Activation energy precision

Many computational studies in heterocyclic chemistry deal with proton transfer reactions between different tautomeric structures. Activation energies of these reactions obtained from quantum chemical calculations need further corrections, since tunneling effects may lower the effective barriers considerably. These effects can either be estimated by simple models or computed more precisely via the determination of the transmission coefficients within the framework of variational transition state calculations [92CPC235, 93JA2408]. 

Benson [499] and Livingstone [500] considered the influence of experimental accuracy on measured rate and temperature coefficients. To measure the rate coefficient to 0.1%, the relative errors in each ctj value must be <0.1% and the reaction interval should be at least 50%. Temperature control to achieve this level of precision must be 0.003% or 0.01 K at 300 K. For temperature control to 1 K, the minimum error in the rate coefficient is 5% and in the activation energy, measured over a 20 K interval, is 10%. No allowance is included in these calculations for additional factors such as self-heating or cooling. 

Fast reactions usually require less precise temperature control, because often, but not invariably, they have low activation energies. The converse is true for very slow reactions. 

A C — C bond must break for isomerization to occur, and t q)ical C — C bond energies are around 350 kJ/mol (Table ). Although 270 kJ/mol is considerably smaller than this, it is a reasonable value for the activation energy because the new n bond begins to form before the C — C bond has broken completely. The value is rounded to two significant figures to match the precision of the k values. 

Identification of such universal relations between activation energies and heats of adsorption for particular classes of reaction can be seen as a more precise and more quantitative formulation of Sabatier s Principle. It is promising tool in the search for new materials on the basis of optimized interaction strength between relevant intermediates and the surface. 

For preparations for oral use, knowledge of the desired dosage form is important, but compatibility with ethanol, glycerin, sucrose, corn syrup, preservatives, and buffers is usually carried out. This type of study also gives an idea of the activation energy, E, of the predominant reaction in solution. The Arrhenius plots (Fig. 16) for compounds in solution are usually quite precise. 

Precision of Activation Energy Measurements. The activation energy of a reaction can be determined from a knowledge of the reaction rate constants at two different temperatures. The Arrhenius relation may be written in the following form. 

It is clear that in low- and intermediate-mobility liquids Xt Xf and P x/xt. If the trapped electron energy is lower than VQ, the smallest energy of quasi-free electrons, by an amount eQ, the binding energy in the trap, then one gets approximately Tt = ktf-1 = v 1exp(e T). In a classical activation process, 0 is an activation energy and V would correspond to vibrational frequency in the trap. However, these associations are not precise, because of the stated... 

The energetic charactiristics of process such as E ACt AH, AG and AS also can be generalized with acceptable precision by means of five parameters equations. As an example in the table there are given the experimental activation energies (E ACt) and its values calculated by equation (3) ... 

Since kc is known with reasonable precision, A T can be determined. The procedure was employed to estimate kT using several different traps. The temperature range for these experiments was limited by experimental constraints but activation energies for trapping 5-hexenyl radicals by MNP and PBN were estimated to be ca. 2.0 and 3.2 kcal mol-1 respectively, within rather large error limits log A for each trap is ca. 8. 

For fitting such a set of existing data, a much more reasonable approach has been used (P2). For the naphthalene oxidation system, major reactants and products are symbolized in Table III. In this table, letters in bold type represent species for which data were used in estimating the frequency factors and activation energies contained in the body of the table. Note that the rate equations have been reparameterized (Section III,B) to allow a better estimation of the two parameters. For the first entry of the table, then, a model involving only the first-order decomposition of naphthalene to phthalic anhydride and naphthoquinone was assumed. The parameter estimates obtained by a nonlinear-least-squares fit of these data, are seen to be relatively precise when compared to the standard errors of these estimates, s0. The residual mean square, using these best parameter estimates, is contained in the last column of the table. This quantity should estimate the variance of the experimental error if the model adequately fits the data (Section IV). The remainder of Table III, then, presents similar results for increasingly complex models, each of which entails several first-order decompositions. 

Our data at three temperatures on KCl do not permit activation energies to be evaluated with precision. Clearly the activation energy for transport in the polymer is considerably larger than it is in free solution and seems larger for Cl" than for K+. 

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