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Compressibility factor

The compressibility factor (Z) is used to alter the ideal gas equation to account for the real gas behaviour.^[1] The compressibility factor is usually obtained from the compressibility chart.^[2]
-is the product of pressure and molar volume divided by the gas constant and thermodynamic temperature. For an ideal gas it is equal to 1.(IUPAC Compendium of Chemical Terminology 2nd Edition (1997))

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Mathematically, it is defined as,

$Z=\frac{P \tilde{V}}{R T}$

where, $P$ is the pressure,

$\tilde{V}$ is the molar volume of the gas,

T

is the temperature, and

R

is the gas constant.

For ideal gas behaviour, $Z = 1$ . Ideal gas behaviour occurs when,

$P_R \ll 1$
$T_R > 2 \,$ (except when $P_R \gg 1$ )

where,

$P_R = \frac{P}{P_{cr}}$ is the reduced pressure and, $T_R = \frac{T}{T_{cr}}$ is the reduced temperature.

$P_{cr} \,$ and $T_{cr} \,$ are the critical pressure and temperature of the fluid, respectively.

The deviation from ideal gas behaviour is largest in the vicinity of the critical point, where $Z$ can be as low as 0.2.

References

^ Properties of Natural Gases. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document)
^ Full-size online chart of compressibility factors