Activation energy measured

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. 

A comparative study [10] is made for crystal-growth kinetics of Na2HP04 in SCISR and a fluidized bed crystallizer (FBC). The details of the latter cem be found in [11]. Experiments are carried out at rigorously controlled super-saturations without nucleation. The overall growth rate coefficient, K, are determined from the measured values for the initial mean diameter, t/po, masses of seed crystals before and after growth. The results show that the values for K measured in ISC are systematically greater than those in FBC by 15 to 20%, as can be seen in Table 2. On the other hand, the values for the overall active energy measured in ISC and FBC are essentially the same. 

Both the reactors are operated in batch, and the concentrations of components involved are measured online by electro-conductivity. Data interpretation is made by the kinetic equation of second order. The results obtained in the range of 25-45"C are given in Table 3. Again, the values for the rate constant measured in SCISR, ks, are S5 tematically higher than those in STR, ksr, by about 20%, and no significant difference betvi een the values for the active energy measured in SCISR and STR has been found. 

It follows from the formula that the experimentally evaluated value of / activation energy on the ZnO surface may be related to the activation energy of oxygen desorption from the zinc oxide surface. This value well agrees with the desorption activation energy measured with the aid of semiconductor detectors in work [109]. 

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. 

J Steffans et al., 1973, 1975. The reference reaction is the attack of the anion of a carboxylic acid of pK, 3.91 on methyl 2,4-dinitrophenyl phosphate at 39° (Kirby and Younas, 1970). The intramolecular reaction is corrected for the better leaving group using y LO=1.26 (Khan et al., 1970), and to 39° using the activation energy measured for the intermolecular reaction with acetate (Kirby and Younas, 1970). 

As has been elaborated elsewhere, activation energies measured for the thermal atropisomerization of these porphyrins and their metal complexes can be correlated with the degree of core rigidity and/or distortion from planarity for the different compounds (31) ... 

Some criticism (23, 24, 34) of our previously presented results does not consider all the kinetic data obtained recently in the systematic study of such families as alkylaromatics, ethers, alcohols. Taken together, the cross tests permitted classification of many of the compounds studied by substituent as well as by relative kt values. This arrangement is shown in Table II. Once this was done, all that remained was to standardize the absolute value of this classification and to check its accuracy. For this purpose, we used several values of kt available from the literature for the compounds studied. Table III lists these values corrected to 60°C., where the authors gave an activation energy measurement for the recombination reaction, but otherwise listed without correction. Considering the slight variation of these constants with temperature they are... 

The rate constant is estimated (9) as = 103M 1 sec."1 at 26°C. with no activation energy measured. These two dimerization reactions thus differ by a factor of 10r>. 

Activation energies, measured so far for only some substrates, range from zero to about 5 kcal/mole depending on whether the substrate is a conjugated diene (0 to 1 kcal/mole) or a low-substituted olefin ( 5 kcal/mole) (see Table IV, p. 23). 

This compares favorably with the 12 kcal/mol activation energy measured experimentally for Fe EDTA-catalyzed nitration (Beckman et al., 1992). 

Finally, the reliability of the various activation energy measurements should be judged. The TDH measurement is unambiguous as long as the Hall factor [Eq. (A17)] is either close to unity or else is not very temperature dependent (or both), and if mixed conductivity effects are either small or can be taken into account. Usually, neither of these problems is very important as far as a major change in the slope of the Arrhenius plot is concerned. The emission experiments, on the other hand, lead to an apparent activation energy of Ei0 + Eai, where Eai is given by the relationship [Pg.122]

Because this value has been found independently of a choice of detailed kinetic processes, the mechanism postulated by Calvert and Steacie for the photolysis of formaldehyde requires modification. If, for example, a reaction such as HCO - - CH20 —> H2 + CO + HCO is operative (58) then the activation energy measured for the rate of hydrogen production can no longer be simply associated with the activation energy of the reaction... 

The apparent kinetic data as discussed in the previous section is given in terms of the dimensionless frequency factors Ai and the activation energy ), measured in kJ/kmol with... 

Except for a few questionable data, the values for the observed active energy measured in the two crystallizers of different types, EiS and EFB, show little difference and can be considered to be more or less identical. On the other hand, the values measured in the impinging stream crystallizer for the overall crystal-growth rate coefficient, KIS, are obviously and systematically larger than those in the fluidized bed crystallizer, A pe. Therefore it can be affirmed without the need for further analysis that, with the observed frequency factors, there must... 

Accordingly, operation was in the chemical regime, that is, governed by kinetics and not controlled by mass transfer [271]. For the Pd catalyst, however, the activation energies measured in the mesh reactor and in a well-behaved batch reactor with commercial Pd/Al203 powder catalyst were different, being about 0 and 41 kj/mol,... 

Burnett (2), using a dilatometric method to study the polymerization in heptane, reported a first-order dependence of the reaction rate on the monomer and the a-TiCl3 concentration, but little or no dependence on the aluminum alkyl. A settling period was observed which could not be correlated with the various components of the reaction system. An activation energy, measured after the settling period, was found to be 7.7 kcal./mole. 

It is interesting to note that, for malonic acid (which is structurally related to DMMA), the activation energy measured from XH NMR Tx measurements [170] is 5.6 kj mol-1, which is significantly lower than in DMMA and is assigned to proton jumps between the two minima of an asymmetric double well potential. This emphasises the importance of the effect of the crystal packing on the asymmetry of the potential function, which defines the mechanism of the proton dynamics in carboxylic acid dimers. 

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