Arrhenius plot

Figure A3.10.20 Arrhenius plot of ethane hydrogenolysis aetivity for Ni(lOO) and Ni(l 11) at 100 Torr and H2/C2Hg = 100. Also ineluded is the hydrogenolysis aetivity on supported Ni eatalysts at 175 Torr and H2/C2H6 = 6.6 [43].

Figure A3.10.25 Arrhenius plots of CO oxidation by O2 over Rli single crystals and supported Rli/Al203 at PCO = PO2 = 0.01 atm [43]. The dashed line in the figure is the predicted behaviour based on the rate constants for CO and O2 adsorption and desorption on Rli under UHV conditions.

The presence of nonlinearity in an Arrhenius plot may indicate the presence of quantum mechanical tunnelling at low temperatures, a compound reaction mechanism (i.e., the reaction is not actually elementary) or the unfreezing of vibrational degrees of freedom at high temperatures, to mention some possible sources. 

Evaluate Ej - E by means of an Arrhenius plot of these data using a/( 1 - a) as a measure of kj/k. Briefly justify this last relationship. 

Exploration of the region 0 < T < requires numerical calculations using eqs. (2.5)-(2.7). Since the change in /cq is small compared to that in the leading exponential term [cf. (2.14) and (2.18)], the Arrhenius plot k(P) is often drawn simply by setting ko = coo/ln (fig. 5). Typical behavior of the prefactor k and activation energy E versus temperature is presented in fig. 6. The narrow intermediate region between the Arrhenius behavior and the low-temperature limit has width... 

Fig. 5. Arrhenius plot of k T) for one-dimensional barrier with to Iota = 1. 0.5, 0.25 for the curves 1-3, respectively 2nVa/hota = 10, prefactor is taken constant.

Fig. 8. Arrhenius plot of dissipative tunneling rate in a cubic potential with Vq = Sficoo and r jlto = 0, 0.25 and 0.5 for curves 1-3, respectively. The cross-over temperatures are indicated by asterisks. The dashed line shows k(T) for the parabolic barrier with the same CO and Va-...

Fig. 13. Arrhenius plot of k(T) for electron transfer from cytochrome c to the special pair of bacteriochlorophylls in the reaction center of c-vinosum.

As an illustration of these considerations, the Arrhenius plot of the electron-transfer rate constant, observed by DeVault and Chance [1966] (see also DeVault [1984]), is shown in fig. 13. 

Fig. 15. Arrhenius plot of the rate constant for the transfer of H and D atoms in the CH-O fragment for the reaction (6.17).

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. 

Fig. 26. Arrhenius plot [ln(fc/a>o) against a>o /2it] for the PES (4.28) with Q = 0.1, C = 0.0357, = 1, F /a>o = 3. Solid line shows instanton result separate points, numerical calculation data from Hontscha et al. [1990] and dashed line, low-temperature limit using (3.32) for fc,D.

An Arrhenius plot of the rate constant, consisting of the three domains above, is schematically shown in fig. 45. Although the two-dimensional instanton at Tci < < for this particular model has not been calculated, having established the behavior of fc(r) at 7 > Tci and 7 <7 2, one is able to suggest a small apparent activation energy (shown by the dashed line) in this intermediate region. This consideration can be extended to more complex PES having a number of equivalent transition states, such as those of porphyrines. 

Fig. 47. Arrhenius plot of diffusion coefficient for (a) H and (b) D atoms on the (110) face of a tungsten crystal at coverage degree 0.1-0.9 as indicated. The cusps on the curves correspond to the phase transition.

Fig. 58. Lower left-hand scale Arrhenius plot of the linewidths (lower and upper curves, for inelastic and quasielastic peaks, respectively). Upper right-hand scale Arrhenius plot of the shift of the inelastic peaks.

Subsequent investigations proved that identical hydration reactions occur on bare aluminum surfaces and bonded surfaces, but at very different rates of hydration [49]. An Arrhenius plot of incubation times prior to hydration of bare and buried FPL surfaces clearly showed that the hydration process exhibits the same energy of activation ( 82 kJ/mole) regardless of the bare or covered nature of the surface (Fig. 11). On the other hand, the rate of hydration varies dramatically, de-... 

Fig. 11. Arrhenius plot of incubation times prior to hydration of FPL aluminum under various conditions. Adapted from Ref. [49).

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. 

Figure 6-1. Arrhenius plot for (he chair-chair ring inversion of cyclohexane. ...

Usually the Arrhenius plot of In k vs. IIT is linear, or at any rate there is usually no sound basis for coneluding that it is not linear. This behavior is consistent with the conclusion that the activation parameters are constants, independent of temperature, over the experimental temperature range. For some reactions, however, definite curvature is detectable in Arrhenius plots. There seem to be three possible reasons for this curvature. 

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. 

Figure 6-2. Curved Arrhenius plot for the hydrolysis of methyl trifluoroacetate in dimethylsulfoxide-water (mole fraction water = 0.973). ...

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. 

Reactions catalyzed by hydrogen ion or hydroxide ion, when studied at controlled pH, are often described by pseudo-first-order rate constants that include the catalyst concentration or activity. Activation energies determined from Arrhenius plots using the pseudo-first-order rate constants may include contributions other than the activation energy intrinsic to the reaction of interest. This problem was analyzed for a special case by Higuchi et al. the following treatment is drawn from a more general analysis. ... 

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. 

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

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