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Ideal Gas Law

PV = nRT and the Behavior of Gases

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The ideal gas law, PV = nRT, combines three simpler gas laws into a single equation relating pressure (P), volume (V), amount of gas in moles (n), and temperature in kelvin (T). R is the universal gas constant (8.314 J/mol·K or 0.08206 L·atm/mol·K). The law assumes gas molecules have no volume and no intermolecular forces — assumptions that hold well at low pressure and high temperature.

The three simpler laws are special cases: Boyle's Law (P₁V₁ = P₂V₂, constant T and n), Charles's Law (V₁/T₁ = V₂/T₂, constant P and n), and Gay-Lussac's Law (P₁/T₁ = P₂/T₂, constant V and n). Real gases deviate from ideal behavior at high pressures and low temperatures, where intermolecular attractions and finite molecular volumes become significant. The van der Waals equation corrects for these effects.

Key Facts

  • Ideal gas law: PV = nRT (P in Pa or atm, V in m³ or L, T in Kelvin)
  • R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K)
  • Boyle's Law: P₁V₁ = P₂V₂ (constant T, n)
  • Charles's Law: V₁/T₁ = V₂/T₂ (constant P, n)
  • Gay-Lussac's Law: P₁/T₁ = P₂/T₂ (constant V, n)
  • STP (standard temperature and pressure): 0°C (273.15 K) and 1 atm; 1 mol ideal gas = 22.4 L

Vocabulary

Pressure
Force per unit area exerted by gas molecules colliding with a container wall; measured in Pa, atm, or mmHg.
Absolute temperature
Temperature measured in kelvin (K); K = °C + 273.15. Must use kelvin in all gas law calculations.
Molar volume
The volume occupied by one mole of an ideal gas; 22.4 L at STP (0°C, 1 atm).
Ideal gas
A theoretical gas whose molecules have negligible volume and no intermolecular forces; obeys PV = nRT exactly.
Partial pressure
The pressure a gas would exert if it alone occupied the container; Dalton's Law: P_total = P₁ + P₂ + ... for a gas mixture.

Common Mistakes to Avoid

  • Using Celsius instead of Kelvin in gas law calculations. All temperatures in gas law equations must be in Kelvin. Room temperature of 25°C must be entered as 298 K.
  • Using inconsistent units for R, P, and V. If using R = 0.08206 L·atm/(mol·K), pressure must be in atm and volume in liters. Mixing units gives wrong answers.
  • Forgetting that the combined gas law requires constant n. Boyle's, Charles's, and Gay-Lussac's laws assume the amount of gas is constant. If gas escapes or is added, use the full ideal gas law.
  • Applying ideal gas law to liquids or solids. The ideal gas law applies only to gases. At very high pressures or near the condensation point, real gases deviate significantly from ideal behavior.

Practice Questions

  1. 1 A balloon contains 0.50 mol of helium at 25°C and 1.0 atm. What is its volume?
  2. 2 A gas occupies 4.0 L at 300 K and 2.0 atm. What volume does it occupy at 400 K and 1.0 atm?
  3. 3 Explain why the ideal gas law breaks down for real gases at very high pressures. Which assumption of the ideal gas model fails first?