Different internet sources say different things.
If possible, can someone explain why it is (or isn't) chemically reactive?
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Graphene in its pristine form, a single sheet of pure sp2 hybridized benzenes, is (relatively speaking) one of the least chemically reactive materials known because of several reasons: one, its enormous size (we keep making larger and larger single "molecules", now thanks to IBM up to 4 inches!). Secondly, its physical hindrance: you can only do bottom/top down chemistry, granted this isn't that big of an issue but it does greatly reduce using large compounds. Last is it's stableness: this thing is crazy stable because of its gigantic p-butts and other effects.
The long story short is that you don't have any functional groups or easy points of entry. The way to think about it is "what does graphene look like and what makes those other molecules reactive?". The answer is...benzene and really any other hydrocarbon with no functional groups. The difference there is their size. But the same rules apply! You can still oxidize graphene, at the edges for example, much like you would benzene. And in the past years, we've seen even more radical methods, the most common being Hummer's Oxidizing, and some other clever ones like a Claisen Rearrangement directly onto the surface of graphene.
Hope that helps!
EDIT: after Greg's comment
Don't apologize! This'll get the discussion going, I was hoping to see more answers other than mine. I think you're right in terms of absolute stability but my statement is a phenomenon harder to describe than mere size. From experience, we noted that on very large graphene flakes, our functionalization of them would distort the sheets, but not break them, creating lots of hindrances and thereby decreasing its reactivity; it basically went from sheet shape to a jumbled up ball. However, on smaller (much smaller) sized flakes, the individual molecules (though hindered and flexed in a similar way) would, at the same concentrations of reactants, get functionalized more, ratio of functional groups to carbons on the sheet.
This is an indirect effect of the massive size of the graphene sheets. So I guess you're right in that size isn't exactly a stability factor but rather, again, it's all about hinderance. However, I wanted to point it out because the massive size of such a flat molecule is quite spectacular and does yield some interesting behavior we don't normally think of.