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A quantitative understanding of pH, acid-base equilibria, and chemical speciation in natural waters including seawater is needed in applications ranging from global change to environmental and water quality management. In a previous study (Humphreys et al., 2022) we implemented a model of solutions containing the ions of artificial seawater, based upon the use of the Pitzer equations for the calculation of activity coefficients and including, for the first time, the propagation of uncertainties. This was extended (Clegg et al., 2022) to include the Tris buffer solutions that are used to calibrate the seawater total pH scale. Here we apply the same methods to develop a model of solutions containing the ions of standard reference seawater, based upon studies by Millero and co-workers. We compare the predictions of the model to literature data for: the dissociation of dissolved CO2 and bicarbonate ion; boric acid dissociation; saturation with respect to calcite, the ion product of water, and osmotic coefficients of seawater. Estimates of the uncertainty contributions of all thermodynamic equilibrium constants and Pitzer parameters to the variance of the calculated quantity are used to determine which elements of the model need improvement, with the aim of agreeing with properties noted above to within their experimental uncertainty. Further studies are recommended. Comparisons made with several datasets for carbonate system dissociation in seawater suggest which are the most reliable, and identify low salinity waters (S <10) as a region for which dissociation constants of bicarbonate are not yet accurately known. At present, the model is likely to be most useful for the direct calculation of equilibria in natural waters of arbitrary composition, or for adjusting dissociation constants known for seawater media to values for natural waters in which the relative compositions of the major ions are different.