k, the enzyme reoxidation rate. It increases linearly with film thickness since there is no... 

This represents the case where the first step is rate determining. (If this situation is known beforehand, one need not work through the steady-state approximation but merely write down dP/dt = k A since the first step is rate limiting and irreversible.)... 

Remember reactions involving more than one step often have one step that is slow compared with the other steps, and the overall rate is limited by the rate of this step, and can be approximated to the rate of this slow step. When this occurs, the slow step is termed the rate-determining step. Not all reactions have a rate-determining step. Sometimes the individual reactions have comparable rates, and the overall rate cannot be approximated to the rate of any individual step. 

So far we considered the surface process in the limit ofproximity to equilibrium which is, for the relaxation experiments discussed, often a sufficient approximation. In order to extend the validity range but also to highlight the situation from a different point of view, let us apply chemical kinetics to the surface process which we now decompose into the individual steps of the reaction sequence.23,24 172 248 The rate determining step is supposed to be one of these surface reaction steps. 

Crystallisation forms the most important and often the rate-limiting step in any structure determination. Much effort has been put into the crystallisation of small atoms or molecules (e.g., silicon, sugar) because of their technological importance. In comparison, systematic work with proteins is more complex. Proteins differ from small molecules in two respects with reference to crystallisation. (1) Proteins are highly solvated, even in the crystal, and so the relative lattice energies obtained from protein-protein contacts are small (Fig. 2). (2) Proteins possess many potential attachment sites of approximately equivalent energy to the small number of specific sites involved in the crystal and so there may be an equal incentive to form an amorphous precipitate or a crystal. The problem is to obtain a crystal rather than an amorphous precipitate as supersaturation conditions are approached. 

The quasi-equilibrium approximation relies on the assumption that there is a single rate-determining step, the forward and reverse rate constants of which are at least 100 times smaller than those of all other reaction steps in the kinetic scheme. It is then assumed that all steps other than the rds are always at equilibrium and hence the forward and reverse reaction rates of each non-rds step may be equated. This gives simple potential relations describing the varying activity of reaction intermediates in terms of the stable solution species (of known and potential-independent activity) that are the initial reactants or final products of the reaction. The variation of the activities of reaction intermediates is, however, restricted by either the hypothetical solubility limit of these species or, in the case of surface-confined reactions and adsorbed intermediates, the availability of surface sites. In both these cases, saturation or complete coverage conditions would result in a loss of the expected... 

Pegaptanib sodium was eliminated from the eye through systemic circulation with a terminal half-life from the vitreous of three to five days in both monkeys and rabbits. The plasma terminal half-life mimicked the vitreous humor half-life, indicative of flip-flop kinetics whereby the rate-limiting step that determines the systemic pegaptanib sodium concentration is the exit of the drug from the eye. From these observations one can estimate the vitreous humor terminal half-life in patients that would approximate the plasma terminal half-life. 

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