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

Ideal Gas Laws Guide

What should I know about 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 — manufacturers recommend checking and adjusting tyre pressure when tyres are cold, since a hot-day reading will be several psi higher than the true cold-tyre pressure purely due to the temperature effect, not an actual change in the amount of air.

What do I need to know about 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 and the finite size of gas molecules, both of which the ideal gas model ignores. The correction becomes most noticeable for gases that are close to condensing (high pressure, low temperature) or that have strong intermolecular attractions, such as ammonia or carbon dioxide.

What's the key thing to understand about 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 bonding, causing it to deviate more from ideal behaviour than non-polar gases of similar molar mass. In general, the more polar a gas molecule and the closer it is to its liquefaction point, the further its real behaviour departs from the ideal gas law's predictions.

What should I know about 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). Autoclaves (used to sterilise medical and laboratory equipment) rely on the same pressure-temperature relationship in reverse: sealing steam in a chamber and letting pressure build raises its temperature well above 100°C, since boiling point rises with pressure — this higher temperature is what kills heat-resistant bacterial spores that survive ordinary boiling.