Arrhenius parameters determination

The elementary rate constants of the polymerization of vinyl acetate have been determined over a temperature range of 50 degrees (Berezhnykh-Foldes and TiidSs, 1964 Tiidos et al., 1967), and Arrhenius parameter determinations became possible for inhibition processes of radical polymerization of vinyl acetate according to equations (40)-(42)... 

The solid and dotted lines on the figure are calculated from the Arrhenius parameters determined by Blades and Sandhu for 1-heptene (9) and Back and Richard for 1-hexene (JO), respectively. Within the error inherent in our method, the results for dodecene are in agreement. 

Arrhenius parameters determined relative to those for 781 CH3 radical recombination... 

The first-order rate coefficients and the Arrhenius parameters determined at higher pressures (generally above 100 torr) agree reasonably well, as can be seen from Table 6 and Fig. 5. The straight line drawn by the least-squares method through the points of the Arrhenius plot gives the first-order rate coefficient as... 

Pritchard et as well as Dodd came to the conclusion that the rate coefficients obtained by the rotating sector method might be highly erratic due to the oversimplification of the mechanism assumed. Thus, the Arrhenius parameters determined by this method should be accepted only with reserve. 

The Arrhenius parameters determined by Wise et al. [31] have been reproduced by Hofer et al. [39] and Flowers et al. [40] using different techniques (a detailed description of this work is given below). All three groups find activation energies of 57-58 kcal/mol. This raises the issue of why Sinniah et al. [33] found a much lower value. Differences in surface preparation or impurities must be considered, but there is no evidence that the surface of Sinniah et al. was of substantially better or worse quality than the others. An error in temperature measurement, caused for example by... 

Sometimes, for Kiies of closely leliilcd. hut noi identical reactions, the cxpentncnul Arrhenius parameters, determined hy similar procedures, have been teported to conform to an eipation of the form ... 

Radical cyclization continues to be one of the most popular radical reaction classes used in synthesis. By far the majority of published cyclization reactions are 5-exo in nature and this year is no exception. The rates of 5-exo cyclization reactions continue to be measured. For example, the rate constants for the 5-exo cyclizations of the 6,6-diphenylhex-5-enyl, 1-methyl-6,6-diphenylhex-5-enyl and the 1,1-dimethyl-6,6-diphenylhex-5-enyl radicals have been measured by laser flash photolysis studies and Arrhenius parameters determined. The relative rate constants for cyclization, and the reaction with PhSeH, were determined at 20 °C. At 20 °C the rates of the three primary, secondary and tertiary radicals with PhSeH were approximately (1.2 0.1) X 10 lmol s The rate constants for alkyl radicals calibrated by competition reactions with PhSeH and PhSH were found to be 30-40% smaller than previously reported and thus it was concluded that derived rate constants for some fast radical reactions may have to be adjusted accordingly. The rate constants for the 5-exo cyclization of secondary radicals on to hydrazones and oxime ethers have been determined. The fastest rate constants were observed for the IV-benzoylhydrazone acceptor. The rate constants were found to be approximately 800 times faster than for the corresponding 5-exo cyclization on to alkenes." Other work has measured the rate constants of cyclization of a range of fluorinated hex-5-enyl, hept-6-enyl, oct-7-enyl and non-8-enyl radicals. Not only were the rate constants measured but the regioselectivity of cyclization was compared with that for the aU-carbon homologues." The 6-exo cyclization of 1,1,2,2-tetrafluoro- and l,l,2,2,3,3,4,4-octafluorohept-6-enyl radicals were found to be approximately 10 times faster than those for the parent... 

In a senes of papers. Tedder and co-workers reported the factors determining the reactivity of perfluormated radicals with various fluoroethylenes Relative Arrhenius parameters for tnfluoromethyl radicals [17] and pentafluoroethyl radicals [/5] were determined, with higher selectivity demonstrated for the higher homologue Selectivity of addition to unsymmetncal olefins was found also to increase with greater radical branching [19]... 

