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I know that vitamin c is notoriously unstable in aerobic conditions, but I'm not sure how to explain why it is - is it due to redox potential, acid strength etc?

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According to Juan Du, Joseph J. Cullen and Garry R. Buettnera[1]:

Ascorbic acid ($\ce{AscH2}$, vitamin C) is a water-soluble ketolactone with two ionizable hydroxyl groups. It has two $\mathrm{p}K_\mathrm{a}$’s, $\mathrm{p}K_1$ is 4.2 and $\mathrm{p}K_2$ is 11.6; thus, the ascorbate monoanion, $\ce{AscH−}$, is the dominant form at physiological pH. Ascorbate is an excellent reducing agent and readily undergoes two consecutive, one-electron oxidations to form ascorbate radical ($\ce{Asc•−}$) and dehydroascorbic acid (DHA). The ascorbate radical is relatively unreactive due to resonance stabilization of the unpaired electron; it readily dismutes to ascorbate and DHA ($K_\mathrm{obs} =\pu{2×10^5 M−1 s−1}$ at $\mathrm{pH} = 7.0$).

image from the first citation

Also,

Ascorbate readily undergoes pH-dependent autoxidation producing hydrogen peroxide ($\ce{H2O2}$).

So, in presence of oxygen, this process is accelerated due to formation of hydrogen peroxide. It is also known that this reaction may happen even faster with a metal as a catalyst[2]


References:

  1. Du, J.; Cullen, J. J.; Buettner, G. R. Ascorbic acid: Chemistry, biology and the treatment of cancer. Biochim Biophys Acta. 2012, 1826 (2), 443–457. DOI: 10.1016/j.bbcan.2012.06.003.

  2. Jiang, D.; Li, X.; Liu, L.; Yagnik, G. B.; Zhou, F. Reaction Rates and Mechanism of the Ascorbic Acid Oxidation by Molecular Oxygen Facilitated by Cu(II)-Containing Amyloid-β Complexes and Aggregates. J. Phys. Chem. B 2010, 114 (14), 4896–4903. DOI: 10.1021/jp9095375.

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