The equations that model a first-order reaction occurring in the four-dimensional parameter space of a CSTR are analyzed using the methods of singularity theory. By reference to experimental data for the hydration of 2,3-epoxy-1-propanol, a direct connection is established between the parameters of the equations and the physical quantities they represent. This simple step suggests a new use for singularity theory as a design tool for chemical reactors, which is illustrated in the latter part of this work by following the pathways of degenerate bifurcations through the codimension 1 and 2 parameter spaces. In the first part of this work, a physical constraint, namely, the boiling point of the reaction mixture, is used to construct a "thermal runaway" curve in the codimension zero operating parameter plane. The shape of this curve reveals the remarkable, but unpleasant, fact that a decrease in the ambient temperature can lead to a thermal runaway. Such unexpected and dangerous thermal misbehavior could not be predicted from the classical codimension zero Hopf and saddle-node bifurcation loci.