Activation energy ratio

We next obtain an expression for the activation energy ratio in terms of EOS properties. Following Naoki [80], the activation energy can be expressed as... 

Quantity related to the divergence D defined in Eq. (143) Activation energy Ratio of activation energy to universal gas constant, E/R Expected value of the residual of Ci... 

Ev/Ep can be calculated from segmental relaxation times for polymers and rotational correlation times of molecular liquids, measured over a range of thermodynamic conditions. Plots of the activation energy ratio versus y can be fit using a value oi apTg = 0.18 0.01 (Casalini and Roland, 2004b), consistent with the Boyer-Spencer rule. 

In eq. (12) E (syndio) is the activation energy for the a process in the syndiotactic isomer and E (iso) is the corresponding activation energy for the isotactic Isomer. The Tg vales refer to the calorimetric Tg s for the appropriate stereoisomers. A comparison of the observed activation energy ratio with those calculated from eq. (13) for the various esters yields, for the methyl esters... 

In the high barrier limit, E is approximately equal to the Arrhenius activation energy. The ratio of... 

There are a few cases where the rate of one reaction relative to another is needed, but the absolute rate is not required. One such example is predicting the regioselectivity of reactions. Relative rates can be predicted from a ratio of Arrhenius equations if the relative activation energies are known. Reasonably accurate relative activation energies can often be computed with HF wave functions using moderate-size basis sets. 

The unsaturation present at the end of the polyether chain acts as a chain terminator ia the polyurethane reaction and reduces some of the desired physical properties. Much work has been done ia iadustry to reduce unsaturation while continuing to use the same reactors and hoi ding down the cost. In a study (102) usiag 18-crown-6 ether with potassium hydroxide to polymerise PO, a rate enhancement of approximately 10 was found at 110°C and slightly higher at lower temperature. The activation energy for this process was found to be 65 kj/mol (mol ratio, r = 1.5 crown ether/KOH) compared to 78 kj/mol for the KOH-catalysed polymerisation of PO. It was also feasible to prepare a PPO with 10, 000 having narrow distribution at 40°C with added crown ether (r = 1.5) (103). The polymerisation rate under these conditions is about the same as that without crown ether at 80°C. 

Fig. 3. The room temperature dark conductivity, (Hem), and conductivity activation energy, AH in eV, plotted as A, a function of vppm of AsH ( ) B, PH (a) and C, B2H ( ) into the premix gas ratio of Sip4 H2 = 10 1. Thepton transition (left to right) refers to i -Si F H alloy, and D refers to doping...

Fig. 6. The three ideal zones (I—III) representing the rate of change of reaction for a porous carbon with increasing temperature where a and b are intermediate zones, is activation energy, and -E is tme activation energy. The effectiveness factor, Tj, is a ratio of experimental reaction rate to reaction rate which would be found if the gas concentration were equal to the atmospheric gas concentration (80).

The same arguments can be applied to other energetically facile interconversions of two potential reactants. For example, many organic molecules undergo rapid proton shifts (tautomerism), and the chemical reactivity of the two isomers may be quite different It is not valid, however, to deduce the ratio of two tautomers on the basis of subsequent reactions that have activation energies greater than that of the tautomerism. Just as in the case of conformational isomerism, the ratio of products formed in subsequent reactions will not be controlled by the position of the facile equilibrium. 

Calculate the ratio of rate constants at 30°C and 20°C for a reaction whose activation energy is 20 kcal/mol. 

It may be unsafe to carry this discussion further until more data are available. Knowledge of the activation parameters would be especially desirable in several respects. Reactivity orders involving different reagents or substrates may be markedly dependent on temperature. Thus, in Table IV both 2- and 4-chloroquinolines appear to be about equally reactive toward sodium methoxide at 86,5°. However, the activation energies differ by 3 kcal/mole (see Section VII), and the relative rates are reversed below and above that temperature. Clearly, such relative rates affect the rs-/ ro- ratios. 

Kinetic studies on 2-, 3-, and 4-chloro-l-methylpyridinium salts showed a 30 10 ratio of the reaction rates at 50° with 4-nitro-phenoxide ion in methanol. The activation energy for reaction at the 4-position is one kilocalorie lower ( 8-fold higher rate) than for reaction at the 2-position. The reversal in rates relative to the corresponding halopyridines is the result of a much higher entropy of activation for the 2-chloro compound. The 3-chloro compound has a favorable entropy of activation also, but the energy of activation is about 13 kcal higher than that of the isomers (cf. Table II and Section III, A, 2). 

