This article addresses the model predictive controller design for a jacket tubular reactor with a simple reversible exothermic reaction (A reversible arrow B). Using energy and mass balance laws, four nonlinear hyperbolic partial differential equations are derived to model the tubular reactor dynamics in terms of two concentrations, the reactor temperature, and the spatially varying jacket temperature. The nonlinear continuous-time model is linearized and discretized in time by the use of the Cayley-Tustin transform without spatial discretization or model reduction. Along these lines, a state-feedback model predictive controller is formulated to realize model stabilization with respect to input and output constraints. To account for the state estimation, a Luenberger observer-based model predictive control (MPC) frame is further developed, and observer gains are obtained as solutions of an operator Riccati equation. Finally, two numerical examples are provided to demonstrate the feasibility and applicability of the proposed MPC designs.