Batch distillation is a commonly used unit operation in specialty chemicals. In order to maximize profitability and improve separations using a batch distillation column, optimal reflux operation can be used. The mathematical and numerical complexities of the optimal control problem get worse when uncertainty is present in the formulation. However, in the specialty chemical industry, thermodynamic properties of not all chemical components of a mixture to be separated are known. In reality, these components are treated as missing components and their composition is merged with known components. These uncertainties in the problem formulation can result in suboptimal solutions. In this work, we are providing a new approach to solve this problem. We use Ito processes and stochastic maximum principle for the formulation of the resulting stochastic optimal control problem. This algorithm is implemented in the MultiBatchDS batch distillation process simulator. Finally, a numerical case study derived from a real-world batch distillation separation problem encountered at Firmenich is presented to show the scope and application of the proposed approach.