Nonlinear backstepping is a recursive design methodology that makes use of the Lyapunov stability theory. Although backstepping can be applied to a larger class of systems than other differential-geometric methods such as feedback linearization, its applicability is limited to "parametric pure-feedback systems". In this work, we apply the idea of backstepping to a benchmark chemical reactor by using a simple transformation of the original nonlinear model of the chemical reactor. This chemical reactor does not fall under the category of systems for which backstepping can be applied. However, the fundamental idea involved in backstepping can still be applied to this process after a certain transformation of the original variables. A robust adaptive nonlinear controller is also designed by introducing uncertainty into all of the estimated parameters. This type of uncertainty leads to nonaffine uncertain parameters that are difficult to handle with the traditional backstepping algorithm. Using Lyapunov theory, we derive a controller that can ensure robust stability.