Ideal Gas Law Calculator

PV = nRT

The ideal gas law combines Boyle's (PV = constant at fixed T, n), Charles's (V/T = constant at fixed P, n), and Avogadro's (V ∝ n at fixed P, T) laws. P = pressure (Pa), V = volume (m³), n = moles, R = 8.314 J/mol·K, T = temperature (K). At STP (0°C, 1 atm = 101,325 Pa): molar volume = RT/P = 8.314 × 273.15 / 101,325 = 0.02241 m³/mol = 22.41 L/mol. At RTP (25°C, 1 atm): molar volume = 8.314 × 298.15 / 101,325 = 24.47 L/mol. The ideal gas law assumes: no intermolecular forces, negligible molecula

Boyle's and Charles's Laws

Boyle's law (fixed T and n): P₁V₁ = P₂V₂. Doubling pressure halves volume. Syringe compression: push plunger halfway = pressure doubles. Diving: at 30m depth (4 atm), lung volume compressed to ¼ of surface volume. Charles's law (fixed P and n): V₁/T₁ = V₂/T₂ (T in Kelvin). Balloon shrinks in the cold (V decreases as T decreases). Hot air balloon rises: heating air at constant pressure increases volume, reducing density below ambient. Gay-Lussac's law (fixed V and n): P₁/T₁ = P₂/T₂. Aerosol warni

Gas Mixtures and Partial Pressure

Dalton's Law of Partial Pressures: total pressure = sum of partial pressures of each gas. P_total = P_A + P_B + P_C + ... Partial pressure of gas A: P_A = x_A × P_total, where x_A = mole fraction of A. Air composition at 1 atm: N₂ (78%): P = 0.78 atm = 79 kPa. O₂ (21%): P = 0.21 atm = 21 kPa. CO₂ (0.04%): P = 0.0004 atm = 0.04 kPa. At altitude (Mt Everest, 0.33 atm): P(O₂) = 0.21 × 0.33 = 0.07 atm — approximately ⅓ of sea-level oxygen partial pressure. This is why supplemental oxygen is used abo

Real vs Ideal Gases

The ideal gas law fails under high pressure and low temperature where: intermolecular attractions are significant (gas molecules attract each other at close range — reduces pressure below ideal). Molecular volume is non-negligible (at high pressure, molecules themselves occupy significant fraction of total volume — increases pressure above ideal). van der Waals equation: (P + a/V²)(V − b) = nRT. a = attraction parameter (stronger intermolecular forces = larger a). b = molecular volume correction