How many studs in a wall that is 32' long 16 on center?

there would be 24 studs, but this does not include the bottom plate, top plate(s) or the necessary tie-in at the corners of the wall

It's actually 25 studs, you need to add one for the end. This is providing you have no partitions, Windows or doors in wall. And as mentioned above if you are going to tie-in to another wall or two you will need extra studs. You will also need 96' of plate material.