Ultra low-density gas law?
As far as I know, both the ideal gas law and the Van der Waals gas equation break down at very low pressures and low densities. What relations give more accurate results for gases in a near-vacuum?
By near-vacuum, I mean pressures on the order of 10^(-8) torr, up to 10^(-14) torr.
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This is not true.
The lower the pressure, the better gasses follow ideal gas laws and Van der Waals. In fact both of them are low pressure and high temperature approximations.
They break down not at low densities, but at high desities. For example they describe vapor well, but not applicable to dense liquid water.