|MadSci Network: Chemistry|
The answer is that the carbon dioxide is much more "soluble" in the rubber that the balloons are made out of. For helium and oxygen, the chains of molecules in the balloon rubber repel the gas molecules, and they have to thread a maze, at best, to escape the balloon. Helium atoms are small enough to permeate and escape from nearly any material. Oxygen molecules are fairly effectively prevented from escaping by their insolubility. You did not actually tell us, but I suspect that your oxygen balloons would lose 10% or less in a day, and that is not really consistent with Graham's Law either. But carbon dioxide is attracted to the chains of rubber molecules, and drawn in between them until it permeates the whole of the rubber. The rubber actually swells in the process. Once that has happened. gas molecules can just as easily escape from either side of the balloon, and so the gas is lost relatively fast. You could partially rectify the problem by using argon (mass 40) instead of carbon dioxide (mass 44) in your experiments. But even if you did that, I am afraid that your experiment is poorly designed to illustrate Graham's Law. The problem is that the process by which a gas escapes from a balloon is not simple gas phase effusion. In the "Polymer Handbook" (Ed. Brandrup & Immergut, 2nd Ed. 1975. Wiley), page III-230, it says: 'The permeation of small molecules through flawless polymer films occurs by the consecutive steps of solution of permeant in the polymer and diffusion of the dissolved permeant.' In the table for Natural rubber which follows (page III-233), the following permeabilities are given: oxygen 23.3, argon 22.8, nitrogen 9.43, carbon dioxide 153. Permeability is governed by solubility and diffusion. There is little difference in the respective diffusion coefficients: 1.73, 1.36, 1.17, and 1.25 for the four gases (note that diffusion coefficients through the polymer do not reflect either molecular size or molar mass directly). The striking difference in the permeability figure for carbon dioxide is associated with solubility in the rubber: heat of solution figures are -4.2 kJ/mol for oxygen, -0.1 for argon, +2.1 for nitrogen, but -12.5 for carbon dioxide.
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