Ideal Gas Law

Beginner

Explore the fundamental relationship between pressure, volume, temperature, and amount of gas.

Gas Particle Simulation
Particle speed represents temperature • Container size represents volume
Process Type
Gas Parameters
Auto-calculated from PV=nRT
Ideal Gas Law Equation

PV = nRT

Left Side (PV):

0.00 × 50.0 = 0.00

Right Side (nRT):

2.0 × 0.0821 × 300 = 49.26

Both sides equal: ⚠️ Check

Current State
Pressure (P)
0.00 atm
0.0 kPa
Volume (V)
50.0 L
0.0500 m³
Temperature (T)
300 K
26.9°C
Moles (n)
2.0 mol
1.20e+24 particles

💡 How to Use:

  • Free Control: Adjust any parameter independently
  • Isothermal (Boyle's Law): Temperature fixed, P and V inversely related
  • Isobaric (Charles's Law): Pressure constant, V and T directly related
  • Isochoric (Gay-Lussac's): Volume fixed, P and T directly related
  • Watch particle speed increase with temperature
  • Container size changes with volume
  • More moles = more particles in the container

Theory

The Ideal Gas Law

The ideal gas law describes the behavior of ideal gases by relating four fundamental properties: pressure (P), volume (V), temperature (T), and number of moles (n).

Ideal Gas Law: PV = nRT

Where:

  • P = Pressure (Pa or atm)
  • V = Volume (m³ or L)
  • n = Number of moles
  • R = Gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K))
  • T = Temperature (Kelvin)

Special Cases

Boyle's Law (Isothermal)

At constant temperature and amount: P₁V₁ = P₂V₂

Pressure and volume are inversely proportional.

Charles's Law (Isobaric)

At constant pressure and amount: V₁/T₁ = V₂/T₂

Volume and temperature are directly proportional.

Gay-Lussac's Law (Isochoric)

At constant volume and amount: P₁/T₁ = P₂/T₂

Pressure and temperature are directly proportional.

Avogadro's Law

At constant temperature and pressure: V₁/n₁ = V₂/n₂

Volume and moles are directly proportional.

Kinetic Molecular Theory

The ideal gas law emerges from the kinetic molecular theory, which makes the following assumptions:

  • Gas particles are in constant, random motion
  • Particles have negligible volume compared to container volume
  • No intermolecular forces between particles
  • Collisions between particles and walls are perfectly elastic
  • Average kinetic energy is proportional to absolute temperature

Real vs Ideal Gases

Real gases deviate from ideal behavior under certain conditions:

  • High pressure: Particle volume becomes significant
  • Low temperature: Intermolecular forces become important
  • Near liquefaction: Condensation effects appear

Applications

  • Weather balloons: Expansion with altitude (decreasing pressure)
  • Scuba diving: Air consumption and decompression calculations
  • Internal combustion engines: Compression and expansion of gases
  • Aerosol cans: Pressure-temperature relationships
  • Hot air balloons: Volume changes with temperature
  • Tire pressure: Temperature effects on pressure
  • Breathing: Lung volume and pressure changes

Discussion