Specific rates

Various specific rate laws and mechanisms are described in the next section the present discussion is in more general terms. For example, why is it that a contact catalyst is able to serve as such, that is, why is it able to provide a reac-... 

Fig. XVIII-27. Specific rates of CO oxidation on single crystal and supported catalysts as a function of temperature. (From Ref 308. Reprinted with permission from American Chemical Society, copyright 1988.)...

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

Quack M and Troe J 1974 Specific rate constants of unimoiecuiar processes ii. Adiabatic channei modei Ber. Bunsenges. Phys. Chem. 78 240-52... 

If all the resonance states which fomi a microcanonical ensemble have random i, and are thus intrinsically unassignable, a situation arises which is caWtA. statistical state-specific behaviour [95]. Since the wavefunction coefficients of the i / are Gaussian random variables when projected onto (]). basis fiinctions for any zero-order representation [96], the distribution of the state-specific rate constants will be as statistical as possible. If these within the energy interval E E+ AE fomi a conthuious distribution, Levine [97] has argued that the probability of a particular k is given by the Porter-Thomas [98] distribution... 

If the state-specific rate constants are assumed continuous, equation (A3.12.65) can be written as [103]... 

Troe J 1983 Specific rate constants k(E, J) for unimolecular bond fissions J. Chem. Phys. 79 6017-29... 

In equation (A3.13.24), /c. is the specific rate constant for reaction from level j, and are energy transfer... 

Cobos 0 J, Hippier H and Tree J 1985 High-pressure falloff curves and specific rate constants for the reactions J. Phys. Chem. 89 342-9... 

Figure C3.2.6. Zones associated witlr the distinctive decay of electronic coupling tlrrough a-helical against p-sheet stmctures in proteins. Points shown refer to specific rates in mtlrenium-modified proteins aird in tire photosyntlretic reaction centre. From Gray H B aird Wiirkler J R 1996 Electron trairsfer in proteins A . Rev. Biochem. 65 537.

In all its reactions the lone pair of thiazole is less reactive than that of pyridine. Table 1-61 shows three sets of physicochemical data that illustrate this difference. These are (1) the thermodynamic basicity, which is three orders of magnitude lower for thiazole than for pyridine (2) the enthalpy of reaction with BF3 in nitrobenzene solution, which is 10% lower for thiazole than for pyridine and (3) the specific rate of quaterni-zation by methyl iodide in acetone at 40°C, which is about 50% lower for... 

Specific rate of methylation by methyl iodide in acetone at 40°C in liter mole sec . 

The power law developed above uses the ratio of the two different shear rates as the variable in terms of which changes in 17 are expressed. Suppose that instead of some reference shear rate, values of 7 were expressed relative to some other rate, something characteristic of the flow process itself. In that case Eq. (2.14) or its equivalent would take on a more fundamental significance. In the model we shall examine, the rate of flow is compared to the rate of a chemical reaction. The latter is characterized by a specific rate constant we shall see that such a constant can also be visualized for the flow process. Accordingly, we anticipate that the molecular theory we develop will replace the variable 7/7. by a similar variable 7/kj, where kj is the rate constant for the flow process. 

Kinetics. Details of the kinetics of polymerization of THF have been reviewed (6,148). There are five main conclusions. (/) Macroions are the principal propagating species in all systems. (2) With stable complex anions, such as PF , SbF , and AsF , the polymerization is living under normal polymerization conditions. When initia tion is fast, kinetics of polymerizations in bulk can be closely approximated by equation 2, where/ is the specific rate constant of propagation /is time [I q is the initiator concentration at t = 0 and [M q, [M and [M are the monomer concentrations at t = 0, at equiHbrium, and at time /, respectively. 

Refractoriness. Refractoriaess is determined by several methods. The pyrometric cone equivalent (PCE) test (ASTM C24) measures the softening temperature of refractory materials. Inclined trigonal pyramids (cones) are formed from finely ground materials, set on a base, and heated at a specific rate. The time and temperature (heat treatment) requited to cause the cone to bend over and touch the base is compared to that for standard cones. 

Another measure of refractoriaess is the hot-compressive strength or hot-load test for refractory bricks or formed specialties. The specimen carries a static load from 69 kPa (10 psi) to 172 kPa (25 psi). It is heated at a specific rate to a specific temperature which is then held for 1.5 h, or it is heated at a specific rate until it fads. The percent deformation or the temperature of fadure is measured. The procedure is described ia ASTM C16. 

The summation term is the mass broken into size interval / from all size intervals between j and /, and S is the mass broken from size internal i. Thus for a given feed material the product size distribution after a given time in a mill may be deterrnined. In practice however, both S and b are dependent on particle size, material, and the machine utilized. It is also expected that specific rate of breakage should decrease with decreasing particle size, and this is found to be tme. Such an approach has been shown to give reasonably accurate predictions when all conditions are known however, in practical appHcations severe limitations are met owing to inadequate data and scale-up uncertainties. Hence it is stiH the usual practice to carry out tests on equipment to be sure of predictions. 

Butylene isomers also can be expected to show significant differences in reaction rates for metaHation reactions such as hydroboration and hydroformylation (addition of HCo(CO). For example, the rate of addition of di(j -isoamyl)borane to cis-2-huX.en.e is about six times that for addition to trans-2-huX.en.e (15). For hydroformylation of typical 1-olefins, 2-olefins, and 2-methyl-l-olefins, specific rate constants are in the ratio 100 31 1, respectively. 

Hydrolysis to Glycols. Ethylene chlorohydrin and propylene chlorohydrin may be hydrolyzed ia the presence of such bases as alkaU metal bicarbonates sodium hydroxide, and sodium carbonate (31—33). In water at 97°C, l-chloro-2-propanol forms acid, acetone, and propylene glycol [57-55-6] simultaneously the kinetics of production are first order ia each case, and the specific rate constants are nearly equal. The relative rates of solvolysis of... 

A thermal oxidizer is a chemical reactor in which the reaction is activated by heat and is characterized by a specific rate of reactant consumption. There are at least two chemical reactants, an oxidizing agent and a reducing agent. The rate of reaction is related both to the nature and to the concentration of reactants, and to the conditions of activation, ie, the temperature (activation), turbulence (mixing of reactants), and time of interaction. 

Effect of Temperature The An henius equation relates the specific rate to the absolute temperature,... 

Typical Units of Specific Rates For order Ot, typical units i... 

When even second-order reactions are included in a group to be analyzed, individual integration methods maybe needed. Three cases of coupled first- and second-order reactions will be touched on. All of them are amenable only with difficulty to the evaluation of specific rates from kinetic data. Numerical integrations are often necessary. 

Conditions that give rise to unsteadiness are changes in feed rate, composition, or temperature. In the case of Fig. 7-6, a sinusoidal input of feed rate is introduced. The output concentration also appears to vary sinusoidally. The amphtude oi the response is lower as the specific rate is increased. 

Chemical reaction always enhances the rate of mass transfer between phases. The possible magnitudes of such enhancements are indicated in Tables 23-6 and 23-7. They are no more predictable than are specific rates of chemical reactions and must be found experimentally for each case, or in the relatively sparse literature on the subject. 

Plots are shown for several specific rates, including k = 0 when no reaction takes place. 

A second order reaction is conducted in two equal CSTR stages. The residence time per stage is T = 1 and the specific rate is /cCq = 0.5. Feed concentration is Cq. Two cases are to be examined (1) with pure solvent initially in the tanks and (2) with concentrations Cq initially in both tanks, that is, with Cio = Coq = Cq. 

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