Ideal Gas Law

In-depth explanation of Ideal Gas Law

The ideal gas law, PV = nRT, combines Boyle's, Charles's, Avogadro's and Gay-Lussac's laws into one equation linking pressure, volume, amount and temperature. Here n is the number of moles, T is the temperature in kelvin, and R is the gas constant. An ideal gas is a hypothetical gas whose particles have no volume and no intermolecular attractions, and the law works best for real gases at low pressure and high temperature where these assumptions hold. The equation allows any one variable to be calculated when the others are known. It is the basis for calculations of molar mass and gas density.

Going deeper: Ideal Gas Law

Key ideas: Rearrangements: n = PV/RT, M = mRT/PV and d = PM/RT. Choose R to match units: 0.08206 L atm per mol K, or 8.314 J per mol K with pressure in pascals and volume in cubic metres. Use it for a single state, unlike the combined law for two states.

Common mistakes and connections: Typical errors are using Celsius, mismatched units for R, and mixing grams with moles. Do not apply it near condensation or at pressures of tens of atmospheres. The law is a limiting law for real gases as pressure goes to zero. Links to the kinetic theory, gas density, Dalton's law and the compressibility factor.

Visualization of Ideal Gas Law

PV = nRT links all four gas variables; adjust T and V and watch the collision rate with the walls (pressure) respond for the fixed particle count. The interactive lesson shows this as a live animation or chart.

Worked example and use case

One mole of gas at 273 K and 1 atm occupies V = nRT/P, which is about 22.4 L.

Where Ideal Gas Law fits in States of Matter & Solutions

Ideal Gas Law is topic 13 of 109 in States of Matter & Solutions.

Related topics

• Gay-Lussac's LawBeginner
• Avogadro's LawBeginner
• Combined Gas LawBeginner
• Gas ConstantBeginner
• Absolute ZeroBeginner
• Dalton's Law of Partial PressuresBeginner

Browse all 109 topics in States of Matter & Solutions