Continuum approximation is often used to treat problems involving reaction mixtures of a vast number of species. Previous studies predicted that in many situations the lumped kinetics of a continuum of reactions, regardless of their kinetics, are of the power law form after a long time. In this article we present experimental support for such asymptotic power law kinetics. The system considered is catalytic deep desulfurization of a petroleum distillate. In addition, a theoretical analysis is made to establish the condition under which the continuum approximation is valid in the long-time limit. The condition turns out not to be very stringent for practical purposes.