How to use PV = nRT
The ideal gas law ties together the pressure, volume, amount, and temperature of a gas: PV = nRT. R is the gas constant; use R = 0.08206 L·atm/mol·K when pressure is in atmospheres and volume in liters, and always put temperature in kelvin (K = °C + 273.15). Rearrange for whatever you need, P = nRT/V, V = nRT/P, n = PV/RT, or T = PV/nR. As a sanity check, one mole of an ideal gas at standard temperature and pressure (273.15 K, 1 atm) occupies 22.4 L.
Uses R = 0.08206 L·atm/mol·K. For SI units (Pa, m³) use R = 8.314 J/mol·K instead.
Related tools: Molar mass & molarity · all biochem tools.
Worked example 1: confirming STP (the default)
1 mole of gas at 273.15 K, occupying the textbook 22.4 L, solving for the pressure this implies.
This comes out to almost exactly 1 atm, confirming the standard "1 mole of ideal gas occupies 22.4 L at STP (0°C, 1 atm)" rule, the tiny 0.0007 atm difference is just rounding in the commonly quoted 22.4 L figure.
Worked example 2: gas volume at body temperature
0.5 mol of a gas at 1 atm and 37°C (310.15 K, body temperature), a common physiology-adjacent setup.
Notice this is meaningfully larger than the 11.2 L you'd get from naively using half of 22.4 L, because 37°C is warmer than STP's 0°C, and volume scales directly with temperature (in kelvin) at constant pressure and moles. Forgetting to convert to kelvin, or assuming STP volumes apply at other temperatures, is a common source of error.
FAQ
Why must temperature be in kelvin?
PV = nRT assumes temperature is measured from absolute zero. Using Celsius would give wrong answers and could even produce a negative or zero volume for a positive Celsius reading, kelvin is the only scale where the proportionality actually holds.
Why does R change value depending on units?
R is a physical constant, but its numeric value depends on the units for pressure and volume. Use 0.08206 L·atm/(mol·K) with atm and liters, or 8.314 J/(mol·K) in SI units (Pa, m³). Mixing unit sets with the wrong R is a common mistake.
What is STP and why 22.4 L/mol?
STP is 0°C (273.15 K) and 1 atm. Plugging n=1, T=273.15 K, P=1 atm into V=nRT/P gives V≈22.4 L, a memorized number that's really just one specific case of PV=nRT, not a separate rule.
Does this work for real gases?
It's a good approximation at low pressure and high temperature, where molecules are far apart. It's less accurate at high pressure or low temperature, where molecular volume and intermolecular forces matter, the van der Waals equation adds correction terms for those effects.
Practice problems
1. A gas occupies 10 L at 2 atm and 350 K. How many moles are present?
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2. 0.2 mol of gas is at 1.5 atm in a 5 L container. What's the temperature?