Relative reactivity wiU vary with the temperature chosen for comparison unless the temperature coefficients are identical. For example, the rate ratio of ethoxy-dechlorination of 4-chloro- vs. 2-chloro-pyridine is 2.9 at the experimental temperature (120°) but is 40 at the reference temperature (20°) used for comparing the calculated values. The ratio of the rate of reaction of 2-chloro-pyridine with ethoxide ion to that of its reaction with 2-chloronitro-benzene is 35 at 90° and 90 at 20°. The activation energy determines the temperature coefficient which is the slope of the line relating the reaction rate and teniperature. Comparisons of reactivity will of course vary with temperature if the activation energies are different and the lines are not parallel. The increase in the reaction rate with temperature will be greater the higher the activation energy. 

In the comparison of 285, 286, and 287 the lower energy of activation for the para azine-nitrogen compounds 285 and 287 was responsible for their more rapid reaction. Both ratios of rates are about the same, the reactivity being greater for the azine-nitrogen compound in each case. Another relationship of moieties in the ortho-position is derived from comparison of 290 and 288, the rate difference being entirely due to the relationship of the activation energies. This ratio is essentially the same as that for 283 and 284, which involved both the entropy and... 

Table XIV, line 3). The rates are equal (only at 20°) due to a large, compensating difference between the entropies of activation. In piperidino-dechlorination, 4-chloroquinoline (Table XI, line 3) has a higher and a lower rate (by about 200-fold at 20°) than 1-chloroisoquinoline (Table XIV, line 1). This reversal of reactivity and of the relationship of the activation energies is attributed to the factors in amination reactions mentioned above. The relative reactivity of the chloro groups in 2,4-dichloroquinoline with methanolic methoxide is given as a 2 1 rate ratio of 4- to 2-displacement. 

A similar thing takes place when we consider flow curves obtained at different temperatures. As seen from Fig. 7, if we take a region of low shear rates, then due to the absence of the temperature dependence Y, the apparent activation energy vanishes. At sufficiently high shear rates, when a polymer dispersion medium flows, the activation energy becomes equal to the activation energy of the viscous flow of a polymer melt and the presence of the filler in this ratio is of little importance. 

Methyl- and 2,6-dimethylpyridine as catalysts with sterically hindered a-com-plexes give greater isotope effects (k2n/k2D up to 10.8). Such values are understandable qualitatively, since the basic center of these pyridine derivatives cannot easily approach the C-H group. The possibility of tunneling can be excluded for these reactions, as the ratio of the frequency factors 4h 4d and the difference in activation energies ED—EU (Arrhenius equation) do not have abnormal values. 

Analysis of the first-order rate coefficient in terms of the two consecutive reactions which were occurring, yielded values of 5.3 xlO-4 and 2.64 xlO-4 the latter value was confirmed as arising from reaction on the first reaction product, 3,4-dichlorodiphenylmethane, because separate 3,4-dichlorobenzylation of this gave a rate coefficient of 2.98 x 10-4. The first-order (overall) rate coefficients obtained at 15 °C (0.665 x 10-4) and 35 °C (6.1 x 10-4) yielded Ea = 19.6, and log A = 14.3, the rate ratio for the consecutive reactions being the same (0.5) at both temperatures later studies have tended to confirm this order of activation energy. 

Figure 4.28. Electrophobic behaviour Effect of catalyst work function on the activation energy E and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt p02 4.8 kPa, Pc2H4 0.4 kPa (a) and CH4 oxidation on Pt p02 =2.0 kPa, Pch4 =2.0 kPa (b)."4 Reprinted with permission from Elsevier Science.

Figure 4.35. Effect of catalyst work function on the activation energy EA, preexponential factor k° and catalytic rate enhancement ratio r/r0 for C2H4 oxidation on Pt/YSZ 4 p02=4.8 kPa, Pc2H4=0-4 kPa,4,54 kg is the open-circuit preexponential factor, T is the mean temperature of the kinetic investigation, 375°C.4 T0 is the (experimentally inaccessible) isokinetic temperature, 886°C.4 25,50...

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