Wait, what?
If we assume 100 mg in a cup of coffee, we can do the math by: 1.010E^(-1)/4.510E^(-8)
which is equal to 2.22*10E^(6) or 2.22M liters of water. You're only off by a factor of 370!
Since one cubic meter is 1000 liters, you're looking at a cubic body of water that is 13 meters or ~40ft on each side.