Case 1
- Pressure
- 101325Pa
- Volume
- 0.0224m³
- Temperature
- 273.15K
0.999377mol
Open with these valuesIdeal Gas Law Calculator
0.999377mol
Result: 0.999377 molpV = nRT rearranged for the amount of substance: n = pV divided by RT. Enter pressure in pascals, volume in cubic metres and temperature in kelvin. One mole fills 22.4 litres at 0 °C and one atmosphere — the first row of the table is exactly that check.
Worked examples
Case 2
- Pressure
- 200000Pa
- Volume
- 0.05m³
- Temperature
- 350K
3.436353mol
Open with these valuesCase 3
- Pressure
- 500000Pa
- Volume
- 2m³
- Temperature
- 500K
240.544710mol
Open with these valuesHow it's calculated
n = p × V ÷ (8.314462618 × T)
- StepEnter the absolute pressure in pascals; one bar is 100000 Pa.
- StepEnter the volume in cubic metres; one litre is 0.001 m³.
- StepEnter the temperature in kelvin: degrees Celsius plus 273.15.
- ResultRead the amount of substance in moles.
What this number means
R = 8.314462618 J/(mol·K) is exact
Since the SI redefinition of 2019 the gas constant follows from the fixed Boltzmann and Avogadro constants. That value belongs to pascals, cubic metres and kelvin; another set of units needs a different R.
Pascals, cubic metres, kelvin — nothing else
The three fields convert nothing for you. Enter 22.4 litres as 0.0224 m³, or the answer reads 999.38 mol instead of 0.9994 mol.
Ideal means no attraction and no size
The model treats molecules as points that ignore one another. Near condensation and at very high pressure a real gas departs from it and needs a real-gas equation with a compressibility factor.
Commonly misread
Volume entered as 22.4 because the gas fills 22.4 litres.
The field reads cubic metres and returns 999.38 mol. One mole takes 0.0224 m³ and gives 0.9994 mol.
Temperature entered as 25 for a room at 25 °C.
The formula then divides by 25 kelvin and prints 10.92 mol instead of 0.9156 mol. Add 273.15 first.
R is 8.314 whatever units the numbers are in.
That figure belongs to pascals, cubic metres and kelvin. With litres and bar the constant is a different number.
Reference table
| Pressure, volume, temperature | Case | Moles |
|---|---|---|
| 1000, 0.01, 273.15 | near vacuum | 0.004403 |
| 101325, 0.0224, 298.15 | molar volume at 25 °C | 0.915579 |
| 101325, 0.0224, 273.15 | molar volume at 0 °C | 0.999377 |
| 200000, 0.05, 350 | small warm vessel | 3.436353 |
| 101325, 1, 300 | a cubic metre of room air | 40.621988 |
| 500000, 2, 500 | hot pressure vessel | 240.544710 |
Questions
What is the ideal gas law?
It links pressure, volume, amount and temperature of a gas as pV = nRT. Rearranged for n it gives the number of moles in a container of known size, pressure and temperature.
What is the value of R?
8.314462618 joules per mole per kelvin. Since the SI redefinition of 2019 the gas constant is exact, because it follows from the fixed Boltzmann and Avogadro constants.
Which units must I use?
Pascals, cubic metres and kelvin, which is the set that matches R in joules. A litre entered instead of a cubic metre inflates the answer a thousandfold.
Why does one mole fill 22.4 litres?
At 101325 pascals and 273.15 kelvin the formula returns 0.9994 moles for 22.4 litres, so a mole takes very slightly more. The round 22.4 is the older textbook figure for those conditions.
When does the ideal gas law fail?
Near condensation and at very high pressure, where molecules attract each other and take up space of their own. Then a real-gas equation with a compressibility factor is needed.
Sources and last check
Information, not professional advice.