Right on jimd. This is the proper response to this question: The word soul in Gen. 2:7 is:
SOUL=H5315
נֶפֶשׁ
nephesh
neh'-fesh
From H5314; properly a
breathing creature, that is,
animal or (abstractly)
vitality; used very widely in a literal, accommodated or figurative sense (bodily or mental): - any, appetite, beast, body, breath, creature, X dead (-ly), desire, X [dis-] contented, X fish, ghost, + greedy, he, heart (-y), (hath, X jeopardy of) life (X in jeopardy), lust, man, me, mind, mortality, one, own, person, pleasure, (her-, him-, my-, thy-) self, them (your) -selves, + slay, soul, + tablet, they, thing, (X she) will, X would have it.
It is the same word in Genesis 1 that described creature Gen. 1:21. Furthermore nothing about man is immortal, only the saved have the promise of immortality at Christ's coming.