Arrhenius plot dependence

Hence, the apparent activation energy found from an Arrhenius plot depends strongly of the conditions under which it was determined (pressure and temperature). The same is true for the order of reaction in the participating species. 

In 1966 we noted that a log tJq - plot published by Spencer and Dillon for an ar-PS fraction consisted of two straight lines intersecting near T . Later studies by ourselves using both first derivatives and regression analysis with residuals revealed double or triple Arrhenius plots (depending on the temperature range of the data) for ar-PSs of 1.1, for a broad... 

The Arrhenius plot of k(T) for H and D transfer is presented in fig. 15. Qualitatively, the conclusions about the isotope effect drawn here on the basis of the one-dimensional model remain correct for more dimensions, but turns out to depend more weakly on m than In k This... 

In fig. 26 the Arrhenius plot ln[k(r)/coo] versus TojT = Pl2n is shown for V /(Oo = 3, co = 0.1, C = 0.0357. The disconnected points are the data from Hontscha et al. [1990]. The solid line was obtained with the two-dimensional instanton method. One sees that the agreement between the instanton result and the exact quantal calculations is perfect. The low-temperature limit found with the use of the periodic-orbit theory expression for kio (dashed line) also excellently agrees with the exact result. Figure 27 presents the dependence ln(/Cc/( o) on the coupling strength defined as C fQ. The dashed line corresponds to the exact result from Hontscha et al. [1990], and the disconnected points are obtained with the instanton method. For most practical purposes the instanton results may be considered exact. 

The temperature dependence of A predicted by Eq. (5-11) makes a very weak contribution to the temperature dependence of the rate constant, which is dominated by the exponential term. It is, therefore, not feasible to establish, on the basis of temperature studies of the rate constant, whether the predicted dependence of A is observed experimentally. Uncertainties in estimates of A tend to be quite large because this parameter is, in effect, determined by a long extrapolation of the Arrhenius plot to 1/T = 0. 

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. 

Arrhenius plots of temperature-dependent conductivity for [EMIM][BF4] (O), [EMIM][(CF3S02)2N] ( ), and [PMMIM][(CF3S02)2N]... 

Figure 12-27. Temperature dependence of the hole mobility in DPOP-PPV at different electric fields Dale for T= 0 have been obtained by extrapolation. The inset shows the intersection of Arrhenius plots at T()=465 K (Ref. 1831).

Figure 14-25. Arrhenius plot of the temperature-dependent mobility of 8T evaporated lilm. Data were recorded at various gale voltages and corrected for the contact scries resistance (taken from Ref. [ 1241).

The time required to produce a 50% reduction in properties is selected as an arbitrary failure point. These times can be gathered and used to make a linear Arrhenius plot of log time versus the reciprocal of the absolute exposure temperature. An Arrhenius relationship is a rate equation followed by many chemical reactions. A linear Arrhenius plot is extrapolated from this equation to predict the temperature at which failure is to be expected at an arbitrary time that depends on the plastic s heat-aging behavior, which... 

Arrhenius equation The equation In k = In A — EJRT for the commonly observed temperature dependence of a rate constant k. An Arrhenius plot is a graph of In k against 1/T. 

In principle this is derived from an Arrhenius plot of In r+ versus 1/T but such a plot may deviate from a straight line. Hence, the apparent activation energy may only be valid for a limited temperature range. As for the orders of reaction, one should be very careful when interpreting the activation energy since it depends on the experimental conditions. Below is an example where the forward rate depends both on an activated process and equilibrium steps, representing a situation that occurs frequently in catalytic reactions. 

In experimental practice, we usually ignore the temperature dependence of the prefactor and extract the activation energy by making an Arrhenius plot, as discussed in Chapter 2. The consequence of collision theory, however, is that a curved plot, rather than a straight line, will result if the activation energy is of the same order of k T. 

The reader may now wish to verify that the activation energy calculated by logarithmic differentiation contains a contribution Sk T/l in addition to A , whereas the pre-exponential needs to be multiplied by the factor e in order to properly compare Eq. (139) with the Arrhenius equation. Although the prefactor turns out to have a rather strong temperature dependence, the deviation of a In k versus 1/T Arrhenius plot from a straight line will be small if the activation energy is not too small. 

The usual derivation of an activation energy from a set of temperature dependent rates as the slope of an Arrhenius plot gives ... 

Because the Arrhenius plots of both TPD experiments are straight lines over a large portion of the data points, the reaction between CO and O is, most likely, an elementary step, with an activation energy of 103 5 kj mol and a pre-exponential factor of s . This analysis is again only valid if coverage dependencies play... 

Ferricyanide catalyses the decomposition of H2O2 at pH 6-8. The reaction is first-order in peroxide but the dependence on oxidant concentration is complex . The Arrhenius plots were curved but averaged values indicated that at pH 7 and 8, respectively, E is 25+2 and 11 + 1.5 kcal.mole". Clearly several processes are contributing to the overall reaction. 

The product distribution of the HDS of thiophene over the Mo(lOO) surface is shown in Table III compared with that reported by Kolboe over a MoS catalyst (14). It is clear that the two are very similar ana that our catalyst mimics the MoS catalyst very closely in this respect. An Arrhenius plot fpigure 2) made in the temperature region mentioned above shows that butadiene is the only product whose rate of formation shows true Arrhenius type dependence and yields an activation energy of 14.4 kcal/mole. At high temperatures the rate of butane formation deviates even more sharply than that of the butenes and does so at lower temperatures (9). 

Evidence on this question may be taken by the behavior of the electrical conductivity CT as a function of temperature. A thermally activated process T dependence on log(CT), Arrhenius plot) is expected if doping takes place, whereas j -i/4 dependence, characteristic of a variable range hopping at the Fermi level is expected for a nondoping situation. 

It has been shown that the rate constants obtained from the slopes of In [intensity] versus plots approximate the rates of the highest-probability matrix sites. Hence, workers have utilized the temperature dependence of these values, or other empirically derived stretched exponential time dependencies, to estimate low temperature Arrhenius plots. The validity of such methods, however, depends critically on obtaining accurate time-dependence data on the fastest matrix sites, which is increasingly difficult as temperatures are raised. 

Arrhenius plots of both 1u( h) and ln(A D) versus T were found to be curved significantly, exhibiting decreasing dependence on temperature at lower temperatures. As described in the Introduction, such nonlinear Arrhenius plots are telling indicators of QMT as temperature is lowered, the classical overbarrier reaction slows more significantly than does one that proceeds via tunneling. Later work showed that the abstraction reaction of 2 to 3 persisted at a measurable rate at least down to 28 K in frozen media, where the decay became nearly temperature independent. 

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