The reaction between nitroxides and carbon-centered radicals occurs at near (but not at) diffusion controlled rates. Rate constants and Arrhenius parameters for coupling of nitroxides and various carbon-centered radicals have been determined.508 311 The rate constants (20 °C) for the reaction of TEMPO with primary, secondary and tertiary alkyl and benzyl radicals are 1.2, 1.0, 0.8 and 0.5x109 M 1 s 1 respectively. The corresponding rate constants for reaction of 115 are slightly higher. If due allowance is made for the afore-mentioned sensitivity to radical structure510 and some dependence on reaction conditions,511 the reaction can be applied as a clock reaction to estimate rate constants for reactions between carbon-centered radicals and monomers504 506"07312 or other substrates.20... 

A detailed account of transport phenomena in crystals is outside the scope of the present review, though it is relevant to point out that factors which determine the rate at which reactants penetrate a barrier layer include the numbers, distributions and mobilities of vacancies. Oleinikov et al. [1173] conclude that Arrhenius parameters are devoid of any physical significance if due allowance is not made for imperfection concentration, which may vary with temperature (and a [77]). 

I or the Living Graph Determination of Arrhenius Parameters on the Web site for this book is very useful for this type of calculation. 

An Arrhenius plot of In k against 1/T is used to determine the Arrhenius parameters of a reaction a large activation energy signifies a high sensitivity of the rate constant to changes in temperature. 

The ability of the stable free radical diphenylpicrylhydrazyl (DPPH) to act as an efficient trap for reactive radicals such as 804 and OH- has been utilised by Bawn and Margerison in their examination of the Ag -S20g couple. The disappearance of the intensely coloured DPPH gave excellent zero-order kinetics the rate as a whole was identical with that found by Fronaeus and Ostman and 2 was given by 3.1 x 10 exp(—17.9x lO /RT) l.mole sec A Sengar and Gupta have also determined Arrhenius parameters for this reduction and have compared them with those for some redox processes (Table 23). 

This type of reaction is involved as an intermediate step in few synthetically useful reactions, in the formation of polysulfones by copolymerization of an olefin with SO 2, as well as in aerosol formation in polluted atmospheres. We will discuss later in some detail the most important chain reactions involving step 11. However, Good and Thynne determined the Arrhenius parameters for the addition of methyl and ethyl radicals to SO2 in gas phase, the rate constants being 5 x 10 and 4 x 10 s respectively at ambient... 

Equations 3.1-6 to -8 are all forms of the Arrhenius equation. The usefulness of this equation to represent experimental results for the dependence of kA on Tand the numerical determination of the Arrhenius parameters are explored in Chapter 4. The interpretations of A and EA are considered in Chapter 6 in connection with theories of reaction rates. 

In this chapter, we describe how experimental rate data, obtained as described in Chapter 3, can be developed into a quantitative rate law for a simple, single-phase system. We first recapitulate the form of the rate law, and, as in Chapter 3, we consider only the effects of concentration and temperature we assume that these effects are separable into reaction order and Arrhenius parameters. We point out the choice of units for concentration in gas-phase reactions and some consequences of this choice for the Arrhenius parameters. We then proceed, mainly by examples, to illustrate various reaction orders and compare the consequences of the use of different types of reactors. Finally, we illustrate the determination of Arrhenius parameters for die effect of temperature on rate. 

Determine the Arrhenius parameters for the reaction C2H4 + C4H6 - C6H10 from the following data (Rowley and Steiner, 1951) ... 

Show that the data obey the Arrhenius relationship, and determine the values of the Arrhenius parameters. 

Determine the Arrhenius parameters A and A for each diether and specify the units of each. 

As an alternative to this traditional procedure, which involves, in effect, linear regression of equation 5.3-18 to obtain kf (or a corresponding linear graph), a nonlinear regression procedure can be combined with simultaneous numerical integration of equation 5.3-17a. Results of both these procedures are illustrated in Example 5-4. If the reaction is carried out at other temperatures, the Arrhenius equation can be applied to each rate constant to determine corresponding values of the Arrhenius parameters. 

In the examples in Sections 7.1 and 7.2.1, explicit analytical expressions for rate laws are obtained from proposed mechanisms (except branched-chain mechanisms), with the aid of the SSH applied to reactive intermediates. In a particular case, a rate law obtained in this way can be used, if the Arrhenius parameters are known, to simulate or model the reaction in a specified reactor context. For example, it can be used to determine the concentration-(residence) time profiles for the various species in a BR or PFR, and hence the product distribution. It may be necessary to use a computer-implemented numerical procedure for integration of the resulting differential equations. The software package E-Z Solve can be used for this purpose. 

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