Reaction rates perpendicular effect

This is indeed the expression (4.106) for the reaction-rate constant of hard spheres impinging on a surface, is the average velocity of the atoms perpendicular to the surface and nd is the effective surface area of an adsorbed atom (5 = A max ... 

Brilman et al. [42] and Lin et al. [44] using a numerical method, Nagy [48] by using an analytical method, investigated the effect of the second, third, etc. particles (perpendicular to the gas-liquid interface) on the absorption rate. They obtained that, in most cases, the first particle determines the absorption rate. However, in special cases, the effect of these particles can also be important. Nagy solved the mass transfer problem analytically for the number of particles in the diffusion path [48]. For the sake of completeness we will give the absorption rate for that case, as well (for details see [48] ). The mass transfer is accompanied here by a first-order chemical reaction. This situation is illustrated in Fig. 1 where three particles are located behind each other. The absorption rate... 

The dominant contributor to the reactivity of vinylcyclopropanes in any radical reaction is the form (4a), the cyclopropylcarbinyl radical system. The opening of a cyclopropylcarbinyl radical to a butenyl radical is among the fastest radical processes known, with a rate constant of 1.3 x 10 sec". - The various stereoelectronic effects of this rearrangement have been reviewed. The structure of (4a), deduced from its ESR spectrum - and in agreement with calculations (STO-36 basis set), is in the bisected conformation shown, predicted to be 1.4 kcal mol more stable than its perpendicularly oriented counterpart. Above -KX) T only the butenyl radical (4b) can be detected. Substituent efiects do not seem to operate here when the substituents are on the cyclopropane (i.e. product stabilization). The cy-clopropylcaibinyl cation and anion have structures similar to (4a), bisect conformations (5) and (6), respectively. A concise summary of solvolytic and mechanistic data for system (5) has recently appeai Reviews of cyclopropylcarbinyl anions and carbenes are also available. - ... 

In mineral dissolution reactions, net effects of dissolution can be translated into linear rates of recession of crystal surfaces in a direction perpendicular them. For dissolution of silicate minerals in water near 25°C under laboratory conditions, the linear dissolution rates are generally carbonate minerals calcite and dolomite, the linear dissolution rates are higher, I0o 1 mmyr 1, and for long period of time this translates into very high dissolution rates of more than 1 meter in 1000 years. 

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