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From this answer, I learned that rising magma may change oxidation state, which I wasn't aware of.

In [#1], the authors state in the abstract

The conventional view holds that the oxidation state of a mantle-derived degassed magma reflects its source

From other research that has been conducted, the authors discussed that the oxygen fugacity (the partial pressure of the "non-ideal" oxygen in the presence of the high pressures and temperatures, presumably of the magma itself) was controlled by a pair of redox reactions (their equations 11 and 12):

$$\ce{S_{(melt)}^2- + Fe2^3+O3_{(melt)} <=> SO2_{(gas)} + 6Fe^2+O_{(melt)} + O_{(melt)}^2-}$$ $$\ce{SO4_{(melt)}^2- + 2Fe^2+O_{(melt)} <=> SO2_{(gas)} + Fe2^3+O3_{(melt)} + O_{(melt)}^2-}$$

Their claim is that the change in the $\ce{Fe^3+}$ to $\ce{Fe^2+}$ ratio is due to the top reaction being favored during decompression (due to the equilibrium shift from the changes in pressure).

I get all of that so far, I think. My question is a more fundamental one, being, if this equilibrium (#11) governing the changes in oxidation states becomes more prevalent as the pressure decreases rapidly, what are the governing equations for when the magma is deeper in the earth? Do they favor the bottom equation (#12) instead, or are the reactions at that temperature and pressure completely different?

It's possible I'm missing what the "changing oxidation states" aspect really means. A clarification of that would certainly be appreciated.

Reference:

  1. Moussallam, Y., Oppenheimer, C., Scaillet, B., Gaillard, F., Kyle, P., Peters, N., & Donovan, A. (2014). Tracking the changing oxidation state of Erebus magmas, from mantle to surface, driven by magma ascent and degassing. Earth and Planetary Science Letters, 393, 200-209. [DOI]
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My question is a more fundamental one, being, if this equilibrium (#11) governing the changes in oxidation states becomes more prevalent as the pressure decreases rapidly, what are the governing equations for when the magma is deeper in the earth?

My interpretation is that at the volcano being studied, the right side of equation 11 is favored at low pressure, and the left side is favored at high pressure (greater depth). Deep magma there contains sulfide ($\ce{S^2-}$) in accordance with equation 11, rather than sulfate ($\ce{SO4^2-}$) which would involve equation 12. So equation 11 applies to all depths being studied and equation 12 does not apply to this volcano at any depth.

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