Ideal Gas Law: formula
Enter the amount of gas in moles, the absolute temperature in kelvin and the volume in liters. The pressure is the amount times the gas constant, 0.082057 liter-atmospheres per mole per kelvin, times the temperature, divided by the volume. Convert Celsius to kelvin by adding 273.15.
The result is given in atmospheres and kilopascals.
Ideal Gas Law: worked example
| Amount of gas (mol) | 1 |
|---|---|
| Temperature (K) | 300 |
| Volume (L) | 24.6 |
| Pressure (atm) | 1 |
| Pressure (kPa) | 101.4 |
The law is an approximation that works well for gases at moderate pressure and high temperature. Real gases deviate at high pressure and near condensation, where other equations apply. Temperature must be in kelvin.
Gauge pressure differs from absolute pressure by one atmosphere.
Ideal Gas Law: changing Amount of gas (mol)
| Amount of gas (mol) | Pressure (atm) | Pressure (kPa) |
|---|---|---|
| 0.8 | 0.801 | 81.1 |
| 0.9 | 0.901 | 91.3 |
| 1 (example) | 1 | 101.4 |
| 1.1 | 1.1 | 111.5 |
| 1.2 | 1.2 | 121.7 |
Ideal Gas Law: compare input ranges
| Input | Tested from | To | Pressure (atm): low input | Pressure (atm): high input | Swing |
|---|---|---|---|---|---|
| Volume (L) | 22 | 27 | 1.1 | 0.912 | 0.207 (21%) |
| Temperature (K) | 270 | 330 | 0.901 | 1.1 | 0.2 (20%) |
| Amount of gas (mol) | 0.9 | 1.1 | 0.901 | 1.1 | 0.2 (20%) |
Ideal Gas Law: individual input comparisons
| Input | Value | Pressure (atm) | Pressure (kPa) |
|---|---|---|---|
| Amount of gas (mol) | 0.8 | 0.801 | 81.1 |
| 0.9 | 0.901 | 91.3 | |
| 1 | 1 | 101.4 | |
| 1.1 | 1.1 | 111.5 | |
| 1.2 | 1.2 | 121.7 | |
| Temperature (K) | 240 | 0.801 | 81.1 |
| 270 | 0.901 | 91.3 | |
| 300 | 1 | 101.4 | |
| 330 | 1.1 | 111.5 | |
| 360 | 1.2 | 121.7 | |
| Volume (L) | 20 | 1.2 | 124.7 |
| 22 | 1.1 | 113.4 | |
| 25 | 0.985 | 99.8 | |
| 27 | 0.912 | 92.4 | |
| 30 | 0.821 | 83.1 |
Ideal Gas Law: combined input changes
| Amount of gas (mol) / Temperature (K) | 240 | 300 | 360 |
|---|---|---|---|
| 0.8 | 0.64 | 0.801 | 0.961 |
| 0.9 | 0.721 | 0.901 | 1.1 |
| 1 | 0.801 | 1 | 1.2 |
| 1.1 | 0.881 | 1.1 | 1.3 |
| 1.2 | 0.961 | 1.2 | 1.4 |
Ideal Gas Law: which assumptions move the result?
Ideal Gas Law: values and definitions
| Quantity and definition | Value used |
|---|---|
| Amount of gas (mol) | 1 |
| Temperature (K) — Kelvin: add 273.15 to a Celsius reading. | 300 |
| Volume (L) | 24.6 |
| Pressure (atm) | 1 |
| Pressure (kPa) | 101.4 |
Ideal Gas Law: half and double Volume (L)
| Volume (L) | Pressure (atm) |
|---|---|
| 12.3 | 2 |
| 24.6 | 1 |
| 49.2 | 0.5 |
Common error: Applying the law to a gas near condensing or at very high pressure. Real gases depart from the ideal formula there, and the result can be well off.
Physics & Mechanics calculators: Gravitational Potential Energy Calculator, Work and Power Calculator, Wavelength and Frequency Calculator, Projectile Motion Calculator, Free Fall Calculator, Centripetal Force Calculator.
Pressure, volume and temperature of a gas are tied together by the amount of gas. Squeeze the same gas into half the space and the pressure doubles. Heat it and the pressure climbs in step with the kelvin temperature, which is why a sealed can is dangerous when it is heated.
Use kelvin, not Celsius. Adding 273.15 to a Celsius reading is the step people skip, and it changes the answer by a large factor.
See the energy on the kinetic energy calculator, the work on the work and power calculator and the temperature on the temperature converter. The pressure and volume converters change units, and the density and molarity calculators cover related chemistry.
Why does the gas law need kelvin?
Because the law depends on absolute temperature, and Celsius or Fahrenheit would give wrong results and even zero or negative pressure.
What is the ideal gas law?
The equation is PV = nRT. Pressure and volume describe the gas state. Amount n counts moles, and temperature T uses an absolute scale.
Choose units consistent with the gas constant R before solving for the missing quantity.
What is the volume of a mole of gas?
At 0°C and one atmosphere, one ideal-gas mole occupies about 22.4 liters. At 25°C and the same pressure, it occupies about 24.5 liters. Temperature matters.
A molar-volume value needs its pressure and temperature conditions attached.