Obviously, we don't want the raft to merely equalize our weight (mostly/fully submerged), but instead, to carry our weight. In order, then, to carry 500 lbs, we want the raft to equalize at 1000 lbs. At this equalization point, the bottles will be halfway submerged, which is perfect.
- The average bottle of water contains 16.9 fl oz of water.
- Our source tells us that 1 gallon of water weighs 8.337 lbs. There are 128 ounces in a gallon, so one ounce of water weighs 0.0651328125 lbs.
- A 16.9 oz bottle of water weighs 1.0074453125 lbs
Archimedes' principle, or the law of upthrust says:
"a body immersed in a fluid is buoyed up by a force equal to the weight of the displaced fluid."
Therefore, because an empty bottle of water displaces 1.01 lbs of water, it will support 1.01 lbs of weight when submerged.
1000/1.01 = 990.1 bottles
So, all of that just means that we'll need ~1000 water bottles for the raft to achieve a 500 lbs design load.
Weight of water: WikiAnswers - Confirmed by numerous Google results