Arrhenius values

From the data listed in Tables I-V, we conclude that most authors would probably accept that there is evidence for the existence of a compensation relation when ae < O.le in measurements extending over AE 100 and when isokinetic temperature / , would appear to be the most useful criterion for assessing the excellence of fit of Arrhenius values to Eq. (2). The value of oL, a measure of the scatter of data about the line, must always be considered with reference to the distribution of data about that line and the range AE. As the scatter of results is reduced and the range AE is extended, the values of a dimin i, and for the most satisfactory examples of compensation behavior that we have found ae < 0.03e. There remains, however, the basic requirement for the advancement of the subject that a more rigorous method of statistical analysis must be developed for treatment of kinetic data. In addition, uniform and accepted criteria are required to judge quantitatively the accuracy of obedience of results to Eq. (2) or, indeed, any other relationship. 

Further problems arise if measurements of the rate of nitration have been made at temperatures other than 25 °C under these circumstances two procedures are feasible. The first is discussed in 8.2.2 below. In the second the rate profile for the compound imder investigation is corrected to 25 °C by use of the Arrhenius parameters, and then further corrected for protonation to give the calculated value of logio/i fb. at 25 °C, and thus the calculated rate profile for the free base at 25 °C. The obvious disadvantage is the inaccuracy which arises from the Arrhenius extrapolation, and the fact that, as mentioned above, it is not always known which acidity functions are appropriate. 

The activation energies for the decomposition (subscript d) reaction of several different initiators in various solvents are shown in Table 6.2. Also listed are values of k for these systems at the temperature shown. The Arrhenius equation can be used in the form ln(k j/k j) (E /R)(l/Ti - I/T2) to evaluate k j values for these systems at temperatures different from those given in Table 6.2. 

Nitrocellulose is among the least stable of common explosives. At 125°C it decomposes autocatalyticaHy to CO, CO2, H2O, N2, and NO, primarily as a result of hydrolysis of the ester and intermolecular oxidation of the anhydroglucose rings. At 50°C the rate of decomposition of purified nitrocellulose is about 4.5 x 10 %/h, increasing by a factor of about 3.5 for each 10°C rise in temperature. Many values have been reported for the activation energy, E, and Arrhenius frequency factor, Z, of nitrocellulose. Typical values foiE and Z are 205 kj/mol (49 kcal/mol) and 10.21, respectively. The addition of... 

Calculated and measured conversions agreed when the Arrhenius temperature dependency indicated in Eq. (27-22) was used with the following values for the parameters ... 

The fact that hot spots are required for explosive initiation can be seen by calculating for the bulk temperature, say 350 K, and the anticipated hot-spot temperature, say 700 K. We take typical values of Arrhenius constants for secondary explosives QjCp 2500 K, //c = 25,(X)0 K, and V = 10 s V Hence... 

The experimental studies of a large number of low-temperature solid-phase reactions undertaken by many groups in 70s and 80s have confirmed the two basic consequences of the Goldanskii model, the existence of the low-temperature limit and the cross-over temperature. The aforementioned difference between quantum-chemical and classical reactions has also been established, namely, the values of k turned out to vary over many orders of magnitude even for reactions with similar values of Vq and hence with similar Arrhenius dependence. For illustration, fig. 1 presents a number of typical experimental examples of k T) dependence. 

The bifurcational diagram (fig. 44) shows how the (Qo,li) plane breaks up into domains of different behavior of the instanton. In the Arrhenius region at T> classical transitions take place throughout both saddle points. When T < 7 2 the extremal trajectory is a one-dimensional instanton, which crosses the maximum barrier point, Q = q = 0. Domains (i) and (iii) are separated by domain (ii), where quantum two-dimensional motion occurs. The crossover temperatures, Tci and J c2> depend on AV. When AV Vq domain (ii) is narrow (Tci — 7 2), so that in the classical regime the transfer is stepwise, while the quantum motion is a two-proton concerted transfer. This is the case when the tunneling path differs from the classical one. The concerted transfer changes into the two-dimensional motion at the critical value of parameter That is, when... 

Difoggio and Corner [1982] and Wang and Comer [1985] have discovered tunneling diffusion of H and D atoms on the (110) face of tungsten. They saw that the Arrhenius dependence of the diffusion coefficient D sharpy levels-off to the low-temperature limit (D = D ) at 130-140 K (fig. 47) the values of depend but slightly on the mass of the tunneling particle for the D and... 

