This study presents the results of a mathematical model proposed for carbochlorination of niobium pentoxide under a stream of chlorine gas in the presence of solid carbon as reducing agent. The model is based on one-dimensional unsteady state regime considering kinetic, diffusion and mass conservation. Solutions for this equation, associated with initial and boundary conditions were obtained using the method of finite differences. In this study, the Nelder and Mead optimization model was used and t-Student’s statistics was applied for goodness of fit analysis. The data obtained experimentally in a previous study, concerning the conversion of niobium pentoxide into niobium pentachloride gas, was processed using a computer software written for an Excel platform on Visual Basic for Applications (VBA). It was found that the experimental results were in accordance with the models outputs, allowing satisfactory representation of the observed reaction mechanism, incorporating the effects of the intervening variables. It was also determined the kinetic constant and the effective diffusivity for the different levels of carbon content and porosity, at temperatures of 700 Celsius degrees and 800 Celsius degrees for a specified gas flow and sample height. It was observed that the best conversion of the niobium pentoxide (96.5 per cent) is obtained at 800 Celsius degrees for 28 per cent porosity and 9 per cent carbon, for diffusion control.