Interchange mechanism rate equation

Realizing that the last four reactions of the ion-atom interchange mechanism listed each have only one-half the statistical probability of occurring as do the first four and assuming no isotope effect on the rate constants, we can write the following set of rate equations ... 

Interchange mechanisms (IA or ID) in a preformed OS complex will generate the following observed rate laws (which cannot distinguish IA from ID) with the equilibrium constant =Kos (equation 1.15) and k = k, (equation 1.16) ... 

Model 2. First note that the stoichiometry of Eq. 10 is symmetrical in A and B, so just interchange A and B in Model 1, put 2 = 0 we will get = k[BY, which is what we want. So the mechanism that will match the second-order rate equation is... 

Substitution of several metal-carbonyl complexes Cr(CO)6 and Mn(CO)5 (amine) show a small dependence on the nature and concentration of the entering hgand. Under pseudo-first-order conditions, the rate laws for these substitutions have two terms, as shown for Cr(CO)6 (as for some substitution reactions with 16e complexes, see equation 5). The second-order term was always much smaller than the first-order term. A mechanism that ascribes the second-order term to dissociative interchange (U) has been suggested for the Mo(CO)5Am system (Am = amine) and involves a solvent-encased substrate and a species occupying a favorable site for exchange. Thus, the body of evidence for the simple metal carbonyls indicates that CO dissociation and is the mechanism of ligand substitution reactions. 

In these equations, M denotes the surface, without prejudice to the question whether the adatom is held at a surface site, or is freely mobile and therefore views the surface as an area of uniform potential. A choice between the two mechanisms can be made using experimental data restricted to the condition of an atomization rate which is slow relative to the rate of interchange of molecules between the gas phase and the surface when this restriction is applicable, it is possible to write... 

Mechanistic studies have been used to attempt to explain the rapid initiation rate of the 18-electron pyridine solvates. Using the reported initiation rate of 4a [6], the upper limit of free energy of activation was determined to be 15.45kcalmol" at 5°C using the Eyring equation [39], Similar to the Grubbs-Hoveyda complexes, these precatalysts have multiple potential pathways by which they can initiate (e.g., interchange or dissociative). An associative mechanism can be ruled out due to the coordinatively saturated, six-coordinate nature of these complexes. 

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