This presentation is about the design of a backstepping observer-based output feedback controller for a class of coupled parabolic Partial Differential Equations (PDEs) with different diffusions. The considered system is endowed with a sensor at the left boundary and an actuation at the right boundary. Firstly, a backstepping observer is designed. Secondly, compared to the existing literature a more relaxed condition is deduced to guarantee the stability of the plant system by means of a controller. Thirdly, using the separation principle, an observer-based output feedback controller is set up based on the designed observer and controller. Finally, the efficiency of the proposed method is shown by taking a simplified model of Chemical Tubular Reactor.