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Carbo, carbonis is rightly used for both the element and charcoal, since charcoal is basically pure carbon. No point in making up new words when a perfectly good one is staring us in the face.

For gaseous I would use vaporeus or spiritosus, definitely not "gaseo-us." That would definitely produce some strange inflections.

In addition, the trend in chemical nomenclature is to use -ium primarily to denote metals. The one notable exception, helium, was a mistake since we inferred its existence through spectroscopy of the Sun. Instead of "hydrogenium" I'd use hydrogen, hydrogenis (-ginis?) or go further back to the Greek "maker of water" -- aquifex, aquificis?

Keep in mind that we are not the first to ponder these problems. For the various "-gen" elements, Latin forms both in -genum and -genium are common (e.g. the Vatican Lexicon Recentis Latinitatis gives both). If what you say about nominclature is true, perhaps that would be a good argument for favoring -genum, but we can't throw out -genium entirely because it is very widespread. Note that while "-gen" is nomrally presented as a Greek prefix meaning "creator of", it is in fact a recent coining. This explains why the Latin forms vary: the is no "proper" classical model to use as a basis.
Likewise, for "Carbon" the Vatican recommends Carbonium, presumably on the model of Italian Carbonio. Indeed, the Romance languages in general seem to distinguish Carbon (It. Carbonio, Fr. Carbone, Es. & Pt. Carbono etc.) from coal (It. carbone, Fr. charbon, Es. carbón, Pt. carvão etc.) So English is not alone in making this distinction. It is not a stretch that we might want to do so in English too. I sympathize with the desire to stick to a classical word when a suitable one already exists, and in other places I might go with Carbo for Carbon myself. But on Wikipedia, I generally favor the neologism, because otherwise we will end up with too many concepts per article. Carbon and Coal might not be so bad, but what happens when cithara becomes about every musical instrument that has ever been called a cithara (the ancient cithara, the guitare, the zither, the sitar, even the piano in some sources)?
For "gas", for better of for worse gasium is a pretty accepted Latin word. Indeed, the word "gas" was coined by Ioannes Baptista van Helmont in the 17th century, when Latin was still the language of science. Thus, it has a longer history in Latin as it does in the modern languages! Of course the adjective should be gaseus vel sim. rather than *gaseous which is just attrocious. If one wishes to avoid neologisms, I would not recommend vapor, as this has a different meaning in modern science. The Vatican dictionary suggests "aëriformis substantia" as a slightly less neologistic equivalent, for what it's worth.
--Iustinus 16:48 iun 28, 2005 (UTC)
In addition 'carbo' is not a mass noun like "charcoal", but a count noun, (carbo - a coal, carbones - coals). Elements are mass nouns, e.g. 'ferrum', 'argentum', 'aurum', etc.... inventing new grammatical properties for a word is no better than inventing new words. :p Speaking of not inventing new words, 'hydrogenium' is apparently attested from the 19th century. Hydrogen, -inis would be an English borrowing, which is just too icky to contemplate—from that stem, if not hydrogen(i)um, it would apparently be something like *hydrogenes (like monogenes), or, borrowing from real Greek, hydrogonum. —Myces Tiberinus 17:13 iun 28, 2005 (UTC)

I changed the link from dioxidum carboni to Dioxidum Carbonii because both genitives (carboni and carbonii) are accepted (vide victionarium wikt:Carbonium) and because the article named Dioxidum Carbonii already exists. I think that there is consensus about "carbonium, -ii" being correct, so this should not be a problem. --Mafrius 21:04 iul 12, 2005 (UTC)