I’m not sure that compressing to a liquid would be necessary.
https://energyeducation.ca/encyclopedia/Gas_centrifuge , which is describing the uranium enrichment process mentioned by Ichengify, states that the separation occurs while the uranium is still a gas, with the heavier fraction just being scooped out.
Also taking a quick look at the natural separation of gasses in Earth’s atmosphere, it seems that the uppermost layer consists mostly of hydrogen, helium and CO2, and that’s just under gravity.
I’m not a chemical engineer, but I’ll have a stab at what the energy for the process might be. No promises that I can reach an answer.