Homogeneous catalysis Homogeneous catalysis In chemistry, homogeneous catalysis is catalysis in a solution by a soluble catalyst. Homogeneous catalysis refers to catalytic reactions where the catalyst is in the same phase as the reactants. Homogeneous catalysis applies to reactions in the gas phase and even in solids. Heterogeneous catalysis is the alternative to homogeneous catalysis, where the catalysis occurs at the interface of two phases, typically gas-solid. The term is used almost exclusively to describe solutions and often implies catalysis by organometallic compounds. The area is one of intense research and many practical applications, e.g., the production of acetic acid. Enzymes are
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)