Activation energy profile

For the n-butenes the activation energy profile shows no difference among the top of the barriers linking the three isomers (Table II). According to the model the theoretical selectivities determined only by the statistical factors should be k2i/kn ku/h2 kn/k2S = 1 3 3. The corresponding experimental selectivities were 1.2 2.9 2.4 and were temperature independent. The relative reactivities predicted by the model compared with those found experimentally are 1-butene cis-2-butene ran -2-butene = 1.0 (0.38 0.06) (0.12 0.03) vs. 1 0.37 0.18, respectively. 

The activation energy profile shows two important differences compared with the butene system (Table II) (a) the absolute activation energy is much higher E2 = 22.6 0.6 kcal/mole vs. E2i = 10.4 0.2 kcal/ mole (b) there is a difference in activation energy in going from either one of the 2-isomers to the other one and to the 1-pentene. 

Figure 2.10 PE-PtHZSM-5 effective activation energy profiles for (a) paraffins (triangles), olefins (squares), and alkyl aromatics (full circles) in helium (b) paraffins (triangles) in hydrogen. (Reproduced by permission of John Wiley Sons, Ltd)...

It follows that the adsorption rate is constant for all adsorption sites, irrespective of the value of the adsorption heat. The desorption rate depends on the adsorption heat in a simple way up to a constant additive factor, the activation energy of the desorption process is equal in magnitude to the adsorption heat of the site considered. The activation energy profiles for the adsorption-desorption process have the form represented schematically... 

Fig. 12.1 Schematic representation of the activation energy profiles for the adsorption-desorption process studied in the experiments of Drazer and Zanette [17]. The different activation energy profiles correspond to adsorption sites characterized by different adsorption heats. All energy profiles start from the same value f7iiquid which corresponds to the liquid phase, increase up to the same maximum value f/max. and then decrease to various final values f7site(l) site(2) f/site(3), ., corresponding to surface sites characterized by various adsorption heats. (From [6].)...

FIGURE 25.12 Computed C—H activation energy profiles (kcal/mol) for species ([MCri-TpXPHj)] [21] where (M = Fe, Ru and Os Tp = hydridotris(3,5-dimethylpyrazolyl)borate) [4c]. 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

Similar difficulties arise in the nitrations of 2-chloro-4-nitroaniline and /)-nitroaniline. Consideration of the rate profiles and orientation of nitration ( 8.2.5) these compounds suggests that nitration involves the free bases. However, the concentrations of the latter are so small as to imply that if they are involved reaction between the amines and the nitronium ion must occur upon encounter that being so, the observed activation energies appear to be too high. The activation energy for the simple nitration of the free base in the case of/>-nitroaniline was calculated from the following equation ... 

Figure 12 11 compares the energy profile for nitration of benzene with those for attack at the ortho meta and para positions of (trifluoromethyl)benzene The presence of the electron withdrawing trifluoromethyl group raises the activation energy for attack at all the ring positions but the increase is least for attack at the meta position... 

Computer Models, The actual residence time for waste destmction can be quite different from the superficial value calculated by dividing the chamber volume by the volumetric flow rate. The large activation energies for chemical reaction, and the sensitivity of reaction rates to oxidant concentration, mean that the presence of cold spots or oxidant deficient zones render such subvolumes ineffective. Poor flow patterns, ie, dead zones and bypassing, can also contribute to loss of effective volume. The tools of computational fluid dynamics (qv) are useful in assessing the extent to which the actual profiles of velocity, temperature, and oxidant concentration deviate from the ideal (40). 

The mechanism of the reaction A - B consists of two steps, with the formation of a reaction intermediate. Overall, the reaction is exothermic, (a) Sketch the reaction profile, labeling the activation energies for each step and the overall enthalpy of reaction, (h) Indicate on the same diagram the effect of a catalyst on the first step of the reaction. 

Step 2 N202 + H2 — N,0 + H,0 Step 3 N20 + H2 — N, + H,0 (a) Which step in the mechanism is likely to be rate determining Explain your answer, (b) Sketch a reaction profile for the overall reaction, which is known to be exothermic. Label the activation energies of each step and the overall reaction enthalpy. 

FIGURE 6.2 (a) Free energy profile for a reaction with an intermediate. AG and AG are the free energy of activation for the first and second stages respectively, (b) Free energy profile for a reaction with an intermediate in which the first peak is higher than the second. 

The number of particles that must be moved for complete equilibration is determined by the minimum of this expression over N. We thus determine an activation free energy profile... 

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