We apply the hypothesis of microscopic chaos to diffusion-controlled reacti
on which we study in a reactive periodic Lorentz gas. The relaxation rate o
f the reactive eigenmodes is obtained as eigenvalue of the Frobenius-Perron
operator, which determines the reaction rate. The cumulative functions of
the eigenstates of the Frobenius-Perron operator are shown to be generaliza
tions of Lebesgue's singular continuous functions. For small enough densiti
es of catalysts, the reaction is controlled by the diffusion. A random-walk
model of this diffusion-controlled reaction process is presented, which is
used to study the dependence of the reaction rate on the density of cataly
sts.