Quasi-equilibrium assumption

The quasi-equilibrium assumption in the above canonical fonn of the transition state theory usually gives an upper bound to the real rate constant. This is sometimes corrected for by multiplying (A3.4.98) and (A3.4.99) with a transmission coefifiwient 0 < k < 1. 

QUASI-EQUILIBRIUM ASSUMPTION QUASI-EQUIVALENCE Quasi-racemic compound,... 

QUASI-EQUILIBRIUM ASSUMPTION RAPID EQUILIBRIUM MECHANISMS Rapid gel filtration of biomacromolecules, RAPID BUFFER EXCHANGE RAPID MIXING... 

Readers might have noticed that the two chain reactions, (i) Reactions 2-121 and 2-122 and (ii) Reactions 2-116 and 2-117, are similar, but were treated differently. Reactions 2-116 and 2-117 were treated using the quasi-equilibrium assumption, but may also be treated using the steady-state concept. The result is a more complicated expression, which would reduce to the experimental reaction rate law if < ii6b- Readers can work this problem out as an exercise. Therefore, the... 

For multisubstrate enzymatic reactions, the rate equation can be expressed with respect to each substrate as an m function, where n and m are the highest order of the substrate for the numerator and denominator terms respectively (Bardsley and Childs, 1975). Thus the forward rate equation for the random bi bi derived according to the quasi-equilibrium assumption is a 1 1 function in both A and B (i.e., first order in both A and B). However, the rate equation for the random bi bi based on the steady-state assumption yields a 2 2 function (i.e., second order in both A and B). The 2 2 function rate equation results in nonlinear kinetics that should be differentiated from other nonlinear kinetics such as allosteric/cooperative kinetics (Chapter 6, Bardsley and Waight, 1978) and formation of the abortive substrate complex (Dalziel and Dickinson, 1966 Tsai, 1978). 

Note that the transfer coefficient obtained here is not in any way related to the symmetry factor. It follows from the quasi-equilibrium assumption and should therefore be a true constant, independent of potential and temperature, as long as the assumptions leading to Eq. 43F are valid. 

The acceleration term is dropped in this equation. Consider the situation that L (, (, and t = x, xr. Now make the following assumptions (1) the relaxation time is independent of particle energy and is a constant and (2) the quasi-equilibrium assumption is made for the term... 

Quasi-equilibrium assumption for all steps, but the second one gives expressions for surface coverage of dinitrogen, hydrogen and ammonia... 

A. Quasi-equilibrium assumption also known as the rapid-equilibrium assumption in which an equilibrium condition exists between the enzyme E, its substrate (A) and the enzyme-substrate complex (EA), i.e. ... 

The steady-state kinetic treatment of random reactions is complex and gives rise to rate equations of higher order in substrate and product terms. For kinetic treatment of random reactions that display the Michaelis-Menten (i.e. hyperbolic velocity-substrate relationship) or linear (linearly transformed kinetic plots) kinetic behavior, the quasi-equilibrium assumption is commonly made to analyze enzyme kinetic data. 

TABLE 11.5 Cleland nomenclature for bisubstrate reactions exemplified. Three common kinetic mechanisms for bisubstrate enzymatic reactions are exemplified. The forward rate equations for the order bi bi and ping pong bi hi are derived according to the steady-state assumption, whereas that of the random bi bi is based on the quasi-equilibrium assumption. These rate equations are first order in both A and B, and their double reciprocal plots (1A versus 1/A or 1/B) are linear. They are convergent for the order bi bi and random bi bi but parallel for the ping pong bi bi due to the absence of the constant term (KiaKb) in the denominator. These three kinetic mechanisms can be further differentiated by their product inhibition patterns (Cleland, 1963b)... 

At low overpotentials Vj > Vq and Vj > Vq and the coverage 0 may again be found by applying the quasi-equilibrium assumption to reaction A. By an identical argument to that above, the coverage will be given by equation (1.94). Hence the current for this mechanism will be given by... 

The rate equations valid for one rapid step (Equation 2.30 or 2.32) can be obtained more easily by applying the quasi-equilibrium assumption directly. For instance, if step I is rapid,... 

The quasi-equilibrium assumption is frequently used in the heterogeneous catalysis, since the surface reaction steps are often rate-Hmiting, while the adsorption steps are rapid. This is not necessarily true for large molecules. Here we consider the application of the quasi-equilibrium hypothesis on two kinds of reaction mechanisms, an Eley-Rideal mechanism and a Langmuir-Hinshelwood mechanism. The rate expressions obtained with this approach are referred to as Langmuir-Hinshelwood-Hougen-Watson (LHHW) equations in the literature, in honor of the pioneering researchers. 

The quasi-equilibrium assumption, that is the basis for the use of the Boltzmann distribution law, may lose its validity for rapid reactions. In such reactions, the most energetic reactant molecules may disappear very rapidly and the concentration of species at the transition state may be lesser than that for a trae equilibrium. In practice, even when EJRTk 3, as in the Cl+HBr—>HCH-Br hydrogen atom abstraction, internal-state nonequilibrium effects are very small [6]. 

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