Mass kinetic assumption

Gas volume relations from equations Gas stoichiometry involving mass Basic assumptions of the kinetic theory of gases Predictions of the kinetic theory... 

In other words, for the forward reaction the rate at which an individual A molecule transforms into a B molecule in the reaction A B does not depend on NA or [A], This assumption is valid if each molecule of A does not interact with other A molecules (even indirectly) in transforming from A to B. Similarly for the reverse reaction, if j does not depend on [B] the reverse kinetics are governed by the law of mass action. (The mass-action assumption is not valid for the overall reaction, for example, if the reaction is catalyzed by an enzyme and the number of sites available for interaction with the enzyme depends on the total number of A and B molecules in the system competing for the enzyme. We shall see that when an enzyme catalyzes a reaction A = B, the overall reaction is typically modeled by a number of subreactions, each of which is governed by mass action.)... 

The application of dimensional analysis to Eq. (38) yields, under the assumption that heat and macroscopic kinetic energy are fundamentally different physical quantities (so that five units are required—heat, mass, length, time, and temperature), the expression... 

The Hamiltonian for this system should include the kinetic and potential energy of the electron and both of the nuclei. However, since the electron mass is more than a thousand times smaller than that of the lightest nucleus, one can consider the nuclei to be effectively motionless relative to the quickly moving electron. This assumption, which is basically the Born-Oppenheimer approximation, allows one to write the Schroedinger equation neglecting the nuclear kinetic energy. For the Hj ion the Born-Oppenheimer Hamiltonian is... 

Previous theoretical kinetic treatments of the formation of secondary, tertiary and higher order ions in the ionization chamber of a conventional mass spectrometer operating at high pressure, have used either a steady state treatment (2, 24) or an ion-beam approach (43). These theories are essentially phenomenological, and they make no clear assumptions about the nature of the reactive collision. The model outlined below is a microscopic one, making definite assumptions about the kinematics of the reactive collision. If the rate constants of the reactions are fixed, the nature of these assumptions definitely affects the amount of reaction occurring. 

Solution Under the assumption of intrinsic kinetics, all mass transfer steps are eliminated, and the reaction rate is determined by Steps 4-6. The simplest possible version of Steps 4-6 treats them all as elementary, irreversible reactions ... 

For fast reactions Da becomes large. Based on that assumption and standard correlations for mass transfer inside the micro channels, both the model for the micro-channel reactor and the model for the fixed bed can be reformulated in terms of pseudo-homogeneous reaction kinetics. Finally, the concentration profile along the axial direction can be obtained as the solution of an ordinary differential equation. 

Let us now consider the situation where [/] [E], We have here a situation that is analogous to our discussion of pseudo-first-order kinetics in Appendix 1. When [/] E in equilibrium binding studies, the diminution of [/]f due to formation of El is so insignificant that we can ignore it and therefore make the simplifying assumption that [/]f = [/]T. Combining this with the mass balance Equations (A2.1) and (A2.2), and a little algebra, we obtain... 

The situation is different for reactions of very hydrophilic ions, e.g. hydroxide and fluoride, because here overall rate constants increase with increasing concentration of the reactive anion even though the substrate is fully micellar bound (Bunton et al., 1979, 1980b, 1981a). The behavior is similar for equilibria involving OH" (Cipiciani et al., 1983a, 1985 Gan, 1985). In these systems the micellar surface does not appear to be saturated with counterions. The kinetic data can be treated on the assumption that the distribution between water and micelles of reactive anion, e.g. Y, follows a mass-action equation (9) (Bunton et al., 1981a). 

In the biomedical literature (e.g. solute = enzyme, drug, etc.), values of kf and kr are often estimated from kinetic experiments that do not distinguish between diffusive transport in the external medium and chemical reaction effects. In that case, reaction kinetics are generally assumed to be rate-limiting with respect to mass transport. This assumption is typically confirmed by comparing the adsorption transient to maximum rates of diffusive flux to the cell surface. Values of kf and kr are then determined from the start of short-term experiments with either no (determination of kf) or a finite concentration (determination of kT) of initial surface bound solute [189]. If the rate constant for the reaction at the cell surface is near or equal to (cf. equation (16)), then... 

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