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In this answer I've asserted (without a "Chemist's license") that as long as oxygen is above it's critical point in both temperature (154.5 K) and pressure (50.4 bar) it's going to be a supercritical fluid.

This comment by a user who I believe is an experienced diver says:

Scuba divers use the idea(l) gas law for air and oxygen bottles to calculate the amount of remaining gas for 200 down to 10 bar. This would not be possible if there is supercritical oxygen in the tank.

In other words, the ideal gas law works pretty well for oxygen between 10 and 200 bar; for a given temperature the amount of oxygen (number of atoms or mass in kg) is close to linearly proportional to pressure.

The comment proposes that this is evidence that the oxygen couldn't be a supercritical fluid.

Question(s):

1. When oxygen is above both 50.4 bar and 154.5 K is it always a supercritical fluid, end of story?


2. If it is, would it nonetheless still tend to follow fairly closely the ideal gas law?

1. Yes. Any fluid with a temperature is above critical temperature and the pressure above the critical pressure is by defintion a supercritical fluid. Don't be mislead by all the claims that supercritical fluids are special and wonky with all sorts of amazing, bizarre properties. This is true of some supercritical fluids near the critical point, but the farther you go away from the critical point, the more like a regular gas supercritical fluids become. (The only exception here is that at gargantuan extremes of P and/or T, eventually fluids will become plasmas, metallic solids, black holes, etc. But as long as it is a fluid of the same substance [no chemical reactions], then it will be supercritical.)



2. 
   

   Yes, supercritical fluids can often be modeled by the ideal gas law. A good look into why would take into the theory of corresponding states. This theory says that most gases will most often have similar compressibilities $Z = fracPVnRT$ when they are in "corresponding" states, which means that at similar temperature and pressure relative to each gas's critical point. There are charts that you can use (approximately) for many, many real gases. Things to realize:

   
   
   
   • The compressibility factor $Z$ is a measure of non-ideality. Ideal gases always have a compressibility factor of 1.0.
   
   
   • You can use the chart to find approximate compressibility factors for many, many real gases if you know that gas's critical temperature $T_c$ and critical pressure $P_c$. The "reduced temperature" is just $fracTT_c$ and likewise for pressure.
   
   
   • If you check out the generalized compressibility factor chart, look at the dependence on reduced temperature! At a reduced temperature of 2.0, the line is nearly flat at $Z = 1.0$. This is an indication that the gas behaves nearly ideally. It takes pretty close approaches of $fracTT_c$ to 1.0 to get strong non-ideality.
   
   
   • Oxygen's critical temperature of 154 K means that a reduced temperature of 2.0 just requires 309 K, about ambient temperature. At these temperatures, oxygen will be fairly ideal, regardless of temperature, up to reduced pressures of 5 or 8, which correspond to 250 to 400 bar or so.