  Earth's water, intrinsic oxidation state, and metal core density are
fundamental chemical features of our planet. Studies of exoplanets provide a
useful context for elucidating the source of these chemical traits. Planet
formation and evolution models demonstrate that rocky exoplanets commonly
formed with hydrogen-rich envelopes that were lost over time. These findings
suggest that Earth may also have formed from bodies with H$_2$-rich primary
atmospheres. Here we use a self-consistent thermodynamic model to show that
Earth's water, core density, and overall oxidation state can all be sourced to
equilibrium between H$_2$-rich primary atmospheres and underlying magma oceans
in its progenitor planetary embryos. Water is produced from dry starting
materials resembling enstatite chondrites as oxygen from magma oceans reacts
with hydrogen. Hydrogen derived from the atmosphere enters the magma ocean and
eventually the metal core at equilibrium, causing metal density deficits
matching that of Earth. Oxidation of the silicate rocks from solar-like to
Earth-like oxygen fugacities also ensues as Si, along with H and O, alloys with
Fe in the cores. Reaction with hydrogen atmospheres and metal-silicate
equilibrium thus provides a simple explanation for fundamental features of
Earth's geochemistry that is consistent with rocky planet formation across the
galaxy.
