If you have read the article How Helium Balloons Work, then you know that a liter of air at sea level weighs about 1.25 grams. A liter is 1,000 cubic centimeters, or about 61 cubic inches -- the size of a 1-liter soda bottle. A liter of helium, on the other hand, weighs about 0.18 grams. If you weigh a 1-liter bottle filled with air and then weigh the same bottle filled with helium, it will weigh about 1.07 grams less. If the bottle itself weighed less than a gram, you couldn't weigh it at all -- it would float! You could turn the scale upside down and put it above the floating bottle to check its negative weight! Generally, a balloon has to be several liters in size before the 1-gram-per-liter weight difference of helium vs. air is enough to overcome the weight of the balloon itself and float.
If you could somehow fill a 1-liter bottle with a vacuum, it would float even better. A perfect vacuum weighs zero grams, so a liter of perfect vacuum weighs 0.18 grams less than a liter of helium. The problem, of course, is that building a lightweight container that can hold a vacuum is not nearly as easy as building a fabric envelope that can hold helium. The phrase Nature abhors a vacuum sums it up nicely. If you could figure out a way to do it, however, you would be set -- your vacuum balloon would float!
Note that you would not need to have a perfect vacuum. Any air that you take out of the envelope will lower the weight and cause lift.
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