Kinetic Molecular Theory Calculator

Calculate molecular velocities and kinetic energies using kinetic molecular theory

Kinetic Molecular Theory Calculator

Root-Mean-Square Velocity: vrms = √(3RT/M)
Calculate molecular velocities and kinetic energies from temperature

m/s

K

g/mol

Common Gas Molar Masses:

• H₂: 2.02 g/mol
• He: 4.00 g/mol
• N₂: 28.01 g/mol
• O₂: 32.00 g/mol
• CO₂: 44.01 g/mol
• Ar: 39.95 g/mol

Understanding KMT

Kinetic Molecular Theory explains gas behavior at the molecular level, relating temperature to the average kinetic energy of gas molecules.

vrms = √(3RT/M)

  • R = 8.314 J/(mol·K)
  • T = temperature (K)
  • M = molar mass (kg/mol)

Types of Molecular Speeds

Most Probable: vp = √(2RT/M)

Average: vavg = √(8RT/πM)

RMS: vrms = √(3RT/M)

vrms > vavg > vp

Where It's Used

  • •Gas Behavior: Understanding pressure and temperature
  • •Diffusion: Predicting gas mixing rates
  • •Reaction Rates: Collision theory
  • •Atmospheric Science: Molecular escape velocities

Molecular Speeds at 25°C (298 K)

GasM (g/mol)vrms (m/s)vrms (km/h)
H₂2.0219276937
He4.0013634907
H₂O (steam)18.026432315
N₂28.015151854
O₂32.004821735
Ar39.954311552
CO₂44.014111480

Note: These are extremely fast speeds! Faster than the speed of sound (~343 m/s at 20°C).

Five Postulates of Kinetic Molecular Theory

1. Particle Size

Gas molecules are point masses with negligible volume compared to container volume.

2. Motion

Molecules are in constant, random, straight-line motion.

3. Collisions

Collisions are perfectly elastic (no energy lost).

4. No Forces

No attractive or repulsive forces between molecules (except during collisions).

5. Temperature

Average kinetic energy is directly proportional to absolute temperature: KE = (3/2)kBT

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