Hydrocarbons linear free energy relationship

The [Ruv(N40)(0)]2+ complex is shown to oxidize a variety of organic substrates such as alcohols, alkenes, THF, and saturated hydrocarbons, which follows a second-order kinetics with rate = MRu(V)][substrate] (142). The oxidation reaction is accompanied by a concomitant reduction of [Ruv(N40)(0)]2+ to [RuIII(N40)(0H2)]2+. The mechanism of C—H bond oxidation by this Ru(V) complex has also been investigated. The C—H bond kinetic isotope effects for the oxidation of cyclohexane, tetrahydrofuran, propan-2-ol, and benzyl alcohol are 5.3 0.6, 6.0 0.7, 5.3 0.5, and 5.9 0.5, respectively. A mechanism involving a linear [Ru=0"H"-R] transition state has been suggested for the oxidation of C—H bonds. Since a linear free-energy relationship between log(rate constant) and the ionization potential of alcohols is observed, facilitation by charge transfer from the C—H bond to the Ru=0 moiety is suggested for the oxidation. 

The guidelines of linear-free energy relationships have also been used to capture not only the hydrocarbon stmcture/function but also catalyst structure/function relationships. Thus Liguras et al. (39) have fashioned a model where the rate constant is a function of the reactant, the reaction family, and the catalyst silicon to aluminum ratio. This fledgling approach considerably reduces the number of kinetic parameters and appears to be quite useful in the modelling of complex kinetics of hydrocarbon feedstocks. 

The aromatic hydrocarbons are stronger reducing agents when electronically excited than in the ground state, and can donate an electron to a species A. The rate of this electron transfer depends on the ease with which A is reduced, and the reaction follows a linear free-energy relationship. When AG° is sufficiently small, such thatk A [3, then the reaction is diffusion controlled, with a rate constant which is constant and is independent of the reaction energy. These effects are indicated in Figure 9.5. 

The rates of radical-forming thermal decomposition of four families of free radical initiators can be predicted from a sum of transition state and reactant state effects. The four families of initiators are trarw-symmetric bisalkyl diazenes,trans-phenyl, alkyl diazenes, peresters and hydrocarbons (carbon-carbon bond homolysis). Transition state effects are calculated by the HMD pi- delocalization energies of the alkyl radicals formed in the reactions. Reactant state effects are estimated from standard steric parameters. For each family of initiators, linear energy relationships have been created for calculating the rates at which members of the family decompose at given temperatures. These numerical relationships should be useful for predicting rates of decomposition for potential new initiators for the free radical polymerization of vinyl monomers under extraordinary conditions. 

Previous studies have shown that there is a correlation between the enthalpy of hydration of alkanes and their accessible surface area [30,31] or related magnitudes. Moreover, relationships between the hydration numbers calculated from discrete simulations for hydrocarbons and both the free energy and enthalpy of hydration of these molecules have also been reported [32] and have been often used to evaluate solvation enthalpies. Analysis of our results, illustrates the existence of a linear relationship between A//n eie and the surface of the van der Waals cavity,. SVw, defined in MST computations for the calculation of the non-electrostatic contributions (Figure 4-1). In contrast, no relationship was found for the electrostatic component of the hydration enthalpy (A//eie data not shown). Clearly, in a first approximation, one can assume that the electrostatic interactions between solute and solvent can be decoupled from the interactions formed between uncharged solutes and solvent molecules. 

For an atom in the enzyme or the substrate to interact with the solvent it must be able to form Van der Waals contact with water molecules. The accessible surface area of an atom is defined as the area on the surface of a sphere, radius R on each point of which the centre of a solvent molecule can be placed in contact with the atom without penetrating any other atoms of the molecule (Fig. 12). R is the sum of the Van der Waals radii of the atom and solvent molecule [27]. There is a linear relationship between the solubility of hydrocarbons and the surface area of the cavity they form in water [28]. It has been estimated that the hydrophobicity of residues in proteins is 100 J/mole/A of accessible surface area [29]. The surface tension of water is 72 dynes/cm so to form a free surface area of water of 1 A costs 435 J/mole/A. The implication is that the free energy of cavity formation in water to receive the hydrophobic group is offset by favourable interactions (dispersion forces) between the solute and water. 

A number of perylene derivatives undergo cyclo addition reaction. Hern-don has shown that the free energies of activation of the reaction of MA with aromatic hydrocarbon has a linear relationship with calculated resonance energy differences. This approach has significant prediction value (see Table 4.5). Recently, kinetic studies of the DA reaction of maleic anhydride with polycyclic aromatics have been reported. 

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