Rate coefficient with olefins

Rate coefficient with olefin in great excess. ka = AHi= 3.3 kcal.mole". ka = Ska. A// = 4.8 kcal.mole". ... 

Several groups investigated the reactions of radical cations in liquid alkenes. In pulse radiolysis studies the radical cations show a strong absorption band around 280 nm, which is attributed to the n-n transition of the alkene monomer radical cation. Monomer radical cations dimerize with diffusion-controlled rate coefficients with the olefin molecules the dimer cations have broad absorption bands in the 600-800 nm range (Mehnert et al. 1981, 1985 Alfassi 1989). Dimerization may proceed via a hydride ion (H ) transfer in the transition-state of radical-molecule reaction (O Fig. 23.7) ... 

The consistency of the values for k shows that plots of lnx versus t will be linear and have the same slope for each participant, and indicates strongly that all three reactions are indeed first order in olefin. A network of the general type of 5.15 can therefore be accepted. An average value for k is 1.73 10 2 min-1. Not unexpectedly, the scatter is largest for the lowest concentrations, where the relative analytical error is greatest. The individual rate coefficients kM, kAQ, and kAR can be calculated with eqns 5.20. The results are ... 

Rate equations in terms of A coefficients. With the rate equations for olefin, paraffin, H2, and CO replaced by the stoichiometric constraints and the yield ratio of paraffin to hydroformylation products, the rate equations for aldehyde and alcohol remain to be established. In terms of A coefficients these are ... 

Mode/ equations. The mathematical model requires eight concentration-independent coefficients a to fcf, k, and k2l. From these it calculates the five A coefficients with eqns 11.8 to 11.12 from these, the rates of aldehyde and alcohol with eqns 11.6 and 11.7 and finally the rates of olefin, paraffin, H2, and CO with eqns 11.2, 11.5, 11.10, 11.11, 11.3, and 11.4, respectively. Alternatively, eqns 11.8 to 11.12 can be used to replace the A coefficients in eqns 11.6 and 11.7 in order to obtain explicit rate equations for aldehyde and alcohol in terms of the phenomenological coefficients. However, the resulting rate equations are more cumbersome. 

This example has shown how the procedures developed in earlier chapters can be used effectively for modeling. The reaction system has seventeen participants olefin, paraffin, aldehyde, alcohol, H2, CO, HCo(CO)3Ph, HCo(CO)2Ph, and nine intermediates. "Brute force" modeling would require one rate equation for each, four of which could be replaced by stoichiometric constraints (in addition to the constraints 11.2 to 11.4, the brute-force model can use that of conservation of cobalt). Such a model would have 22 rate coefficients (arrowheads in network 11.1, not counting those to and from co-reactants and co-products), whose values and activation energies would have to be determined. This has been reduced to two rate equations and nine simple algebraic relationships (stoichiometric constraints, yield ration equations, and equations for the A coefficients) with eight coefficients. Most impressive here is the reduction from thirteen to two rate equations because these may be differential equations. 

Consider as a prototype the network 11.13 of n-heptene hydroformylation, keeping in mind that die arrows represent multistep pathways and that the reactions of higher straight-chain olefins involve still more parallel pathways of internal olefin isomers to aldehyde isomers and on to alcohol isomers. In such networks, all but one of the aldehyde-to-alcohol conversions involve the reaction of an aldehyde group on a secondary carbon atom, so that all these pathways can be assumed to involve essentially the same rate coefficients of their steps. Only the conversion of the straight-chain aldehyde (n-octanal to n-octanol in network 11.13) must be expected to occur with somewhat different rate coefficients. Likewise, all con-... 

The expected change in Bronsted exponent with change in reactivity is illustrated by the results [49] shown in Table 9 for the hydrolysis of vinyl ethers (mono alkoxy-activated olefins) which occurs by initial slow protonation of olefinic carbon as in mechanism (28). The value of R which is the catalytic coefficient for an acid of pK 4.0 calculated from results for carboxylic acids with pK around 4.0 is taken as a measure of the reactivity of the system. The correlation of a with reactivity is scattered but the trend is in the expected direction. The results are quite similar to those shown for the ionization of ketones in Table 2. For the proton transfers shown in Table 9 the Bronsted exponent has not reached the limiting value of zero or unity even when reaction in one direction is very strongly thermodynamically favourable. The rate coefficient in the favourable direction is probably well below the diffusion limit, although this cannot be checked for the vinyl ethers. Non-limiting values for the Bronsted exponent have also been measured in the hydrolysis of other vinyl ethers [176]. 

