Determining the Activation Energy

We can calculate the activation energy for a reaction by manipulating the Arrhenius equation. Taking the natural log of both sides of Equation 14.19, we obtain 

We can also use Equation 14.20 to evaluate in a nongraphical way if we know the rate constant of a reaction at two or more temperatures. For example, suppose that at two different temperatures Tj and I2 a reaction has rate constants k and ki. For each condition, we have 

Equation 14.21 provides a convenient way to calculate a rate constant fcj at some temperature T] when we know the activation energy and the rate constant k2 at some other temperature T.  

Analyze We are given rate constants, k, measured at several temperatures and asked to determine the activation energy, and the rate constant, k, at a particular temperature. 

Plan We can obtain from the slope of a graph of In fc versus 1/T. Once we know E , we can use Equation 14.21 together with the given rate data to calculate the rate constant at 430.0 K. 

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Prepare the appropriate graph and determine the activation energy for this reaction. 

We can determine the activation energy from a series of measurements by plotting the logarithm of the rate constant against the reciprocal temperature, as rearrangement of Eq. (45) sho vs ... 

How can one determine the activation energy for an activated adsorption process ... 

Again, assume the volume of the reactor to be constant. Determine the activation energy for the reaction. 

Measuring the rate of the catalytic reaction at different temperatures and determining the activation energy through an Arrhenius plot may reveal mass... 

If one has data on the reaction rate constant at several temperatures, this equation provides the basis for the most commonly used method for determining the activation energy of a reaction. If E is temperature invariant, a plot of in k versus the reciprocal of the absolute temperature should be linear with slope —(E/R). A typical plot is shown in Figure 3.9 for the reaction H2 + I2 - 2HI. The slope corresponds to an activation energy of 44.3 kcal/mole. 

A somewhat less accurate method for determining the activation energy involves integration of equation 3.3.55 over the interval between two data points, assuming that E is constant. 

In summary, to apply the Marcus theory of electron transfer, it is necessary to see if the temperature dependence of the electron transfer rate constant can be described by a function of the Arrhenius form. When this is valid, one can then determine the activation energy AEa only under this condition can we use AEa to determine if the parabolic dependence on AG/ is valid and if the reaction coordinate is defined. 

These data appeared to be very useful for the estimation of the relative O H bond dissociation energies in hydroperoxides formed from peroxyl radicals of oxidized ethers. All reactions of the type R02 + RH (RH is hydrocarbon) are reactions of the same class (see Chapter 6). All these reactions are divided into three groups RO + R (alkane, parameter bre = 13.62 (kJ moC1)172, R02 + R2H (olefin, bre = 15.21 (kJ mob1)1 2, and R02 + R3H (akylaromatic hydrocarbon), hrc 14.32 (kJ mol )12 [71], Only one factor, namely reaction enthalpy, determines the activation energy of the reaction inside one group of reactions. Also,... 

Figure 2.14 Simulated TDS spectra and the results of a number of different analysis procedures for determining the activation energy of desorption. The solid line represents the input for the simulations. Note that only the complete analysis [16] and the leading edge procedure of Habenschaden and Kiippers [29] give reliable results. The Chan-Aris-Weinberg curves [28] extrapolate to the correct activation energies at zero coverage (from de Jong and Niemantsverdriet [31]).

The student used the ratios in Mixture I and ran the experiment at two different temperatures. Calculate the rate, the rate constant, log k and 1/T for each temperature studied. From the data, plot k versus 1/T and determine the activation energy. Given that the activation energy for the reaction is 8.6 x 104 Joules, calculate the % error. 

In the present study we use the acid catalyzed crosslinking reaction directly (Scheme 1) as a means to estimate the amount of acid generated in a typical AHR resist. We then use the model proposed by Seligson and coworkers to determine the activation energy of crosslinking for a variety of crosslinking resins as they might be used in a resist formulation. Where... 

