Collisions factors

Denoting the rate constant by k, absolute temperature by T, the gas constant by R, and a collision factor by Z ... 

Assuming a reaction order of one concerning hydrogen and a reaction order of zero regarding carbon monoxide (according to Post et al.20), the activation energy Ea and the collision factor k0 can be derived via the Arrhenius relation ... 

Activation Energy, and Collision Factor, Arlt of Carbon Nanomaterial-Supported Co Catalysts and Commercially Used Fischer-Tropsch Catalysts... 

The resulting activation energies Eh as well as the collision factors mCOO are displayed in Table 2.2. The most active material among the nanomaterials is the Co/MW catalyst, with the highest values for both kinetic parameters (Ek and f m co.o)- The lowest activation energy and collision factor, in contrast, is seen with the herringbone material. 

Chemical adsorption or surface complexation as given in Eq. (6.21) attempts to relate to the "collision" factor A in Eq. (6.12) to the surface concentrations of adsorbed ions. By analogy to the treatment of activated processes the following "general" rate law for the rate of nucleation of the mineral (AB) on a foreign surface could then be proposed... 

Table 6.3 Values for the activation energy E and collision factor A for some primary and secondary explosive substances...

Explosive substance Activation energy E/kJ mol 1 Collision factor A... 

Primary explosives have low values for the activation energy and collision factor compared with secondary explosives. Therefore, it takes less energy to initiate primary explosives and makes them more sensitive to an external stimulus, i.e. impact, friction, etc., whereas secondary explosives have higher values for the activation energy and collision factor, and are therefore more difficult to initiate and less sensitive to external stimulus. 

Figure 3. Variation of collision factor with temperature for propane-air mixtures using the Semenov equation...

DeZubay (12) has calculated the change in the collision factor with temperature (propane-air mixtures) by use of the Semenov equation based on the following conditions activation energy of 33 keal. per gram-mole flame velocities at an air-fuel ratio of 14.1 of 38.4, 58.2, and 83.3 cm. per second at inlet temperatures of 537°, 672°. and 852° R., respectively flame temperatures [extrapolated to an air-fuel ratio of 14.1 (50)] of 4022°, 4091°, and 4185° R. at inlet temperatures of 537°, 672°, and 852° R., respectively. This variation of A vs. inlet temperature is shown in Figure 3. 

The collision factor and the activation energy were obtained previously for propane by the simultaneous application of the Semenov equation (Equation 31) at two fuel-air ratios where the values of the flame velocity and flame temperatures were available. The accuracy of this method for determining A and E is expected to be fair, since for accuracy, the Semenov equation must meet the condition that E/RT 10. For propane, E/RT is of the order of 8. 

It follows from this equation that the rates of chemical reactions can, in general, be affected by manipulation of either collision factors or activation parameters or both. And, of course, reaction rates will be very sensitive to temperature change—a key consideration in the evolution of complex pathways of interdependent chemical processes that are necessary for maintenance of biologic organisms. 

Biological reactions nearly always occur in the presence of enzymes as catalysts. The enzyme catalase, which acts on peroxides, reduces the E for the reaction from 72 kJ/mol (uncatalyzed) to 28 kJ/mol (catalyzed). By what factor does the reaction rate increase at normal body temperature, 37.0°C, for the same reactant (peroxide) concentration Assume that the collision factor. A, remains constant. 

As several works devoted to the nonlinear optical properties of metal nanoparticles include a size dependence of the linear dielectric function, it seems to us relevant to introduce and briefly comment now the most widespread approach used to describe such a dependence. It consists in modifying the phenomenological collision factor F in the Drude contribution (Eq. 2) as ... 

A is a constant for a particular system, called the collision factor. The effect of the surfactants used as the emulsifying agent is seen in the value of E, the energy barrier to coalescence, which includes both mechanical and electrical barriers. 

According to Davies, a rate of 10-2 times the collision factor (i.e., Ae E/kT = 10 2 A in equation 8.9) is a fast rate of coalescence, corresponding to complete coalescence of that phase within an hour, whereas a rate of 10-5 A is a very slow rate, corresponding to a stability of the order of several months for that phase in a dispersed form. Therefore, if the rate of coalescence of one phase is of the order of 10 5 A and the rate of coalescence of the other phase is considerably faster, then a stable emulsion will be formed with the phase having the slower rate as the dispersed phase. On the other hand, if the rate of coalescence of both phases is of the order of 10 2A, then both phases will coalesce rapidly and the emulsion will break, regardless of which phase has the slower rate. 

One of the most useful theories of activation is the collision theory of reactions. This theory assumes that the activated molecules are formed from collisions with other normal reactant species. Such thermally activated molecules decompose to or react with other molecules. The number and frequencies of collisions indicate that not all collisions are effective in producing an activated molecule. As it was shown before [13], the key point is the effective collision factor in the theory. In the case of a heterogeneous reaction, if the surface catalyst concentration is relatively small compared with the bulk concentration of the reactants, the number of active sites for the catalytic reaction will suffice for the reaction to occur. Therefore, the catalytic reaction has one more advantage only a small quantity of the additive is enough for the reaction. 

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