Homogeneous catalysis heterogeneous catalysis is the petrochemical alkylation process, where the liquid reactants are immiscible with a solution containing the catalyst. Heterogeneous catalysis offers the advantage that products are readily separated from the catalyst, and heterogeneous catalysts are often more stable and degrade much slower than homogeneous catalysts. However, heterogeneous catalysts are difficult to study, so their reaction mechanisms are often unknown. Enzymes possess properties of both homogeneous and heterogeneous catalysts. As such, they are usually regarded as a third, separate category of catalyst. Homogeneous catalysis In chemistry, homogeneous catalysis is catalysis in a solution by a soluble catalyst. Homogeneous catalysis refers
A priori probability case of the hydrogen atom or Coulomb potential (where the evaluation of the phase space volume for constant energy is more complicated) one knows that the quantum mechanical degeneracy is formula_56 with formula_57. Thus in this case formula_58. In statistical mechanics (see any book) one derives the so-called distribution functions formula_59 for various statistics. In the case of Fermi-Dirac statistics and Bose-Einstein statistics these functions are respectively These functions are derived for (1) a system in dynamic equilibrium (i.e. under steady, uniform conditions) with (2) total (and huge) number of particles formula_61 (this condition determines the constant formula_62), and (3)