Over recent years, nanofiltration (NF) has been considered as an effective way to improve processing steps in metallurgical and hydrometallurgy applications dealing with mixtures of metal ions in sulphuric-acid-dominated solutions. The principal advantage of NF membranes over reverse osmosis (RO) membranes is their ability to allow for a practically free passage of acid, while metallic species, especially multi-charged species, are efficiently rejected. In general, these sulphuric solutions cover a range from strongly acidic solutions with pH below 1 up to moderately acidic solutions of pH 3. Over this range, changes in the feed acidity influence both the aqueous electrolyte solution speciation (SO42-/HSO4-/H+) and the membrane acid-base properties (protonation of carboxylic and amine groups). However, few studies have been published on the trans-membrane transport of inorganic species coupled to changes in their speciation as well as to the properties of the membrane phase. In this study, experimental data on the sulphuric acid rejection for pH values from 1 to 3 have been obtained with an aromatic poly(piperazine) amide membrane (NF270) at various trans-membrane pressures. The results were modelled by a novel version of the Solution-Electro-Diffusion model taking into account equilibrium reactions, and a general (quasi) analytical solution was obtained for the transport of weak electrolytes of arbitrary valence type. The equilibrium weak acid reaction made the total sulphate (SO42-/HSO4-) rejection decrease strongly as the fraction of single-charged hydrogen sulphate (HSO4-) in the feed increased. From the modelling procedure, permeances to H+, HSO4- and SO42- over the studied pH range were determined.