During process design of reactive distillation systems, there is often uncertainty in the value of the reaction equilibrium constant (Keq), whether it is determined experimentally or calculated from thermochemical data. The effect of the reaction equilibrium constant on the existence and location of reactive azeotropes (constant boiling reactive mixtures) is explored for chemical equilibrium systems with a single chemical reaction. With a known set of starting points, arc-length continuation was used to track solutions of the equations for reactive azeotropy as a function of the reaction equilibrium constant. The results, portrayed in bifurcation diagrams, reveal that azeotropes may appear or disappear as the equilibrium constant is varied. Results for the esterification of acetic acid with ethanol indicate three distinct regions of phase behavior. The first regime (Keq < 0.449) contains a quaternary saddle reactive azeotrope. At intermediate values of the reaction equilibrium constant (0.449 < Keq <12.5), there are no reactive azeotropes in the system. In the third regime (Keq < 12.5), a minimum-boiling quaternary reactive azeotrope appears. In addition, for three reported literature values of the reaction equilibrium constant, each one lies in a different regime. Other examples also illustrate the broad taxonomy of reactive azeotropic systems.