Understanding the Ideal Gas Law (PV = nRT)

The ideal gas law, PV = nRT, is the summary equation for gas behavior when intermolecular forces and particle volume are negligible. It lets you solve for any one variable — pressure, volume, moles, or temperature — when the other three are known, and it underpins gas stoichiometry in chemistry courses.

What each variable represents

• P — pressure (atm, kPa, mmHg, or Pa depending on R)
• V — volume (liters or m³)
• n — amount of gas in moles
• T — absolute temperature in kelvin (K = °C + 273.15)
• R — ideal gas constant, chosen to match your P and V units

Choosing the right R constant

The value of R depends on units. Common choices: R = 0.08206 L·atm/(mol·K) when P is in atm and V in liters; R = 8.314 J/(mol·K) or kPa·L/(mol·K) for SI-style work. Mismatching R with your pressure and volume units is the most frequent error in gas law problems.

Special cases: Boyle's, Charles's, and combined gas laws

When one variable is held constant, the ideal gas law simplifies. Boyle's law (P₁V₁ = P₂V₂) applies at constant T and n. Charles's law (V₁/T₁ = V₂/T₂) at constant P and n. The combined gas law handles simultaneous P, V, and T changes. Each specialized law is a rearrangement of PV = nRT.

Molar volume at STP

One mole of an ideal gas at standard temperature (273 K) and pressure (1 atm) occupies 22.4 L. This molar volume shortcut avoids using R directly when conditions are at STP — but always confirm whether your problem specifies STP or gives explicit P and T values.

When the ideal gas law fails

Real gases deviate at high pressure and low temperature when molecules are close together and intermolecular attractions matter. For most introductory problems near room temperature and moderate pressure, the ideal model is adequate. Industrial and cryogenic applications may require the van der Waals equation or compressibility factors.

Frequently asked questions