A model of the biochemical processes related the removal of pollutants from wastewater in a batch reactor is considered, where the following hypotheses are assumed: (i) the affinity between the microorganisms and the substrates are described by Monod; (ii) the agitation system guarantees homogeneity of the medium; and (iii) there is a superior limit for the microbial population, representing a closed system. The last hypothesis leads to the choice of a Gompertz model for the biomass growth, since it naturally describes a limited population. As an application, the model was used to describe the autotrophic removal of nitrate from wastewater, on controlled conditions, using elemental sulphur as electron donor. The experiment obtained the time evolution of the concentration of nitrate and sulphate, and the initial and final biomass concentration. These time profiles were then used to evaluate the proposed model, considering the chi-squared statistics and parameters estimation. All the instrumental uncertainties and statistical variation were considered on the analysis in order to obtain a relevant confidence level for the model, making the study statically robust. It is shown that the hypotheses (i) and (ii) hold with confidence level of 98%. Hypothesis (iii) could not be verified since the experiment conditions were not favourable for the population to reach a maximum.