Activation-limited reaction

The values, ranging from 3 to 6 M are seven orders of magnitude smaller than the selectivity observed for activation limited reactions with stable cations, and can be used as evidence that the reaction with azide ion is a diffusion controlled process. Choosing a value for the rate constant for a diffusion-limited... 

Solution reactions that are much slower than diffusion-limited reactions are called activation-limited reactions. After an encounter occurs, the molecules undergo numerous collisions inside a cage of other molecules before finally reacting. The rate of collisions is very large (see Example 9.12), but only a small fraction of them will lead to reaction. If this fraction depends only on the temperature, the rate will be proportional to the number of encounters as well as to the fraction of collisions that lead to reaction. Since the number of 2-3 encounters is proportional to the number of type 2 molecules and the number of type 3 molecules, an activation-limited bimolecular elementary reaction is first order with respect to each reactant and second order overall, just as with a diffusion-limited reaction and a gas-phase reaction. The rate of a reaction between molecules of the same substance is second order with respect to that substance, and its temperature dependence should be similar to that of a gas-phase reaction. 

The temperature dependence of rate constants for both gaseous and liquid-state reactions is usually well described by the Arrhenius formula, Eq. (12.3-2). For activation-limited reactions, the activation energies are roughly equal to those for gas-phase reactions. This is as expected, since the collisional activation is very similar to that of gaseous reactions. In the case of diffusion-limited reactions, the temperature dependence of the rate constant is governed by the diffusion coefficients. Diffusion coefficients in liquids commonly have a temperature dependence given by Eq. (10.4-5), which is also of the same form as the Arrhenius formula ... 

The activation energies are somewhat smaller than for activation-limited reactions, often near the values for the energies of activation for diffusion processes. 

Catalyst Effectiveness. Even at steady-state, isothermal conditions, consideration must be given to the possible loss in catalyst activity resulting from gradients. The loss is usually calculated based on the effectiveness factor, which is the diffusion-limited reaction rate within catalyst pores divided by the reaction rate at catalyst surface conditions (50). The effectiveness factor E, in turn, is related to the Thiele modulus,

first-order rate constant, a the internal surface area, and the effective diffusivity. It is desirable for E to be as close as possible to its maximum value of unity. Various formulas have been developed for E, which are particularly usehil for analyzing reactors that are potentially subject to thermal instabilities, such as hot spots and temperature mnaways (1,48,51). 

Similarly, triphenylphosphine dichloride (TPPCI2) can activate aromatic carboxylic acids in pyridine through the formation of acyloxyphosphonium salts (Scheme 2.30).313 A side reaction between tire intermediate acyloxyphosphonium species and a second carboxyl endgroup leading to the formation of anhydrides has been reported.313 This chain-limiting reaction decreases tire molar mass, while the presence of anhydride linkages in tire chains adversely affects the thermal and hydrolytic stability of the final polyester. 

Active control of metabolite flux involves changes in the concentration, catalytic activity, or both of an enzyme that catalyzes a committed, rate-limiting reaction. 

On the other hand, the low temperature dependance of the rate constants with activation energies around 5 kcal/mole indicates a diffusion limited reaction rate which could refer to diffusion of oxygene into the fibers of the board, i.e. into the fiberwalls. The corresponding negative activation energy for the groundwood based hardboard and the effect of fire retardants there upon are difficult to understand. 

There are two limiting cases in this model, one in which the reaction is diffusion limited (ka J>> d), the other in which the reaction is activation limited ( d >S> ka). In the activation limited process, Eq. (17) simplifies to... 

Qualitatively, one can now deduct the apparent activation energy As for the case of a diffusion-limited reaction. If we plot the logarithm of the product of the efficiency factor and the constant for the speed of reaction ln[kij] against 1/T, a typical curve with three regimes can be seen (see Figure 11.15). 

The reaction kinetic study suggested that dye molecules in DDSNs have limited reaction activity although they are accessible to outside species. If highly reactive dye molecules are desirable in DDSNs, less dense silica nanomatrixes should be considered, such as mesoporous nanostructures. 

Our interest in thermally activated unimolecular reactions is in the change of kuni with pressure from the high to the zero pressure limit, and in the pressure dependence of the isotope effect over that range. One particularly interesting study carried out by Rabinovitch and Schneider (reading list) focused on the isomerization of methyl isocyanide, CH3NC, to methyl cyanide, CH3CN... 

It is convenient initially to classify elementary reactions either as energy-transfer-limited or chemical reaction-rate-limited processes. In the former class, the observed rate corresponds to the rate of energy transfer to or from a species either by intermolecular collisions or by radiation, or intramolecular-ly due to energy transfer between different degrees of freedom of a species. All thermally activated unimolecular reactions become energy-transfer-limited at high temperatures and low pressures, because the reactant can receive the necessary activation energy only by intennolecular collisions. 

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