A partial differential equation for the number density of a D-dimensional grand canonical ensemble is used to derive a simple expression for the reaction rate of transition state theory as a function of temperature and chemical potential. The reaction rate equation is valid for both Bose-Einstein and Fermi-Dirac statistics. In the limiting case where the chemical potential goes to minus infinity, it is shown that this reaction rate equation reduces to the well-known Eyring reaction rate equation of transition state theory. By expanding the reaction rate equation in a Taylor series about the equilibrium activity, it is shown how rate equations can be derived giving the approach to equilibrium. (C) 1997 American Institute of Physics.