Reaction rate Arrhenius plots

On account of this relation, the temperature dependence of kinetic parameters can often be linearized, when the logarithm of the reaction rate is plotted against 1/T, which is often called an Arrhenius plot (for examples, cf. p. 556 in Ref. 9). 

The Arrhenius relation given above for Are temperature dependence of air elementary reaction rate is used to find Are activation energy, E, aird Are pre-exponential factor. A, from the slope aird intercept, respectively, of a (linear) plot of n(l((T)) against 7 The stairdard enAralpv aird entropy chairges of Are trairsition state (at constairt... 

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).

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-... 

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. 

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. ... 

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... 

A ten to hundredfold decrease in the velocity of the reaction, seen as a break down of the Arrhenius plot, is observed at a temperature which, for any given pressure, is always higher than that thermodynamically foreseen for the beginning of the a-/3 transition (this discrepancy is smallest at 265 mm Hg pressure). The marked decrease of the rate of reaction is characteristic of the appearance of the /3-hydride phase. The kinetics of reaction on the hydride follows the Arrhenius law but with different values of its parameters than in the case of the a-phase. 

The temperature dependence of a reaction rate lies in the rate constant and, as we shall see in Section 13.12, that temperature dependence gives valuable insight into the origins of rate constants. In the late nineteenth century, the Swedish chemist Svante Arrhenius found that the plot of the logarithm of the rate constant (In k) against the inverse of the absolute temperature (1 IT) is a straight line. In other words,... 

An Arrhenius plot of In k against 1/T is used to determine the Arrhenius parameters of a reaction a large activation energy signifies a high sensitivity of the rate constant to changes in temperature. 

To summarize, the surface kinetics (or near surface kinetics) is the limiting step at lower temperature and diffusion is the rate limiting step at higher temperature. It is possible to switch from one rate-limiting step to the other by changing the temperature. This is illustrated in Fig. 2.9, where the Arrhenius plot (logarithm of the deposition rate vs. the reciprocal temperature) is shown for several reactions leading to the deposition of silicon,... 

The case of m = Q corresponds to classical Arrhenius theory m = 1/2 is derived from the collision theory of bimolecular gas-phase reactions and m = corresponds to activated complex or transition state theory. None of these theories is sufficiently well developed to predict reaction rates from first principles, and it is practically impossible to choose between them based on experimental measurements. The relatively small variation in rate constant due to the pre-exponential temperature dependence T is overwhelmed by the exponential dependence exp(—Tarf/T). For many reactions, a plot of In(fe) versus will be approximately linear, and the slope of this line can be used to calculate E. Plots of rt(k/T" ) versus 7 for the same reactions will also be approximately linear as well, which shows the futility of determining m by this approach. 

Figure 5.1 shows an Arrhenius plot for the reaction O -b N2 NO -b N the plot is linear over an experimental temperature range of 1500 K. Note that the rate constant is expressed per molecule rather than per mole. This method for expressing k is favored by some chemical kineticists. It differs by a factor of Avogadro s number from the more usual k. 

Fig. 2 shows the plot of ln[(CEcVCEc] vs. time during first 2 h. Quite good straight lines were obtained, and the pseudo first-order reaction rate constants for 120,130 and 140 °C were 0.002421, 0.002481 and 0.002545 h, respectively. From the Arrhenius plot of the first order reaction rate constants, one can estimate the activation energy as 41.5 kJ/mol. 

The measured [ OH]/[ OH] branching ratio versus inverse temperature is plotted in Fig. 4. If the two species are produced by two parallel pathways, the total reaction rate is a simple sum of the two pathway-resolved rates. In this case, the data points in an Arrhenius plot should fall on a straight line with a slope proportional to the difference in activation energies for the two competing pathways. A fit to the data in Fig. 4 yields the result that the barrier to O atom abstraction is 1.0 0.4kcal mol larger than for H atom abstraction. Although... 

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. 

Figure 7.14. The temperature-programmed reaction and corresponding Arrhenius plot based on rate expression (21) enables the calculation of kinetic parameters for the elementary surface reaction between CO and O atoms on a Rh(lOO) surface.

The NO + CO reaction is only partially described by the reactions (2)-(7), as there should also be steps to account for the formation of N2O, particularly at lower reaction temperatures. Figure 10.9 shows the rates of CO2, N2O and N2 formation on the (111) surface of rhodium in the form of Arrhenius plots. Comparison with similar measurements on the more open Rh(llO) surface confirms again that the reaction is strongly structure sensitive. As N2O is undesirable, it is important to know under what conditions its formation is minimized. First, the selectivity to N2O, expressed as the ratio given in Eq. (7), decreases drastically at the higher temperatures where the catalyst operates. Secondly, real three-way catalysts contain rhodium particles in the presence of CeO promoters, and these appear to suppress N2O formation [S.H. Oh, J. Catal. 124 (1990) 477]. Finally, N2O undergoes further reaction with CO to give N2 and CO2, which is also catalyzed by rhodium. 

Figure 2. Arrhenius plots of differential rates of NO reduction ( ) and of CH4 oxidation (o) during the SCR reaction, and for CH4oxidation by Oj alone (A) over CoZSM-5 (A) and HZSM-5 (B) catalysts. Feed contained 0.28% CH4, 0.21 % NO (when used) and 2.6% O2 in He.

Figure 8. Rate of carbon monoxide oxidation on calcined Pt cube monolayer as a function of temperature [27]. The square root of the SFG intensity as a function of time was fit with a first-order decay function to determine the rate of CO oxidation. Inset is an Arrhenius plot for the determination of the apparent activation energy by both SFG and gas chromatography. Reaction conditions were preadsorbed and 76 Torr O2 (flowing). (Reprinted from Ref. [27], 2006, with permission from American Chemical Society.)...

Figure 5.4-36. Fit of first-order kinetics for three Figure 5.4-37. Arrhenius plot for rate constants isothermal reaction periods (reprinted with obtained from the isothermal reaction periods permission from Landau et al. (1994). Copyright (reprinted with permission from Landau et al. (1994) American Chemical Society). (1994). Copyright (1994) American Chemical...

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