Solving Nonpolar Solubility: CO2 & CH4

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aclark609
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This is not a homework question. It's the beginning of August for pete's sake.

I read that like dissolves like, but what about the density of the molecules that are being dissolved? For instance in a solution (gaseous or liquid) of CO2 and CH4, they are both nonpolar, so they mix. However, CO2 is quite a bit more dense. So wouldn't it settle to the bottom?

The above situation doesn't make sense to me on why they dissolve in the first place either. I understand how ionic molecules dissolve in a polar substance. For instance, NaCl in H2O. The crystalline substance, NaCl, is more or less picked apart by water molecules due to attraction of opposite charges, but there is a lack of opposite charge attraction in NON polar molecules other than dispersion forces from what I understand. What makes a nonpolar substance dissolve another one? Is this a situation where "It just does?"
 
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The force of gravity is really quite trivial compared to intermolecular forces, even those as weak as induced dipole-induced dipole interactions. So the density of the compounds ends up not really mattering. Another approach to thinking about this is entropy. Things in our universe like to become more chaotic, this is the second law of thermodynamics. So if you put two liquids or gases together they usually mix (unless mixing is too energetically unfavorable, such as in the case of oil and water.)