Reverse Osmosis (RO) is a membrane-based technology for water desalination. Of paramount importance is the understanding of ion selectivity in mixtures of salts, i.e., to what extent the membrane retains one ion more than another in a multicomponent salt solution. We apply continuum transport theory to describe a large set of data for the ion selectivity of RO membranes treating brackish groundwater with more than 10 different monovalent and divalent ions. The model is based on the Donnan steric partitioning pore model extended to include ions of multiple charge states, such as bicarbonate/carbonic acid, ammonia/ammonium, and hydroxyl/hydronium ions and the acid-base reactions between them and with the membrane charge. By adjusting for each ion the ratio of ion size over pore size, we can fit the model to the data. We note that the fitted ion sizes do not always follow a logical order based on the ionic or hydrated size of the ions and that rejection of divalent cations is overestimated in some cases. We discuss possible theoretical improvements to address these discrepancies. Our results highlight the potential of continuum transport theory to describe in detail multicomponent ion transport in RO membranes. The development of a detailed and validated physics-based model is an important step toward achieving improved operation and design of RO-based desalination systems.