Activation energy second limit

The transition is fully classical and it proceeds over the barrier which is lower than the static one, Vo = ntoColQl- Below but above the second cross-over temperature T 2 = hcoi/2k, the tunneling transition along Q is modulated by the classical low-frequency q vibration. The apparent activation energy is smaller than V. The rate constant levels off to its low-temperature limit k only at 7 < Tc2, when tunneling starts out from the ground state of the initial parabolic term. The effective barrier in this case is neither V nor Vo,... 

Generally, under either isothermal or noniso-thermal conditions, intrapartiole diffusional limitations are undesirable because they reduce the selectivity below that which can be achieved in their absence. The exception to this generalization is a set of endothermic reactions that take place in nonisothermal pellets where the second reaction has an activation energy that is greater than that of the first. 

The second intermediate s identity has been debated since the mid-1980s. In 1984, Liu and Tomioka suggested that it was a carbene-alkenc complex (CAC).17 Similar complexes had been previously postulated to rationalize the negative activation energies observed in certain carbene-alkene addition reactions.11,30 A second intermediate is not limited to the CAC, however. In fact any other intermediate, in addition to the carbene, will satisfy the kinetic observations i.e., that a correlation of addn/rearr vs. [alkene] is curved, whereas the double reciprocal plot is linear.31 Proposed second intermediates include the CAC,17 an excited carbene,31 a diazo compound,23 or an excited diazirine.22,26 We will consider the last three proposals collectively below as rearrangements in the excited state (RIES). 

The apparent first-order rate coefficient is 1.5x 1010 exp(—28,200/RT ) sec-1. This expression has undoubtedly been obtained for a pressure-dependent region. If, as an extreme case, it is assumed that the unimolecular process occurred in the second-order region and if approximately one half of the classical degree of vibrational freedom are active, an upper limit of kx — 1.5 x 1015 exp(—46,000/Rr) sec-1 is obtained. The mean Pb-CH3 bond dissociation energy in tetramethyl lead19,142 is 37.6 kcal.mole-1. Dx should therefore be about 40 kcal.mole-1. 

This second-order decomposition of hydrogen peroxide has been studied independently, and its rate parameters are known. The activation energy is ca. 48 keal., and its lifetime is about 1 second at about 900°K. At temperatures of ca. 450° to 550°C., it proceeds at a sufficiently rapid rate to be responsible for initiating the normal explosion limit, which one finds for stoichiometric hydrocarbon-oxygen mixtures. 

If the activation energy difference, (E34 — E32), is known, rate constant ratios may be evaluated. Conversely, if the latter are known, (E34 - E32) may be evaluated. If second explosion limits for a series of undiluted mixtures of hydrogen and oxygen are compared, Equation 42 becomes... 

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