Does a mixture have to involve dissolving a solid into a different phase?
Dissolving is really just mixing of particles amongst other particles of different phase(s).
Although nonpolar covalent substances (like carbon graphite or diamond) can be solids sometimes (due to many tetravalent bonds in a large network), it does not matter if the solute in the mixture is not a solid.
It just means that we need to redefine the dissolving process with different terminology.
Furthermore, solubility is a spectrum. At some point we draw a line and say something is "insoluble", when we really mean, "poorly soluble".
See here for a general guideline of what counts as "poorly soluble" ("very slightly soluble" or "practically insoluble" are good benchmarks).
Liquids can mix, and that kind of "dissolving" is called miscibility, or the tendency to mix. A nonpolar substance does not mix well with water, but it does not mean it does not mix.
Furthermore, the liquid that there is less of is still the solute.
The solute could very well be a gas, and they do in fact dissolve in liquids. Not necessarily well, but it occurs.
- the solubility of
#"O"_2(g)#among the air in water at #25^@ "C"#and #"1 atm"#is about #ul"0.0082 g/L"#. This is pretty small, as you will see when you compare with #"AgCl"#(which is considered insoluble).
The solubility of
#"AgCl"(s)#in water (which is hardly at all) is about #ul"0.00514 g/L"#at #50^@ "C"#, even less than #"O"_2#gas, despite being at a higher temperature.
The solubility of
#"NaCl"(s)#in water (which is huge) is #ul"359 g/L"#, over 40000 times more soluble than for #"O"_2#gas.
The difference there is that gases can escape the liquid, so they follow trends with regards to temperature and pressure that only seem unintuitive at first glance.
In short, gas solubility in water increases at lower temperature and higher pressure, and vice versa, backwards compared to most solids in water.