The early Earths environment is controversial. Climatic estimates range from hot to glacial, and inferred marine pH spans strongly alkaline to acidic. Better understanding of early climate and ocean chemistry would improve our knowledge of the origin of life and its coevolution with the environment. Here, we use a geological carbon cycle model with ocean chemistry to calculate self-consistent histories of climate and ocean pH. Our carbon cycle model includes an empirically justified temperature and pH dependence of seafloor weathering, allowing the relative importance of continental and seafloor weathering to be evaluated. We find that the Archean climate was likely temperate (0-50 {deg}C) due to the combined negative feedbacks of continental and seafloor weathering. Ocean pH evolves monotonically from 6.6 (+0.6,-0.4) (2{sigma}) at 4.0 Ga to 7.0 (+0.7,-0.5) (2{sigma}) at the Archean-Proterozoic boundary, and to 7.9 (+0.1,-0.2) (2{sigma}) at the Proterozoic-Phanerozoic boundary. This evolution is driven by the secular decline of pCO2, which in turn is a consequence of increasing solar luminosity, but is moderated by carbonate alkalinity delivered from continental and seafloor weathering. Archean seafloor weathering may have been a comparable carbon sink to continental weathering, but is less dominant than previously assumed, and would not have induced global glaciation. We show how these conclusions are robust to a wide range of scenarios for continental growth, internal heat flow evolution and outgassing history, greenhouse gas abundances, and changes in the biotic enhancement of weathering.
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