Equilibrium protonation to give the carbonium ion can be observed in 80 % (v/v) methanol—water containing buffers. Proton removal from the carbonium ion (pX ca. 2.7 in this solvent) by acetate and chloroacetate is thermodynamically favourable but occurs with rate coefficients of 19.1 and 4.7 1 mole-1 sec-1, respectively, which are well below the values which would be found for normal proton transfer. Protonation of the olefin by hydrogen ion is thermodynamically favourable but occurs slowly with rate coefficient 23 1 mole-1 sec-1. These results clearly show that protonation of olefinic carbon belongs to the category of slow proton transfers. 

The rate coefficients for electron treinsfers of this type, reaction (10), are known to be high, of the order of 10 —10 1 mole sec . The position of the equilibrium will depend on the electron affinities of the two olefins. The electron affinity of naphthalene, for instance, is higher than that of styrene and considerable amounts of N should be present with equivalent quantities of the two hydrocarbons. The situation is more favourable for formation of styrene" if sodium biphenyl is used. The equilibrium will be grossly perturbed, however, by subsequent reaction of the M " species so that none is detectable by ESR measurements even with equimolar amounts of naphthalene" and styrene [86]. This follows because the M" species can dimerize... 

This olefin polymerizes with TiCl4/Al(i-Bu)3 (Al/Ti = 1/2) to form low molecular weight polymers [185]. Rates are first order in monomer concentration and from the initial values the apparent propagation rate coefficient is ca. 6 x 10 1 mole sec at 50°C, the activation energy being 9.5 kcal mole . This is very similar to the rates observed with propene and butene-1, and suggests that fep has a comparable magnitude. 

Unwashed new clothing samples (Table IIC), fiberglass insulation products with formaldehyde resins (Table IID), paper products (Table HE), fabrics (cotton, nylon, olefin, and blended) (Table HF), and carpets (Table HG), had substantially 3 to > 100 fold) lower formaldehyde release rate coefficients, as measured by this method, than did pressed wood products or urea formaldehyde foams (1, 15). 

Rate equations of multistep reactions with reverse steps contain additive terms in the denominator, but not the numerator. Examples from previous chapters include nitration of aromatics and olefin hydroformylation (see Examples 4.4 in Section 4.4 and 6.2 in Section 6.3, respectively). In all such cases, the number of phenomenological coefficients can be reduced by one if numerator and denominator are divided by one of the terms of the latter. The result is a "one-plus" rate equation, with a "1" as the leading term in the denominator. (This procedure is superfluous if all terms in the denominator consist only of coefficients, or of coefficients multiplied with the same concentration or concentrations, so that they can be combined to produce a true power-law rate equation.)... 

The rate coefficients of H atom additions to other simple olefins have most frequently been calculated from relative rates in competitive reactions. In most cases, the values are composites of the rate coefficients for terminal and non-terminal addition. For 1-butene, for example, the available rate data are summarized in Table 3.1 find it quite impressive to see how close the various determinations are to each other. All of these values of k are the mean for attack at both the 1 and 2 positions of the 1-butene. Falconer and Sunder [37] have shown that non-terminal attack occurs to the extent of 5.7%. As with propene, this would mean the log rate for non-terminal attack will be about 7.7 at 298°K. 

With other olefins, competition studies have produced a relative reactivity sequence, the data in which can be recalculated to give absolute rate coefficients. Assuming log k for ethylene is correct at a best value ... 

Rujimethabhas and Jones [136] have compiled a list of relative reactivities for some perfluoro-olefins with nitrogen atoms (see Table 39). The uncertainty in the initial step of the reaction forbids assigning any absolute rate coefficients, and, indeed, a rather different series of average overall rates and relative rates are obtained depending on... 

