Collision rate reactive

Carbenium ions are generally so reactive that the rate of their addition reactions with monomer or with a basic scavenger can be very close to the collision rate. 

Therefore, Eact = RT, which shows that even when threshold energy E() is zero, the Eact has a non-zero value. In case of line of center model, a collision is reactive only if the component of the relative translational energy along the line joining the centre of mass of the two molecules exceeds E0. In case of line of centers of model, the rate constant is given by... 

The rate of aggregation of fully renneted micelles is very sensitive to temperature. At room temperature it is appreciably less than the diffusional collision rate, which led Payens (1977) to consider the possibility that only a fraction of the surface is reactive (so-called hot spots). The idea of hot spots is consistent with the low fractal dimension of micelle clusters formed during renneting and leads to only a proportion of all encounters between fully renneted micelles being successful. In effect, a statistical prefactor is included in the reaction kernel to reduce the diffusion rate to a level comparable with experiment. However, Payens developed the idea of hot spots only within his theory of the aggregation of fully renneted micelles. 

Another consequence of these forces is that reactive ion-molecule collisions ( ion-molecule reactions ), in contrast to neutral gas reactions, in many cases do not possess activation energy barriers and thus proceed at the collision rate [37]. 

In these expressions k is the rate constant, p and E are the entropy term and the energy of activation respectively for breaking the chemical bonds Z is the collision rate. It will be noted that the first and third of the additional factors for interfacial reaction, i.e. the surface pressure II and the film cohesion have been included in the accessibility function tj). This is defined as the relative accessibility of the potentially reactive groups in the film it is unity at high areas when II 0 and when the cohesion also becomes negligible. 

Arrhenius believed that for molecules to react upon collision they must become activated, so the parameter came to be known as the activation energy. His ideas were refined by later scientists. In 1915 A. Marcelin pointed out that, while molecules make many collisions, not all collisions are reactive. Only those collisions for which the collision energy (i.e., the relative translational kinetic energy of the colliding molecules) exceeds some critical energy result in reaction. Thus, Marcelin gave a dynamic interpretation for the activation energy inferred from reaction rates. 

Pan states that CH4 is more reactive than ammonia so that there is likely to be some mass transfer limitation on methane as well as ammonia. Making an assumption that the surface mole fractions of reactants will be of the order of half the bulk gas-phase levels, approximate reaction probabilities for NH3 and CH4 can be calculated. Collision rates are about 2 x 10 molecules cm" s" so that the reaction probability for ammonia and methane is about 10" and for oxygen about 2.5 x 10". These are sufficiently close to the values for independent oxidation of CH4 and NH3 to make it likely that the same surface reactions are also involved in the co-oxidation. 

The published data on the reaction of N" " with O2 is more complicated than the reactions discussed above. Three drift tube studies show flat translational energy dependencies with the rate constant approximately half the collision rate. " In contrast, both HTFA data " and a previous NO A A temperature dependence data found the rate constant to increase with increasing temperature until the rate saturates at approximately the collision limit. The results indicated that rotational energy had a large influence on the reactivity and translational energy did not. This is in contrast to the other results summarized in this chapter. Therefore, we have very recently reexamined the rate constants for this reaction in both the HTFA and a selected ion flow tube (SIFT) in our laboratory. 

Reaction is not under free dilfusion control or there is preformed reactive complex or the dilfusion is two-dimensional (on surface) or one-dimensional (along a polymer strand) or molecular attractions arc enhancing collision rates or the assumed mechanism is wrong or there is an unexpected catalytic effect and so on. 

The rate results from Stem-Volmer plots depend directly upon the assumption that k is equal to the collision rate. This can be checked by diluting the sample gas with different inert collision partners. Unfortunately, because the product yield drops as the pressure is increased, these experiments have generally been done with neat samples. However, the Stem-Volmer plot also contains an internal check on the strong collision assumption. Suppose that a single collision does not completely stabilize the excited molecule so that it can continue to react, but at a lower rate. Residual reactivity at the... 

Since all collisions are reactive, is k if- The term 4-iTpD is the rate constant for diffusion resulting from the concentration gradient. The microscopic rate constant k is the limiting rate constant for infinitely fast translatory diffusion D = °°. In practice k has been assumed to be no greater than the rate constant for collisions in the vapor phase (4). 

We saw in Section 1.2(i) that the position of the fall-off on the pressure scale is determined by the competition between the rates of decay to products and of deexcitation of the reactive molecules. Also, we will see shortly that the calculation of the unimolecular rate constant through the use of equations (2.26), (3.4) and (4.9) gives a virtually exact representation of the shape of the fall-off, but that the pressure at which the fall-off occurs is only reproduced correctly if the relaxation rate g is chosen to be about an order of magnitude smaller than the collision rate Z[M], For this reason, Nordholm introduced the idea of an effective strong collision whose rate constant is given by [78.N]... 

If the assumption is made that all collisions are reactive collisions (obviously reasonable only for reactions with large rate constants), one can ignore the effects of nonreactive collisions on power absorption and use Eq. (14) for power absorption at resonance. Combining Eq. (26a) with Eq. (14) and using Eq. (53a) for P(t), one obtains... 

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