Working out how to calculate PV=nRT is easier with Ideal Gas Law, which answers as you type. Type Pressure (Pa), Volume (m³) and Temperature (K) into Ideal Gas Law; each keystroke re-runs the math. Ideal Gas Law ties each output to its formula. Students and professionals reach for Ideal Gas Law when speed matters. Nothing is uploaded while Ideal Gas Law works, and the figures stay put. Ideal Gas Law handles free online ideal gas law calculator the same way as related figures — one of the Science tools on CalcProMaster. Ideal Gas Law is designed for real people. Labels stay plain. Ideal Gas Law answers the next Science question you meet.
What the defaults give
101,325 Pa, 0.0224 m³ and 273 K give 1.0000 mol.
That is the definition of molar volume at standard temperature and pressure: 22.4 litres per mole.
The formula
PV = nRT, rearranged to n = PV ÷ RT
P is absolute pressure in pascals, V is volume in cubic metres, T is absolute temperature in kelvin, and R is 8.314 J/(mol·K). The gas constant carries the units that make the equation work; mixing pascals with litres, or Celsius with kelvin, is the usual source of an answer that is off by a factor of a thousand.
Worked examples
101,325 Pa, 0.0224 m³, 273 K → 1.0000 mol
Half the pressure → 0.5000 mol in the same volume
Double the pressure → 2.0000 mol
Half the volume → 0.5000 mol
Half the temperature (136.5 K) → 2.0000 mol
The temperature row surprises people: cooling a fixed volume at fixed pressure increases the number of moles, because the gas becomes denser. It is the same relationship as a hot-air balloon needing a large volume to lift a small mass.
What the ideal part means
The model assumes point particles with no volume of their own and no attraction between them. Real gases approach that behaviour at low pressure and high temperature, and deviate as they are compressed or cooled toward condensation. At one atmosphere and room temperature, most common gases are within a percent or two; near the boiling point of a gas, or at hundreds of atmospheres, the error can be large.
Van der Waals adds two corrections for that: a volume term that accounts for the space the molecules occupy, and an attraction term that reduces the effective pressure. For engineering calculations near saturation, an equation of state or tabulated data is the right tool rather than this equation.
Using the result
Moles convert to mass by multiplying by molar mass: 1 mol of nitrogen is 28 g, of oxygen 32 g, of carbon dioxide 44 g. That chain — pressure, volume, temperature, moles, mass — is how a cylinder or a room full of gas is quantified.
Standard conditions are not universal: 273.15 K and 100 kPa is the IUPAC convention, while 273.15 K and 101.325 kPa gives 22.414 L. The difference is under 1.5% but matters when a supplier quotes a cylinder capacity in normal cubic metres.
Frequently Asked Questions
Why 22.4 litres per mole?
Because one mole of an ideal gas at 273 K and 101,325 Pa occupies 0.0224 m³. Enter those values and the equation returns 1.0000 mol.
Should temperature be in Celsius?
No. The equation needs kelvin, so add 273.15 to the Celsius figure. Using Celsius directly gives a wrong and sometimes negative result.
Why does cooling increase the moles?
At fixed volume and pressure, cooling makes the gas denser, so more moles fit in the same space. The equation returns a larger n for a smaller T.
When does real gas behaviour matter?
At high pressure or near condensation. At atmospheric pressure and room temperature most gases are within a couple of percent of ideal.
How do I get mass instead of moles?
Multiply the moles by the molar mass. Nitrogen is 28 g/mol, oxygen 32 g/mol and carbon dioxide 44 g/mol.
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