Ummm, this isn't a question of PSI, but rather volume. Think about how much space is inside your tire. The bottle would have to be just as large as the tire in order to fill the tire. I would guess that the little tank shown, at 200 psi, MIGHT do one tire from 15-20psi back up to 40psi...maybe. If I use my 30 gallon tank, I can do one 34" tire from 15lbs up to 45lbs. The compressor will kick back on at 65-70lbs. That little tiny tank ain't gonna cut it. CO2 or nitrogen, for your goal of small space, fast inflation.
Yeah you learn that on like day 2 of physics class. I remembered that this morning on the way to work but didn't have time to delete it before you replied.