In this paper we mathematically investigate the kinetics underlying the hydrogenolysis of xylitol over a metal based catalyst by using ordinary differential equations. The primary motivation for mathematically investigating this reaction lies on the fact that some of the value added products from this reaction are sourced from fossil fuels, which are not environmentally friendly. They have been reported by different researchers that they are the primary drive of global warming which leads to climate change, which causes severe disturbances in the Earth´s natural systems and economies. Xylitol, on the other hand, which is readily available from biomass have been reported as an alternative raw material for some of the value added products. A reaction mechanism proposed from experimental data is used to formulate a system of ordinary differential equations which is then analyzed using some qualitative analysis tools from mathematics. Numerical simulations are performed to try and ascertain the long time behavior of the system's solutions. Results showed that the solutions to the system approaches a lower dimensional invariant set with \( X_k=0 \) for \( k=1,2,...8 \) and \( X_k > 0 \) for \( k=9,10,11 \). These numerical results were found to be in agreement with the experimental results from the chemistry point of view. Therefore, it is believed that this model can be extended for use in other sugar alcohols higher than xylitol, like sorbitol as means to maximize the yields of the desired products.