The Ideal Gas Law Explained
The ideal gas law ties together the four things you can measure about a gas — pressure, volume, amount and temperature — in a single equation. Learn to rearrange it and match the gas constant to your units, and most gas problems become routine.
P is pressure, V is volume, n is the number of moles, T is the absolute temperature, and R is the gas constant. Rearrange it to solve for whichever quantity is missing: n = PV ÷ RT, V = nRT ÷ P, and so on.
What "ideal" assumes
The law treats gas particles as having no volume of their own and no attraction to each other. Real gases approach this behaviour at low pressure and high temperature, where the particles are far apart. It breaks down at high pressure or low temperature, near the point where a gas would condense — but for typical general-chemistry conditions the ideal gas law is an excellent approximation.
Choosing the right R
R has different numerical values depending on the units, so match it to your pressure and volume:
| Value of R | Use when |
|---|---|
| 0.08206 L·atm·mol⁻¹·K⁻¹ | Pressure in atm, volume in litres (most common) |
| 8.3145 J·mol⁻¹·K⁻¹ | SI units (pascals, cubic metres); energy and kinetic-theory work |
| 62.36 L·mmHg·mol⁻¹·K⁻¹ | Pressure in mmHg or torr |
The simplest habit: convert pressure to atm and volume to litres, then use 0.08206. One value of R covers nearly every problem you will meet.
Temperature must be in kelvin
The law uses absolute temperature, so always convert: T(K) = T(°C) + 273.15. Using Celsius is the single most common mistake, and because temperature can appear in a denominator, the error does not just shift the answer — it can change it dramatically or even make it negative.
Worked example
How many moles of gas occupy 18.5 L at 11.2 atm and 28.2 °C?
n = PV ÷ RT = (11.2 × 18.5) ÷ (0.08206 × 301.35) = 8.38 mol
STP and the molar volume
At standard temperature and pressure (0 °C and 1 atm), one mole of any ideal gas occupies 22.4 L. This molar volume is a shortcut that drops straight out of PV = nRT, and it is handy for gas stoichiometry — though check whether your course defines STP as 1 atm (giving 22.4 L) or 1 bar (giving 22.7 L).
When the gas changes conditions
If a fixed amount of gas moves between two states, the combined gas law is quicker because R and n cancel:
Use PV = nRT when you need an absolute amount, and the combined gas law when a sample is simply changing pressure, volume or temperature.
Common mistakes
- Leaving temperature in Celsius instead of converting to kelvin.
- Mismatching R with the units — using 0.08206 with pressure in kPa, for example.
- Mixing mL and L, or forgetting that the volume must match the R you chose.
Solve for any of P, V, n or T on the Ideal Gas Law Calculator, switch states with the Combined Gas Law Calculator, and connect gas amounts to reactions in How to Approach Stoichiometry.
The General Chemistry Workbook's gases chapter covers the combined gas law, Dalton's law and gas stoichiometry with full solutions.
Frequently Asked Questions
P is pressure, V is volume, n is the number of moles, R is the gas constant and T is the absolute temperature in kelvin. The equation relates all four measurable properties of a gas at once.
Use 0.08206 L·atm·mol⁻¹·K⁻¹ with pressure in atm and volume in litres, which covers most problems. Use 8.3145 J·mol⁻¹·K⁻¹ in SI units for energy and kinetic-theory work. Always match R to your units.
The gas laws use absolute temperature, which starts at absolute zero. Celsius can be negative and has an arbitrary zero, so using it gives wrong or even impossible answers. Convert with T(K) = T(°C) + 273.15.
It assumes particles have no volume and no attractions, so it fails at high pressure and low temperature, where particles are close together and near condensing. At ordinary conditions it is a very good approximation.
Use the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, when a fixed amount of gas changes between two states. It is faster because R and n cancel. Use PV = nRT when you need an absolute amount such as moles.