Ideal Gas Law
The ideal gas law connects pressure, volume, amount of substance and temperature. Rearranging it with molar mass gives the familiar ideal-gas density equation used throughout gas-property calculations.
The ideal gas law
PV=nRTPressure must be absolute and temperature must be expressed on an absolute scale such as kelvins.
Deriving gas density
Since mass m=nM and density ρ=m/V, substituting into PV=nRT gives ρ=PM/(RT). This shows directly why density rises with pressure and falls with absolute temperature for an ideal gas.
Specific gas constant form
The same equation can be written ρ=p/(Rspecific T), where the gas-specific constant equals universal R divided by molar mass.
Real gases and compressibility
Real molecules interact and occupy finite volume. A common correction is ρ=PM/(ZRT). For high-pressure hydrogen, CO₂ near the critical region and saturated fluids, use a validated equation of state rather than assuming Z=1.
Common mistakes
Gauge pressure, Celsius temperature inserted directly into gas laws, mixed pressure units and incorrect molar mass are the usual offenders. Each can produce a numerically tidy but physically wrong answer.
Frequently asked questions
Does the ideal gas law use gauge pressure?
No. Use absolute pressure.
Can I use Celsius in PV=nRT?
No. Use an absolute temperature scale such as kelvins.
When does the ideal gas law become inaccurate?
High pressure, low temperature and conditions near phase change can produce significant real-gas deviations.
Sources & references
We prefer standards bodies, government/scientific agencies and primary technical references. Reference values can vary with conditions, grade, composition or measurement method.
Related calculators & guides
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