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Would molecules like $\ce{C2, H2}$, etc., be considered 1 mole of diatomic [element] or 2 moles of [element]?

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You can have 1 mole of $\ce{C_2}$ which contains 2 mole of $\ce{C}$ just as you can have for example 1 mole of $\ce{C_2H_5OH}$ which contains 2 mole of $\ce{C}$, 6 mole of $\ce{H}$ and 1 mole of $\ce{O}$.

The point is that you always have to mention whether you are indicating moles of molecule or moles of atoms. That is why a statement like: "I have 1 mole of oxygen" is ambiguous, because it could be referring to oxygen gas (i.e. $\ce{O_2}$) or to atomic oxygen (i.e. $\ce{O}$).

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    $\begingroup$ C2 is available from your regular supplier, but it certainly exists, has been monitored spectroscopically and used in reactions, see my comment to this question $\endgroup$ – Klaus-Dieter Warzecha Feb 2 '14 at 20:41
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    $\begingroup$ Of course I meant that it is NOT commercially available ;) $\endgroup$ – Klaus-Dieter Warzecha Feb 2 '14 at 23:34
  • $\begingroup$ @KlausWarzecha good to know! Never heard about it. $\endgroup$ – Michiel Feb 3 '14 at 6:19
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$\ce{C_2}$ is the blue-green Swan band emission of comets' ion tails and the blue in gas flames. The big question is its electronic structure (presumably not $\ce{•C#C•}$). Its paper synthesis in cryogenic gas matrix (UV cleavage) or in vacuum (flash pyrolysis or UV) seems to be easy, from

ROO-C(=O)-C#C-C(=O)-OOR, the peresters of acetylenedicarboxylic acid with R = $\ce{-CF_3}$, $\ce{-C(CH_3)_3}$, or $\ce{-Si(CH_3)_3}$.

Strings of alpha-omega diradical polycarbyne, $\ce{(-C#C-)_n}$ or $\ce{(=C=C=)_n}$ (your choice in LCAO, same in MO), in carbon arcs are suggested to pericyclicly close to fullerenes.

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  • $\begingroup$ I'm not quite sure of how this answers my question. Could you explain a little further and use words a high school student could understand? $\endgroup$ – Gandalf the White Feb 3 '14 at 1:45
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    $\begingroup$ $\ce{C_2}$ is one mole of $\ce{C_2}$ and two moles of carbon atoms. A box of eggs is one dozen eggs and 12 eggs simultaneously. The fun is in the footnotes. How can you make it on a bench top, what can you do with it? The cold synthesis byproduct is squaric acid. It's a hoot of a compound, including derived squarylium dyes, <P> link.springer.com/static-content/images/967/… $\endgroup$ – Uncle Al Feb 3 '14 at 2:02
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    $\begingroup$ What an eccentric performance. $\endgroup$ – Leonardo Feb 3 '14 at 2:19
  • $\begingroup$ The diradical recombines with the two liberated alkoxy radicals to an acetylene diether. That antarafacially 2+2 dimerizes to the squaric acid precursor. Aqueous acid triiodide to oxidize and hydrolyze. God save us from the congenitally inconsequential. $\endgroup$ – Uncle Al Feb 3 '14 at 23:21

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