Linear free energy relationships in heterogeneous catalysis VII. Reactivity of ring hydrogens in catalytic dehydrogenation of cyclohexanes

The rates of dehydrogenation of various methyl-substituted cyclohexanes catalyzed by chromia-alumina and molybdena-alumina were numerically analyzed in terms of the varying reactivities of the ring hydrogens classified into several groups, from the viewpoint of the LFER. It is demonstrated that the rate, v(R,T), can be represented as the sum of the reactivities of the ring hydrogens, vH(m,T), as v(R,T) = ∑ w(R,m) vH(m,T), where w(R,m) is the number of mth hydrogens in a reactant R. The logarithm of the reactivity of ring hydrogen is, in turn, linearly related to the delocalizability, DrR(H), a quantum-chemical reactivity index for hydrogen abstraction reactions, as log vH(m,T) = log vH(O,T) + γ(T)ΔDrR(Hm)2.303RT, where vH(O,T) is the reactivity of an imaginary hydrogen whose delocalizability is 1.0, and γ(T) is a proportional constant. Furthermore, from the temperature dependence, γ(T) has been correlated to the isokinetic temperature, T8, and as the result the rates are expressed as follows: v(R,T) = vH(O, ∞) exp (−EA(0)RT) ∑ w(R,m) exp γD (1 − TT8)ΔDrR(Hm)RT where γD is a constant independent of temperature. Thus, the rate of dehydrogenation of any reactant at any temperature can be calculated with the knowledge of delocalizabilities inherent to ring hydrogens and four parameters characteristic for a catalyst, i.e., vH(O, ∞), EA(O), γd, and T8. This equation is in accordance with the reaction scheme where the dehydrogenation to monoolefin is the slow step.