We study a chemical reaction model with a one-dimensional reaction coordinate that moves in a parabolic barrier joined to a parabolic well. A different dynamic friction is present in the well and the barrier regions. It is found that, in the limit of large solvent response times, the reaction rate has singularities that can be interpreted as critical phenomena. The model is shown to have two main scaling regimes, governed by large barrier damping and large well damping, respectively. In either of these two regimes, there are nine subregimes, depending on whether the well or the barrier coupling is strong, intermediate, or weak. The behavior of the rate in these subregimes is governed by a multitude of critical exponents. However, in either of the main regimes, scaling reduces the number of independent exponents to just three, which result from the barrier friction, the well friction, and the barrier height.