The addition of H atoms to benzene and tpluene has been investigated by a number of the same workers who studied H-atom additions to the simple olefins. The reaction with benzene and other aromatics is slower than that with ethylene, as would be expected. The greater reliability of the data obtained for additions to olefins makes the rate coefficient obtained by measuring the relative reactivity versus propene [11], and that from the more recent work on toluene [208], the preferred rate determinations. (See Table 61.)... 

No attempt has been made to provide the intensive detail found in Howard s review of oxyradicals [10], the review of Hendry et al. [43] of H-atom transfer to several radicals or Anbar and Neta s review of HO-radical reactions [44]. Instead, we have attempted to extend the scope of those reviews in two ways (i) rate coefficients are provided for R02-radical addition to many olefins, for ring closures to form cyclic ethers, and for intramolecular abstraction (ii) for each reaction, we have estimated the best value Arrhenius parameters (A-factor and E) and, where such values have been measured they are also listed. We believe the value of absolute rate coefficients is improved substantially by the availability of reliable Arrhenius parameters, with which one can calculate the values of rate coefficients at other temperatures for use in experimental or modelling studies. 

The rapidity of the reaction can be seen by the large effect low pressures ( 1 torr) of oxygen can have on the free radical polymerization of a reactive olefin such as styrene [22]. The reaction rate coefficients are expected to be typical for exothermic radical—radical reactions with essentially no activation energy. Thus, if R is alkyl, log(feQ/l mole-1 s-1) would be 9.0 0.5, and be independent of temperature. For simple resonance-stabilized radicals, log(feD/l mole-1 s-1) would be 8.5 0.5. 

Van Sickle et al. [18,94] were able to separate addition from H-atom transfer and ring closure from 02 addition for a series of simple olefins at 50—90°C. Mayo and Miller [22,23] had earlier examined the effect of 02 pressure on the formation of styrene oxide. Their data on k0/kr together with a value for the ring closure in the 2-hydroperoxy-2,4-dimethyl-4-pentyl radical [38] and in the polyperoxybutadienyl radical [72] comprise most of the reliable data base from which to estimate absolute rate coefficients and parameters. 

Absolute rate coefficients and Arrhenius parameters have been obtained for the cycloaddition reaction of S( F2,1,0) atoms with a representative series of olefins and acetylenes. The activation energies are small, and they exhibit a trend with molecular structure which is expected for an electro-philic reagent The A-factors show a definite trend which can be attributed to steric repulsions and a generalized secondary a-isotope effect explained by activated complex theory. Secondary a-H/D kinetic isotope effects have been measured and their origin discussed. Hartree-Fock type MO calculations indicate that the primary product of the S( F) + olefin reaction is a ring-distorted, triplet state thi-irane, with a considerable energy barrier with respect to rotation around the C-C bond. 

Stereochemistry, substituent effects and activation parameters of most ketene reactions are consistent with a one-step cycloaddition polar effects of substituents and solvents, as well as the isotope effect, often require, however, that a fair amount of charge separation (that is, unequal bond formation) characterises the transition state. It has been kinetically proved that cycloadditions of enamines to ketenes can also proceed through a dipolar intermediate this is so for the reaction between dimethylketene and N-isobutenylpyrrolidine . In the latter case, the rate coefficient for the formation of the intermediate strongly depends on solvent polarity itacetonuriie/ cyclohexane = 560. Use of the Same criteria used for ketenes (as far as experimental data allow it) in the case of the 1,2-cycloadditions of fluorinated olefins results, instead, in the conclusion that a two-step biradical mechanism is operating. Results for 1,2-cycloaddition of sulfonyl isocyanates to olefins, cases (g) and (h) in Table 17, give indications of dipolar intermediates during the course of these reactions. 

It is with the limitation of being unable to assess the acidity of the medium independently of the type of indicator employed, that interpretation of the dependency of the rate of acid-catalysed dehydration of alcohols and hydration of olefins must be approached. As each of the various acidity functions run parallel to each other, a plot of the logarithm of the rate coefficient of an acid-catalysed reaction against an acidity function should give a linear correlation. The slope of such a plot, however, will only be unity if the ratio of activity coefficients of the substrate and its activated complex vary in the same way with changes in the reaction medium as the ratio of activity coefficients of the indicator molecule and its conjugate acid. 

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