Activation energies

The largest values of primary kinetic deuterium isotope effects are found for reactions where the bond to hydrogen is about one-half broken (kn/ D values are 6-8). Smaller values are found in reactions in which the bond to hydrogen is less than or more than one-half broken. Normally, kn/ D values less than maximum correspond to bond cleavage of . Primary kinetic deuterium 

The electrophilic nitration of benzene using acetyl nitrate involves the replacement of a hydrogen on the benzene ring by a nitro group. The reaction is second order overall, first order in benzene, and first order in the nitrating agent—v = [C7 nr, acetyl nitrate]. 

Use of fully deuterated benzene gave ku/ko = 1. These data suggest diat the nitrating agent attacks the benzene ring in tire rate-determining step, but C-H 

even diough loss of hydrogen is required for the product to be formed, its removal is not taking place in die rate-determining step of the reaction—it must take place after die rate-determining step. 

The base-promoted bromination of ketones is a second-order process, first order in ketone and first order in base dius v = /c ketone base. The bromine concentration does not appear in die rate law that is, the reaction is zero order in [Br2]. 

A more elaborate theoretical approach develops the concept of surface molecular orbitals and proceeds to evaluate various overlap integrals [119]. Calculations for hydrogen on Pt( 111) planes were consistent with flash desorption and LEED data. In general, the greatly increased availability of LEED structures for chemisorbed films has allowed correspondingly detailed theoretical interpretations, as, for example, of the commonly observed (C2 x 2) structure [120] (note also Ref. 121). 

Since AE ct SO, and Ejj, is a maximum at the transition state, one can see that Eq. (40) implies that the softness of the system is also a maximum in the transition state, while the hardness is a minimum. This statement is in agreement with theoretical calculations that show that in the transition state, which corresponds to the less stable configuration of the system, the hardness attains its lowest value. 

assume that the softness of the initial state, when all the reactants are far away from each other, is roughly equal to the sum of the softnesses of the reactants when they are isolated from each other, and consider the case of a reaction between several molecules, in which only a specific atom of each one of the reactants participates directly in the bond breaking and bond forming processes. In this context, if it is assumed that the changes in all the other atoms of the reacting molecules can be neglected, one finds that 

In previous publications, it had already been inferred [8,9,21-26,43], that the larger the fukui function, the greater the reactivity, and this statement had already been successfully used to explain several aspects of the chemical reactivity of different systems. The present approach allows one to understand that this may be due to the fact that the sites with the largest values of the appropriate condensed fukui function may be associated with the weakest bonds, and with those reaction paths with the smallest activation energy barriers. 

It is important to mention that if one makes use of the experimental values of I and A in Eq. (11), to determine the hardnesses in Eq. (40) in the form given by Eqs. (41) and (42), and if one sets Ng = 1 and a = 1, one finds that this expression provides the correct trends, and reasonable estimates of the activation energies. Through this approach, one also finds that if a is determined to reproduce the experimental activation energy, one is led to values that correlate rather well with other theoretical estimates of the looseness of the transition state [17,44]. 

The expressions derived for the bond energies and the activation energies may be used to analyze the behavior of reaction energies with respect to the changes in the hardness. 

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Enzymes act by lowering the overall activation energy of a reaction sequence by involving a series of intermediates, or a mechanism, different from the spontaneous uncatalysed reaction. 

Here, r is positive and there is thus an increased vapor pressure. In the case of water, P/ is about 1.001 if r is 10" cm, 1.011 if r is 10" cm, and 1.114 if r is 10 cm or 100 A. The effect has been verified experimentally for several liquids [20], down to radii of the order of 0.1 m, and indirect measurements have verified the Kelvin equation for R values down to about 30 A [19]. The phenomenon provides a ready explanation for the ability of vapors to supersaturate. The formation of a new liquid phase begins with small clusters that may grow or aggregate into droplets. In the absence of dust or other foreign surfaces, there will be an activation energy for the formation of these small clusters corresponding to the increased free energy due to the curvature of the surface (see Section IX-2). 

It was noted in Section XVII-1 that chemisorption may become slow at low temperatures so that even though it is favored thermodynamically, the only process actually observed may be that of physical adsorption. Such slowness implies an activation energy for chemisorption, and the nature of this effect has been much discussed. 

Fig. XVIII-13. Activation energies of adsorption and desorption and heat of chemisorption for nitrogen on a single promoted, intensively reduced iron catalyst Q is calculated from Q = Edes - ads- (From Ref. 130.)...

This means that desorption activation energies can be much larger than those for adsorption and very dependent on 6 since the variation of Q with 6 now contributes directly. The rate of desorption may be written, following the kinetic treatment of the Langmuir model. 

In the case of nitrogen on iron, the experimental desorption activation energies are also shown in Fig. XVIII-13 the desorption rate was given by the empirical expression... 

Fig. XVIII-15. Oxygen atom diffusion on a W(IOO) surface (a) variation of the activation energy for diffusion with d and (b) variation of o- (From Ref. 136. Reprinted with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

Just as the surface and apparent kinetics are related through the adsorption isotherm, the surface or true activation energy and the apparent activation energy are related through the heat of adsorption. The apparent rate constant k in these equations contains two temperature-dependent quantities, the true rate constant k and the parameter b. Thus... 

The apparent activation energy is then less than the actual one for the surface reaction per se by the heat of adsorption. Most of the algebraic forms cited are complicated by having a composite denominator, itself temperature dependent, which must be allowed for in obtaining k from the experimental data. However, Eq. XVIII-47 would apply directly to the low-pressure limiting form of Eq. XVIII-38. Another limiting form of interest results if one product dominates the adsorption so that the rate law becomes... 

Some early observations on the catalytic oxidation of SO2 to SO3 on platinized asbestos catalysts led to the following observations (1) the rate was proportional to the SO2 pressure and was inversely proportional to the SO3 pressure (2) the apparent activation energy was 30 kcal/mol (3) the heats of adsorption for SO2, SO3, and O2 were 20, 25, and 30 kcal/mol, respectively. By using appropriate Langmuir equations, show that a possible explanation of the rate data is that there are two kinds of surfaces present, 5 and S2, and that the rate-determining step is... 

Calculate also the activation energy for the reaction, again in kcal/mol, assuming that the Coulomb repulsion maximizes at 3 -y 10 cm separation of the nuclear centers. Assuming a successful cold-fusion device, how many fusions per second would generate one horsepower (1 hp) if the conversion of heat into work were 10% efficient ... 

Another limitation of tire Langmuir model is that it does not account for multilayer adsorption. The Braunauer, Ennnett and Teller (BET) model is a refinement of Langmuir adsorption in which multiple layers of adsorbates are allowed [29, 31]. In the BET model, the particles in each layer act as the adsorption sites for the subsequent layers. There are many refinements to this approach, in which parameters such as sticking coefficient, activation energy, etc, are considered to be different for each layer. 

Temperature progranuned desorption (TPD), also called thenual desorption spectroscopy (TDS), provides infonuation about the surface chemistry such as surface coverage and the activation energy for desorption [49]. TPD is discussed in detail in section B 1.25. In TPD, a clean surface is first exposed to a gaseous... 

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