Rate constant ratio

Considering a bimolecular reaction A+li <-P, one correspondmgly obtains for tire rate constant ratio... 

Eig. 2. Efficiency to a primary intermediate as % of maximum (zero conversion) efficiency x axis is feed conversion. Parameters are oxidation rate-constant ratios ( 2 / i) for primary intermediate vs feed and reactor type A, plug-flow or batch B, back-mixed. 

A typical oxidation is conducted at 700°C (113). Methyl radicals generated on the surface are effectively injected into the vapor space before further reaction occurs (114). Under these conditions, methyl radicals are not very reactive with oxygen and tend to dimerize. Ethane and its oxidation product ethylene can be produced in good efficiencies but maximum yield is limited to ca 20%. This limitation is imposed by the susceptibiUty of the intermediates to further oxidation (see Figs. 2 and 3). A conservative estimate of the lower limit of the oxidation rate constant ratio for ethane and ethylene with respect to methane is one, and the ratio for methanol may be at least 20 (115). 

Experimental studies show that the ozone concentration iacreases with specific energy (eV/O2) before reaching a steady state. The steady-state ozone concentration varies iaversely with temperature but directiy with pressure, reaching a maximum at about 101.3 kPa (1 atm). Above atmospheric pressure the steady-state ozone concentration decreases with pressure, apparentiy due to the pressure dependence of the rate constant ratio for the... 

According to this important result, the ratio of product concentrations is equal to the ratio of rate constants, independently of time. Even if the reactions are too fast to follow by conventional techniques, final product analysis will give the rate constant ratio (provided no subsequent reactions introduce artifactual changes). 

Parallel reactions of the Schemes VI and VII type have attracted much interest because of their analytical utility. If a mixture of two or three reactants can be arranged to undergo parallel reactions, with appropriate rate constant ratios, it may be possible to determine the composition of the initial mixture. Brown and Fletcher introduced the extrapolation technique discussed above for this purpose, and many modifications of the approach have since been made. ... 

In order to begin, we choose values for n, and /I2, which is equivalent to defining the rate constant ratio A i/A 2, namely, ki/k2 = ni/ 2 = r. For this illustrative example the values ni = 9, /12 = 3 were chosen. The operation is to make nine selections... 

The effectiveness of inhibitors is measured in terms of the rate constant ratio kz/kp and the stoichiometric coefficient. The stoichiometric coefficient is the moles of radicals consumed per mole of inhibitor. These parameters may be determined by various methods. A brief description of the classical kinetic treatment for evaluating k7/kp follows. Consider the reaction scheme shown which describes ideal inhibition and retardation (Scheme 5.11). 

When both A] and A2 are present in large excess over B, and [Ai] and [A2] are thus effectively constant, it follows that the ratio of final and initial concentrations gives the rate constant ratio ... 

When a mixture of disulfides was used (e.g., CH3SSCH3 and n-BuSSn-Bu), it was possible to determine the ratios of the two different products. Determine the rate constant ratio for the two disulfides, mcAbu. 

Assuming the deuteriomethanes do not arise in any other manner, show how the ratio of CD4 to CD3H, determined mass-spectroscopically, can afford a value for the rate constant ratio. 

Figure 8. Plot used to determine average rate constant ratios of the CnH2l+ chain. (C2H4) + indicates only empirical formula but not...

The kinetic data fit a mechanism of successive reactions sequent to only one primary ion equally well, provided that the first step can yield 1.37 methyl radical/100 e.v. and is pressure dependent and that the succeeding pressure independent step yields methyl radicals with a lesser efficiency and leads to a pressure independent yield of 0.58 methyl radicals/100 e.v. If the first step is either Reaction 9a or Reaction 17b, one can once more use the rate constant ratios given earlier to estimate the yields of the possible primary precursor ions. Hence, either G-(C2H2+) = 1.9 ions/100 e.v., or G(C2H4+) = 1.52 ions/100 e.v. The... 

Kinetic examination of the methane yield shows behavior quite similar to that of methyl radical a pressure dependent yield of 0.406 molecule/100 e.v., a pressure independent yield of 0.126 molecule/100 e.v., and a rate constant ratio of kq/kf = 1.5 X 106 mole-1 cc. for the competing steps. 

