impermeable (adj.) 1690s, from French imperméable or directly from Late Latin impermeabilis, from assimilated form of in- "not, opposite of" (see in- (1)) + permeabilis (see permeable). Related: Impermeability.
airtight (adj.) also air-tight, "impermeable to air," 1760, from air (n.1) + tight. Figurative sense of "incontrovertible" (of arguments, alibis, etc.) is from 1929.