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I noticed a piece of jewelry has tarnished, so I looked up information about silver tarnishing. I read that this is due to the formation of silver sulfide on the surface of my necklace and that the sulfur is pulled from the air.

My question is, how abundant are sulfur containing compounds in the air? I know sulfur is by no means rare, but I guess I'm just confused as to why pretty much everything silver ends up tarnishing -- a box of silverware unopened for years can be tarnished.

How abundant are sulfur containing compounds in the air? Is the tendency of silverware to tarnish often/easily due to reactivity? If so, why doesn't carbon react to silver in the same manner and thus give way to a carbon-based tarnish?

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The tarnishing of silver by sulfur is primarily due to hydrogen sulfide. Hydrogen sulfide is found throughout the Earth's lower atmosphere, and has many sources including the human body$\pu{^1}$.

The amount of hydrogen sulfide naturally found in the air has been estimated as $\pu{0.11-0.33 ppb}$ ($\pu{0.15-0.46 ug/m3}$). Lower levels ($\pu{0.02-0.07 ppb}$; $\pu{0.03-0.1ug/m3}$) have been observed in some remote areas$\pu{^2}$.

Although these are relatively low concentrations compared to many other trace gases found in our atmosphere, silver is highly reactive towards hydrogen sulfide and thus tarnishing of silver is a ubiquitous issue. Additionally, some tarnish results from the oxidation of silver by oxygen.

Regarding your question about silver tarnishing from carbon, it's a matter of reactivity. The overwhelming source of carbon in the air is carbon dioxide, and methane to a much lesser extent. Neither of these gases are reactive towards silver nearly to the degree of hydrogen sulfide and oxygen.

1) Toxilogical Profile for Hydrogen Sulfide and Carbonyl Sulfide, U.S. Dept. of Health and Human Services, November, 2016
2) Ambient Air Guidelines for Hydrogen Sulfide, CAS Registry Number: 7783-06-4, March 27, 2006

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