Operating a reactive batch distillation (RBD) process in an optimal manner is of paramount importance for improving product quality and profitability in the face of changing market conditions. However, implementation of an open loop optimal control policy may lead to significant reduction in yield and amount of desired product produced when unmeasured disturbances occur during operation. In this work, an observer error feedback-based multirate nonlinear internal model control (NIMC) scheme is developed for optimal trajectory tracking in the face of unmeasured disturbances. In particular, mismatch in the initial conditions and process parameter variations that can occur during RBD operation are considered. To reduce the time required for online computations, a recently proposed reduced order RBD model [Reddy et al. Compt. Chem. Eng., 2017, 106, 40-56] is used for the controller synthesis. Because the thermodynamic model associated with the RBD process has discontinuities, a multirate version of unscented Kalman filter (UKF) has been developed on the basis of the reduced order model for solving the state estimation problem associated with the proposed NIMC formulation. The efficacy of the proposed approach has been demonstrated by simulating an optimal trajectory tracking problem in the RBD process involving production of butyl acetate. The proposed multirate NIMC formulation is found to be computationally efficient and work reasonably well when tested on the RBD process for solving the set point tracking problem in the presence of unmeasured disturbances. In particular, it is advantageous to operate the RBD process using the proposed UKF-NIMC scheme when the system is subjected to unmeasured disturbances.