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ℹ️ The ideal gas law assumes ideal behavior. Real gases deviate significantly at high pressures (above ~10 atm) and low temperatures near condensation. Use van der Waals equation for real gas conditions.
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Sources & Methodology
Gas constant and STP values per NIST Chemistry WebBook and IUPAC recommendations.
NIST Chemistry WebBook — Gas Constant and Unit Conversions
R = 8.314462618 J/(mol·K) = 0.082057366 L·atm/(mol·K). webbook.nist.gov
IUPAC — Standard Conditions and Molar Volume
STP: 0°C, 100 kPa (1 bar). Molar volume at STP = 22.711 L/mol. iupac.org
Atkins' Physical Chemistry, 11th Ed.
Derivation of ideal gas law, van der Waals equation, and conditions of validity.
PV = nRT where R = 0.08206 L·atm/(mol·K)
P in atm, V in liters, n in moles, T in Kelvin
T(K) = T(°C) + 273.15 = (T(°F) - 32) × 5/9 + 273.15
P in atm, V in liters, n in moles, T in Kelvin
T(K) = T(°C) + 273.15 = (T(°F) - 32) × 5/9 + 273.15
PV = nRT
Example: 2 mol gas, 25°C (298.15 K), 1.5 atm.
V = nRT/P = (2 × 0.08206 × 298.15) / 1.5 = 48.92 / 1.5 = 32.61 L
V = nRT/P = (2 × 0.08206 × 298.15) / 1.5 = 48.92 / 1.5 = 32.61 L
Last reviewed: April 2026
Understanding the Ideal Gas Law
The ideal gas law PV = nRT combines three foundational gas laws — Boyle's Law (pressure-volume), Charles's Law (volume-temperature), and Avogadro's Law (volume-moles) — into a single equation. It describes the behavior of an ideal gas: a theoretical gas composed of point-sized molecules with no intermolecular forces.
The universal gas constant R = 0.08206 L·atm/(mol·K) is derived from absolute measurements of ideal gas behavior. When using SI units, R = 8.314 J/(mol·K). Always convert temperature to Kelvin before using the equation — negative Kelvin temperatures are physically impossible.
Gas Constant R in Different Units
| R Value | Units | Use When |
|---|---|---|
| 0.08206 | L·atm/(mol·K) | Chemistry — most common |
| 8.314 | J/(mol·K) = Pa·m³/(mol·K) | Physics / thermodynamics |
| 0.08314 | L·bar/(mol·K) | With bar pressure units |
| 62.36 | L·mmHg/(mol·K) | With mmHg / Torr units |
| 1.987 | cal/(mol·K) | Thermochemistry |
💡 Standard Conditions Quick Reference: STP (Standard Temperature & Pressure, IUPAC 1982) = 0°C and 1 atm → 1 mol occupies 22.414 L. New IUPAC STP (post-2002) = 0°C and 100 kPa (1 bar) → 1 mol occupies 22.711 L. SATP (Standard Ambient) = 25°C, 1 bar → 1 mol occupies 24.789 L. Always check which standard your problem uses.
Frequently Asked Questions
PV = nRT. P = pressure, V = volume, n = moles, R = gas constant (0.08206 L·atm/mol·K), T = temperature in Kelvin. Describes ideal gas behavior where molecules have no volume or intermolecular forces.
R = 0.08206 L·atm/(mol·K) in chemistry units. Also: 8.314 J/(mol·K), 0.08314 L·bar/(mol·K), 62.36 L·mmHg/(mol·K). Choose R based on your pressure unit.
P = nRT/V. Example: 2 mol, 300 K, 10 L: P = (2 × 0.08206 × 300) / 10 = 4.92 atm.
T(K) = T(°C) + 273.15. Always use Kelvin in gas law equations. 0°C = 273.15 K, 25°C = 298.15 K, 100°C = 373.15 K. Never use Celsius directly in PV=nRT.
STP = 0°C and 1 atm. One mole of ideal gas at STP occupies 22.414 L. New IUPAC STP (post-2002) = 0°C and 100 kPa (1 bar), giving 22.711 L/mol.
Ideal gases assume zero molecular volume and no intermolecular forces. Real gases deviate at high pressure (molecules too close) and low temperature (forces significant). Van der Waals equation: (P + a/V²)(V - b) = nRT corrects for real behavior.
1. Molecules have negligible volume. 2. No intermolecular forces. 3. Elastic collisions. 4. Random motion. Best at low pressure and high temperature. Worst near condensation point or at very high pressures.
Boyle's Law (P₁V₁ = P₂V₂) is PV=nRT with constant T and n. If n and T are constant, PV = nRT = constant, so P₁V₁ = P₂V₂.
Charles's Law (V/T = constant) is PV=nRT with constant P and n. V/T = nR/P = constant, so V₁/T₁ = V₂/T₂.
At 25°C (298.15 K) and 1 atm: V = nRT/P = (1 × 0.08206 × 298.15) / 1 = 24.47 L. At STP (0°C, 1 atm): 22.41 L.
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