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How It Works
The ideal gas law PV = nRT connects pressure, volume, amount of gas, and temperature through a single equation. If you know any three of these quantities you can solve for the fourth. The calculator also supports a density form for working with mass instead of moles, and Boyle's law for constant-temperature processes.
The universal gas constant R equals 0.08206 L·atm/(mol·K) when using atmospheres and liters, or 8.314 J/(mol·K) in SI units. Temperature must always be in kelvin (absolute) for gas law calculations.
Example Problem
A 2.0 mol sample of nitrogen gas is held in a 10.0 L container at 300 K. What is the pressure?
- Write the ideal gas law: P = nRT / V
- Substitute values: P = (2.0)(0.08206)(300) / 10.0
- Result: P ≈ 4.92 atm
For Boyle's law: if a gas at 2 atm occupies 5 L, compressing it to 2 L at constant temperature gives P₂ = (2 × 5) / 2 = 5 atm.
Frequently Asked Questions
What is the ideal gas law formula?
The ideal gas law is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is absolute temperature in kelvin. It assumes gas molecules have negligible volume and no intermolecular forces.
When does the ideal gas law not work?
The ideal gas law becomes inaccurate at very high pressures (above ~10 atm) or very low temperatures near a gas's condensation point. Under those conditions, intermolecular forces and molecular volume matter, and equations like the van der Waals equation give better results.
Why must temperature be in kelvin for gas laws?
Gas law equations require absolute temperature because pressure and volume are proportional to the thermal energy of the gas molecules. Zero kelvin represents zero molecular kinetic energy. Using Celsius or Fahrenheit would produce incorrect results because those scales have arbitrary zero points.
What is the difference between Boyle's law and the ideal gas law?
Boyle's law (P₁V₁ = P₂V₂) is a special case of the ideal gas law that applies when temperature and the amount of gas are constant. The full ideal gas law covers any combination of changing pressure, volume, moles, and temperature.
How do you calculate moles of a gas from pressure and volume?
Rearrange the ideal gas law to n = PV / (RT). For example, a gas at 1 atm in a 22.4 L container at 273.15 K contains about 1 mol — this is the standard molar volume at STP.
Related Calculators
- Specific Gas Constant Calculator — find the gas constant for a particular gas from its molecular weight.
- Temperature Conversion Calculator — convert between Celsius, Fahrenheit, Kelvin, and Rankine.
- Thermal Expansion Calculator — calculate how materials expand or contract with temperature changes.
- Thermal Diffusivity Calculator — compute heat diffusion rate for gases and solids.
- Density Equation Calculator — find gas density from mass and volume.
- Pressure Unit Converter — convert between atm, Pa, psi, and other pressure units.
References:
Tipler, Paul A. 1995. Physics For Scientists and Engineers. Worth Publishers. 3rd ed.
Lindeburg, Michael R. 1992. Engineer In Training Reference Manual. Professional Publication, Inc. 8th ed.