Molecular activation energy

If we identify Sa as a minimum energy required to break out of a cage (a molecular activation energy), then from the Boltzmann probability distribution of Eq. (9.3-42) we see that the probability for a molecule to have this energy is... 

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.)... 

The reaction step in mechanism (5.F) is entirely comparable to the same reaction in low molecular weight systems. Such reactions involve considerably larger activation energies than physical processes like diffusion and, hence, do proceed slowly. 

This situation seems highly probable for step-growth polymerization because of the high activation energy of many condensation reactions. The constants for the diffusion-dependent steps, which might be functions of molecular size or the extent of the reaction, cancel out. 

Fig. 8. Variation of activation energy with kinetic molecular diameter for diffusion in 4A 2eohte (A), 5A 2eohte (0)> carbon molecular sieve (MSC-5A) (A). Kinetic diameters are estimated from the van der Waals co-volumes. From ref. 7. To convert kj to kcal divide by 4.184.

Activated diffusion of the adsorbate is of interest in many cases. As the size of the diffusing molecule approaches that of the zeohte channels, the interaction energy becomes increasingly important. If the aperture is small relative to the molecular size, then the repulsive interaction is dominant and the diffusing species needs a specific activation energy to pass through the aperture. Similar shape-selective effects are shown in both catalysis and ion exchange, two important appHcations of these materials (21). 

Rheology of LLDPE. AH LLDPE processiag technologies iavolve resia melting viscosities of typical LLDPE melts are between 5000 and 70, 000 Pa-s (50,000—700,000 P). The main factor that affects melt viscosity is the resia molecular weight the other factor is temperature. Its effect is described by the Arrhenius equation with an activation energy of 29—32 kj/mol (7—7.5 kcal/mol) (58). 

Diffusion of the molecular gases can be compHcated by reactions with the glass network, especially at the sites of stmctural defects. The diffusion coefficient of water, for example, shows a distinct break around 550°C (110). Above 550°C, the activation energy is approximately 80 kj /mol (19 kcal/mol), but below 550°C, it is only 40 kJ/mol (9.5 kcal/mol). Proposed explanations for the difference cite the fact that the reaction between water and the sihca network to form hydroxyls is not in equiUbrium at the lower temperatures. 

Oxidation. AH inorganic siUcon hydrides are readily oxidized. Silane and disilane are pyrophoric in air and form siUcon dioxide and water as combustion products thus, the soot from these materials is white. The activation energies of the reaction of silane with molecular and atomic oxygen have been reported (20,21). The oxidation reaction of dichlorosilane under low pressure has been used for the vapor deposition of siUcon dioxide (22). 

Approximate calculations of this activation energy have been made in a number of examples using the quanmm theory of molecular binding, by making assumptions concerning the stmcture and paitition functions of the Uansition state molecule. 

Table 3.3. Correlation between Intramolecular Strain from Molecular Mechanics (MM) Calculations and Activation Energies for Dissociation of C—C Bonds in Substituted Ethanes"...

The final phase of resole manufacture is known as the condensation stage (Scheme 3). This is the actual process by which molecular weight is developed and involves the combination of the hydroxymethyl phenol intermediates to form oligomers. It can be reasonably well separated from the resole methylolation reaction in practice by maintaining reaction temperatures below about 70°C. The activation energy for condensation is higher than that for methylolation. This is not to say that condensation does not occur at temperatures below 70°C. It simply means that the methylolation is much faster than condensation at this temperature. 

Simple collision theory does not provide a detailed interpretation of the energy barrier or a method for the calculation of activation energy. It also fails to lead to interpretations in terms of molecular structure. The notable feature of collision theoiy is that, with very simple means, it provides one basis for defining typical or normal kinetic behavior, thereby directing attention to unusual behavior. 

We ll consider the molecular dissociation reaction first (upper illustration). We want to determine the transition structure and to predict the activation energy for the reaction. In order to do so, we ll need the following information ... 

These values suggest that the two hydroxycarbene isomers convert into one another very easily. The barrier to molecular dissociation of the cis form is significant, however, and so this structure probably does not dissociate directly, but rather first converts to the trans isomer, which is subsequently transformed into formaldehyde, which dissociates to carbon monoxide and hydrogen gas. The article from which this study was drawn computes the activation energy for the trans to cis reaction as 28.6 kcal- moT at RMP4(SDQ)/6-31G(d,p) (it does not consider the other reactions). 

Anhydrous NaC102 crystallizes from aqueous solutions above 37.4° but below this temperature the trihydrate is obtained. The commercial product contains about 80% NaC102. The anhydrous salt forms colourless deliquescent crystals which decompose when heated to 175-200° the reaction is predominantly a disproportionation to C103 and Cl but about 5% of molecular O2 is also released (based on the C102 consumed). Neutral and alkaline aqueous solutions of NaC102 are stable at room temperature (despite their thermodynamic instability towards disproportionation as evidenced by the reduction potentials on p. 854). This is a kinetic activation-energy effect and, when the solutions are heated near to boiling, slow disproportionation occurs ... 

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