Ideal Gas Laws Calculator (Boyle, Charles, Gay-Lussac, Combined)

Ideal Gas Laws Guide

The Three Simple Laws

Boyle's Law (constant T): P₁V₁ = P₂V₂. Pressure and volume are inversely proportional at constant temperature. Example: 2L gas at 101.3kPa compressed to 1L: P₂ = 101.3×2/1 = 202.6kPa. Charles' Law (constant P): V₁/T₁ = V₂/T₂ (T in Kelvin). Volume proportional to absolute temperature. Example: 2L gas at 25°C (298K) heated to 100°C (373K): V₂ = 2×373/298 = 2.50L. Gay-Lussac's Law (constant V): P₁/T₁ = P₂/T₂. Pressure proportional to absolute temperature. Car tyre pressure increases on a hot day —

PV = nRT

R = 8.314 J/mol·K (universal gas constant). T must be in Kelvin (°C + 273.15). P in Pascals (1 kPa = 1000 Pa). V in m³ (1 L = 0.001 m³). n = number of moles. Example: 1 mol of ideal gas at STP (0°C, 101.325 kPa): V = nRT/P = 1×8.314×273.15/101325 = 0.02241 m³ = 22.41 L. Standard molar volume at STP: 22.4 L/mol. At room temperature (25°C, 101.325 kPa): 24.5 L/mol. Real gases deviate from ideal at high pressures and low temperatures — the van der Waals equation corrects for intermolecular forces a

Deviations from Ideal Behaviour

Ideal gas assumptions: molecules have negligible volume. No intermolecular forces (except during collisions). Elastic collisions. Real gases deviate most at: high pressure (molecular volume becomes significant). Low temperature (intermolecular attractive forces matter). Van der Waals equation: (P + an²/V²)(V − nb) = nRT. a accounts for attractive forces, b accounts for molecular volume. Noble gases (He, Ne, Ar): closest to ideal. CO₂: significant deviation at high pressure. NH₃: strong hydrogen

Gas Law Applications

Weather balloons: as altitude increases, atmospheric pressure decreases. Balloon expands (Boyle's Law). Eventually bursts when external pressure too low. SCUBA tanks: compressed air at 200-300 bar, ~0.01 L/bar volume. At depth, partial pressure of N₂ increases — causes narcosis at great depths. Nitrogen narcosis is essentially alcohol-like impairment. Breathing at depth: air consumption rate increases proportionally with depth pressure (1 tank lasts half as long at 10m as at surface). Autoclave