rare vs rarity

rare is not a noun while rarity is a noun.

Word	Noun	Adjective	Verb	Adverb
rare	No	Yes	No	No
rarity	Yes	No	No	No

rare (noun)	rarity (noun)
	something unusual -- perhaps worthy of collecting
	a rarified quality
	noteworthy scarcity

rare (adjective)	rarity (adjective)
marked by an uncommon quality; especially superlative or extreme of its kind
recurring only at long intervals
(of meat) cooked a short time; still red inside
not widely distributed
having low density
not widely known; especially valued for its uncommonness