In this equation, klko) is the rate constant for basic hydrolysis of XCH2COOR divided by the rate constant for basic hydrolysis of CH3COOR, ( o)a is the similar rate-constant ratio for acid catalysis, and 0.181 is an arbitrary constant. The parameter CT/ is a substituent constant for a group X, substimted at a saturated... 

The latter equation, shown graphically in Fig. 73, expresses quantitatively the expected rapid increase in cross-linking with conversion. The rate constant ratio cor-... 

On the experimental side, evidence was accumulating that there is more than one kind of reducing species, based on the anomalies of rate constant ratios and yields of products (Hayon and Weiss, 1958 Baxendale and Hughes, 1958 Barr and Allen, 1959). The second reducing species, because of its uncertain nature, was sometimes denoted by H. The definite chemical identification of H with the hydrated electron was made by Czapski and Schwarz (1962) in an experiment concerning the kinetic salt effect on reaction rates. They considered four... 

FIGURE 6.1 Plot of the logarithm of rate constant ratios against g1/2/(l + jx1/2), where jU is the ionic strength. See text for explanation. Reprinted from Czapski and Schwarz (1962), with permission from Am. Chem. Soc. ... 

Partition rate constant ratios from product analyses 72... 

In this chapter we review published results of studies of the kinetics and products of stepwise nucleophilic substitution and elimination reactions of alkyl derivatives, and we present a small amount of unpublished data from our laboratory. Our review of the literature is selective rather than comprehensive, and focuses on work that provides interesting insight into the factors that control the rate constant ratio ks/kp for partitioning of carbocations, and that provides an understanding of how the absolute rate constants ks and kp that constitute this ratio change with changing carbocation structure. 

The determination of large values of the rate constant ratio ks/kpfrom the low yields of alkene product that forms by partitioning of carbocations in nucleophilic solvents. These rate constant ratios may then be combined with absolute rate constants for the overall decay of the carbocation to give absolute values of kp (s ).14 16 For example, the reaction of the l-(4-methylphenyl)ethyl carbocation in 50/50 (v/v) trifluoroethanol/water gives mainly the solvent adducts and a 0.07% yield of 4-methylstyrene from proton transfer to solvent, which corresponds to kjkp = 1400. This can be combined with ks = 6 x 109 s V4 to give kp = 4.2 x 106 s l (Table 1). 

In summary, there now exists a body of data for the reactions of carbocations where the values of kjkp span a range of > 106-fold (Table 1). This requires that variations in the substituents at a cationic center result in a >8 kcal mol-1 differential stabilization of the transition states for nucleophile addition and proton transfer which have not yet been fully rationalized. We discuss in this review the explanations for the large changes in the rate constant ratio for partitioning of carbocations between reaction with Bronsted and Lewis bases that sometimes result from apparently small changes in carbocation structure. 

The quantitation of products that form in low yields requires special care with HPLC analyses. In cases where the product yield is <1%, it is generally not feasible to obtain sufficient material for a detailed physical characterization of the product. Therefore, the product identification is restricted to a comparison of the UV-vis spectrum and HPLC retention time with those for an authentic standard. However, if a minor reaction product forms with a UV spectrum and HPLC chromatographic properties similar to those for the putative substitution or elimination reaction, this may lead to errors in structural assignments. Our practice is to treat rate constant ratios determined from very low product yields as limits, until additional evidence can be obtained that our experimental value for this ratio provides a chemically reasonable description of the partitioning of the carbocation intermediate. For example, verification of the structure of an alkene that is proposed to form in low yields by deprotonation of the carbocation by solvent can be obtained from a detailed analysis of the increase in the yield of this product due to general base catalysis of carbocation deprotonation.14,16... 

It is often difficult to understand at an intuitive level the explanation for the effect of changing substituents on the rate constant ratio kjkp for partitioning of carbocations between nucleophilic addition of solvent and deprotonation. In these cases, insight into the origins of the changes in this rate constant ratio requires a systematic evaluation of substituent effects on the following ... 

To what extent are the variations in the rate constant ratio /cs//cpobserved for changing structure of aliphatic and benzylic carbocations the result of changes in the Marcus intrinsic barriers Ap and As for the deprotonation and solvent addition reactions It is not generally known whether there are significant differences in the intrinsic barriers for the nucleophile addition and proton transfer reactions of carbocations. 

The net effect of the two orrAo-methyl groups at Me-[10+] is a 4200-fold decrease in the rate constant ratio As/Ap for partitioning of the carbocation between nucleophilic addition of solvent and proton transfer.27... 

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