We apply recurrent neural networks (RNNs) to predict the time evolution of the concentration profile of multiple species resulting from a set of interconnected chemical reactions. As a proof of concept of our approach, RNNs were trained on a synthetic dataset generated by solving the kinetic equations of a system of aqueous inorganic iodine reactions that can follow after nuclear reactor accidents. We examine the minimum dataset necessary to obtain accurate predictions and explore the ability of RNNs to interpolate and extrapolate when exposed to previously unseen data. We also investigate the limits of our RNN by evaluating the robustness of the training initialization on our dataset.