Compressibility Factor (Z = PV/nRT)

Z is the honest answer to "how wrong is the ideal gas law here?" expressed as a single multiplier. A cylinder holding 2 mol at 400 K reading 1.20 MPa in 5.00 L gives $Z = 6000/6651.6 = 0.902$, meaning the gas occupies about 10% less volume than an ideal gas would at the same pressure and temperature. Below 1, attraction is winning. Above 1, the molecules' own bulk is. At low pressure everything tends back to 1, which is why the ideal gas law survives at all.

The elegant part is the theorem of corresponding states: plot Z against reduced pressure $P_r = P/P_c$ at fixed reduced temperature $T_r = T/T_c$ and almost every non-polar gas falls on the same generalised chart. Nelson and Obert drew those charts in 1954 and process engineers still read them, because one chart covers nitrogen, methane, propane and argon alike. Natural gas metering leans on this heavily, where the correction is called supercompressibility and moves the invoice by percent-level amounts on a high-pressure line.

Two cautions. Z is not a property you can look up for a substance, only for a substance at a state, so quoting "the Z of methane" without a pressure and temperature says nothing. And when you use Z to correct a flow measurement, be certain which pressure and temperature the meter reports at, because applying a Z evaluated at line conditions to a volume already corrected to standard conditions double-counts the correction and is a classic custody-transfer dispute.