  We study the limit of high activation energy of a special Fokker-Planck
equation, known as Kramers-Smoluchowski (K-S) equation. This equation governs
the time evolution of the probability density of a particle performing a
Brownian motion under the influence of a chemical potential H/e. We choose H
having two wells corresponding to two chemical states A and B. We prove that
after a suitable rescaling the solution to (K-S) converges, in the limit of
high activation energy (e -> 0), to the solution of a simple system modeling
the diffusion of A and B, and the reaction A <-> B.
  The aim of this paper is to give a rigorous proof of Kramer's formal
derivation and to embed chemical reactions and diffusion processes in a common
variational framework which allows to derive the former as a singular limit of
the latter, thus establishing a connection between two worlds often regarded as
separate.
  The singular limit is analysed by means of Gamma-convergence in the space of
finite Borel measures endowed with the weak-* topology.
