Isokinetic consecutive reactions in heterogeneous catalysis

The formal kinetics of a system of irreversible ''isokinetic'' consecutive reactions (i.e. reactions having the same rate and the same rate constants) has been established, considering a common (pseudo-) first order rate constant k. The characteristics of the kinetics of all intermediates have been determined. The nth intermediate goes through a maximum located at time t(n)(max=)n/k and is equal to (a/n!) (n/e)(n), a being the initial number of moles of the reactant. For large values of n (n>4), this maximum tends to a/root 2 pi n. The selectivity in the nth intermediate has been found equal to ((kt)(n-1)/n!)(n-kt). Other relationships independent of time with dimensionless parameters correlating the partial conversion tau(n) of each intermediate product with the total conversion tau of the initial reactant have also been determined, tau(n) has been found to vary as a function of tau as: tau(n) = (1 - tau)/n. The maximum of tau(n) for the first intermediate tends to 1/e, whereas for higher values of n, this maximum tends to (1/root 2 pi n). A new concept of ''molecular exposure'', expressed in moles x second (or in molecules x second), has been defined. It corresponds to the surface area comprised between each curve and the x-axis. It has been demonstrated that it remains constant, as well for the reactant as for all the intermediates formed in isokinetic reactions. It is equal to a/k. Some examples from the literature on the catalytic conversion of hydrocarbons such as mono-and dihydrogenations of diolefins and deuterium-alkane isotopic exchange, illustrate and substantiate this kinetic model.