Another method for determining the activation energy involves using a modification of the Arrhenius equation. If we try to use the Arrhenius equation directly, we have one equation with two unknowns (the frequency factor and the activation energy). The rate constant and the temperature are experimental values, while R is a constant. One way to prevent this difficulty is to perform the experiment twice. We determine experimental values of the rate constant at two different temperatures. We then assume that the frequency factor is the same at these two temperatures. We now have a new equation derived from the Arrhenius equation that allows us to calculate the activation energy. This equation is ... 

It is also possible to use microcalorimetry to obtain useful information about the kinetic processes of the instability (i.e., aggregation, proteolysis) when thermal irreversibility prevails. Scan rates will often distort the onset behavior of the melting transition that can necessarily impose a shift in the Tm, as discussed further in the following text. The scan rate dependence of the Tm may then be used to determine the activation energy of the instability, provided an Arrhenius kinetic model describes the behavior. 

The techniques used for the determination of appearance energies are essentially identical to those described above for lEs. However, even when using the most accurately defined electron or photon energies, great care has to be taken when AEs are to be determined because of the risk of overestimation due to kinetic shift. Provided that there is no reverse activation energy for the reaction under study, the AE value also delivers the sum of heats of formation of the dissociation products. If substantial KER is observed, the AE may still be used to determine the activation energy of the process. 

Cure Kinetics. The cure kinetics of the mixed system to the B-stage were determined by the method outlined by Senich, MacKnight and Schneider (7) for two epoxy resins cured with dicyandianide by dynamic spring analysis (DSA). Senich et al. (7) used the elapsed time to the loss peak maximum of tan delta as a measure of the rate of the reaction at each temperature and for each frequency. The slope of an Arrhenius plot of In (tmax) vs. 1/T was then used to determine the activation energy. 

The face-by-face (R,a ) Isotherms on sucrose crystals growing from pure solutions allow us to determine the activation energies and, to some degree, the growth mechanisms for each of the F faces. 

Determine the activation energy for the diffusion of an Ag atom between adjacent threefold sites on Cu(lll) using the NEB method. Note that the energy of the end points in your calculation will not be exactly equal because fee and hep sites on the Cu(lll) surface are not identical. Compute the frequencies for this hopping process. 

Baier, Giesen et al. have described the dynamics of step and island on Ag(lll) and Cu(lOO) [31], as well as on Au(lOO) [32] electrodes in the electrolyte. Baier and Giesen [33] have determined the activation energies of mass transport processes on Ag(lll) electrodes in the aqueous electrolyte. Haftel and Einstein [34] have studied the influence of the electrochemical potential on energy landscapes close to step-and island edges Ag(lll) and Ag(lOO). A model of the metal/solution interface involving hydrophilicity of Ag(lll) and based on the capacitance analysis, has been published by Emets et al. [35] Electron... 

Only in the case that the activation energy is more or less independent of the reaction conditions can we determine the activation energy for the mechanism and only in this case can the activation energy be interpreted as an energy barrier. Fortunately, for most reactions of practical interest, the dependence of the activation energy on the reaction conditions is weak except at extreme reaction conditions. 

TPD is one of the simpler experimental techniques and the rate equation makes it obvious that it should be possible to determine the activation energy for desorption from a TPD spectrum. However, a general problem in TPD is that we cannot measure the coverage during the experiment. Also determination of the absolute reaction rate is rather difficult. 

One possibility is to determine the activation energy from a detailed simulation of the experiment. While this is doable, we will here rewrite the rate equation for TPD to eliminate the rate and the coverage. 

Person 1 Determine the activation energy, Ea,n, and preexponential factor, for the rate of dissolution of Ti. 

An equation developed by Kissinger and modified by others can be used to determine the activation energy using the temperamre at which the transformation rate is a maximum, Tp, for various heating rates [5] ... 

The rate constant for the chemical reaction 2N2Os - 4N02 +02 doubles from 22.5°C to 27.47°C. Determine the activation energy of the reaction. (9)... 

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