The diffusion coefficient corresponding to the measured values of /ch (D = kn/4nRn, is the reaction diameter, supposed to be equal to 2 A) equals 2.7 x 10 cm s at 4.2K and 1.9K. The self-diffusion in H2 crystals at 11-14 K is thermally activated with = 0.4 kcal/mol [Weinhaus and Meyer 1972]. At T < 11 K self-diffusion in the H2 crystal involves tunneling of a molecule from the lattice node to the vacancy, formation of the latter requiring 0.22 kcal/mol [Silvera 1980], so that the Arrhenius behavior is preserved. Were the mechanism of diffusion of the H atom the same, the diffusion coefficient at 1.9 K would be ten orders smaller than that at 4.2 K, while the measured values coincide. The diffusion coefficient of the D atoms in the D2 crystal is also the same for 1.9 and 4.2 K. It is 4 orders of magnitude smaller (3 x 10 cm /s) than the diffusion coefficient for H in H2 [Lee et al. 1987]. 

It is noteworthy that the above rule connects two quite different values, because the temperature dependence of is governed by the rate constant of incoherent processes, while A characterizes coherent tunneling. In actual fact, A is not measured directly, but it is calculated from the barrier height, extracted from the Arrhenius dependence k T). This dependence should level off to a low-temperature plateau at 7 < This non-Arrhenius behavior of has actually been observed by Punnkinen [1980] in methane crystals (see fig. 1). A similar dependence, also depicted in fig. 1, has been observed by Geoffroy et al. [1979] for the radical... 

Then vkt is calculated from the vX values as (-ln(l-vX)). The independent function Temperature vx is expressed as 1000 K/vT for the Arrhenius function. Finally the independent variable vy is calculated as In(vkt). Next a linear regression is executed and results are presented as y plotted against Xi The results of regression are printed next. The slope and intercept values are given as a, and b. The multiple correlation coefficient is given as c. 

The conductivity of solid dielectrics is roughly independent of temperature below about 20°C but increases according to an Arrhenius function at higher temperatures as processes with different activation energies dominate [ 133 ]. In the case of liquids, the conductivity continues to fall at temperatures less than 20°C and at low ambient temperatures the conductivity is only a fraction of the value measured in the laboratory (3-5.5). The conductivity of liquids can decrease by orders of magnitude if they solidify (5-2.5.5). 

The effeet of temperature satisfies the Arrhenius relationship where the applieable range is relatively small beeause of low and high temperature effeets. The effeet of extreme pH values is related to the nature of enzymatie proteins as polyvalent aeids and bases, with aeid and basie groups (hydrophilie) eoneentrated on the outside of the protein. Einally, meehanieal forees sueh as surfaee tension and shear ean affeet enzyme aetivity by disturbing the shape of the enzyme moleeules. Sinee the shape of the aetive site of the enzyme is eonstrueted to eoirespond to the shape of the substrate, small alteration in the strueture ean severely affeet enzyme aetivity. Reaetor s stirrer speed, flowrate, and foaming must be eontrolled to maintain the produetivity of the enzyme. Consequently, during experimental investigations of the kineties enzyme eatalyzed reaetions, temperature, shear, and pH are earefully eontrolled the last by use of buffered solutions. 

Thus curvature in an Arrhenius plot is sometimes ascribed to a nonzero value of ACp, the heat capacity of activation. As can be imagined, the experimental problem is very difficult, requiring rate constant measurements of high accuracy and precision. Figure 6-2 shows a curved Arrhenius plot for the neutral hydrolysis of methyl trifluoroacetate in aqueous dimethysulfoxide. The rate constants were measured by conductometry, their relative standard deviations being 0.014 to 0.076%. The value of ACp was estimated to be about — 200 J mol K, with an uncertainty of less than 10 J moE K. ... 

AC is interpreted as the difference in heat capacities between the transition state and the reactants, and it may be a valuable mechanistic tool. Most reported ACp values are for reactions of neutral reactants to products, as in solvolysis reactions of neutral esters or aliphatic halides. " Because of the slight curvature seen in the Arrhenius plots, as exemplified by Fig. 6-2, the interpretation, and even the existence, of AC is a matter of debate. The subject is rather specialized, so we will not explore it deeply, but will outline methods for the estimation of ACp. 

These apply to a bimolecular reaction in which two reactant molecules become a single particle in the transition state. It is evident from Eqs. (6-20) and (6-21) that a change in concentration scale will result in a change in the magnitude of AG. An Arrhenius plot is, in effect, a plot of AG against 1/T. Because a change in concentration scale alters the intercept but not the slope of an Arrhenius plot, we conclude that the values of AG and A, but not of A//, depend upon the concentration scale employed for the expression of reactant concentrations. We, therefore, wish to know which concentration scale is the preferred one in the context of mechanistic interpretation, particularly of AS values. 

Prepare the solutions and measure the pH at one temperature of the kinetic study. Of course, the pH meter and electrodes must be properly calibrated against standard buffers, all solutions being thermostated at the single temperature of measurement. Carry out the rate constant determinations at three or more tempertures do not measure the pH or change the solution composition at the additional temperatures. Determine from an Arrhenius plot of log against l/T. Then calculate Eqh using Eq. (6-37) or (6-39) and the appropriate values of AH and AH as discussed above. 

The effect of temperature on k is generally represented by the Arrhenius equation and the values of k lue obtained from experimental data. 

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