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I poured some water in a balloon, inflated, and tied it up. Over a period of couple weeks, all water in the balloon is gone. But the balloon is still at about 2/3 of original inflated size.

I thought the the air molecules are much smaller than water vapor. Why the water is all vaporized?

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  • $\begingroup$ How humid is the air there? I propose that oxygen, nitrogen and argon enter and leave the balloon at rates accounting for RMS velocity and relative pressure between the balloon and the surrounding air. Water does as well. In a dry environment the rate should favor water leaving the balloon. In a very dry environment the net loss of water may be faster than the net loss of air, especially since water vapor has a higher RMS velocity than other components of air. $\endgroup$ – Brinn Belyea Sep 16 '14 at 4:11
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The air in the balloon will be saturated (with water vapour) and the air outside not. As a result there will be a vapour density (or partial pressure) gradient between the inside and outside of the balloon that will drive the mass flow of water vapour through the balloon and to the outside.

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Guessing, I would say that the water diffused through the plastic. Many plastics absorb water quite well. However I'm only guessing.

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