The main component of this data set comprises calculated inorganic iron concentrations (Fe' = sum of iron hydroxide species). Inorganic iron is the most bioavailable chemical form of Fe in the ocean. Concentrations of Fe' were calculated according to two models, which we refer to as the discrete ligand model and the continuous binding site model. The discrete ligand model, which is currently applied to calculate Fe speciation in global biogeochemical models, combines dissolved Fe concentrations, conditional stability constants and ligand concentrations to obtain inorganic iron, whilst the continuous distribution model uses the NICA-Donnan model to obtain Fe'. The data supports the manuscript "Climate change decreases biologically available iron pool in the surface ocean." In this manuscript we use the continuous binding site model to show that surface ocean Fe' is sufficient for Fe-replete phytoplankton. We apply new estimates of Fe' to a simple phytoplankton growth model to show that both Fe' and relative growth rates will decrease under the high-end future climate scenario (SSP5-8.5) in all Fe-limited ocean regions, and will mitigate current projections of increased primary productivity in Fe-limited high latitudes regions such as the Southern Ocean. Overall, we demonstrate that Fe-binding site heterogeneity is critical for iron speciation, and must be considered when predicting the response of marine primary producers to ongoing changes in ocean chemistry.