Root Mean Square Velocity Calculator
Calculate RMS velocity, average velocity, and most probable velocity of gas molecules using kinetic theory
Calculate Gas Molecule Velocities
Temperature of the gas (absolute temperature required for calculations)
Select a common gas or choose "Custom" to enter your own molar mass
Gas Molecule Velocity Results
Velocity Unit Conversions
Additional Information
Velocity Analysis
Example Calculation
Oxygen at Room Temperature
Gas: Oxygen (O₂)
Temperature: 27°C (300.15 K)
Molar Mass: 0.032 kg/mol
Calculations
v_rms = √(3RT/M)
v_rms = √(3×8.314×300.15/0.032)
v_rms = 483.7 m/s
v_ave = √(8RT/πM) = 445.6 m/s
v_mp = √(2RT/M) = 394.9 m/s
Velocity Formulas
RMS Velocity
v_rms = √(3RT/M)
Root mean square of velocities
Average Velocity
v_ave = √(8RT/πM)
Mean velocity of distribution
Most Probable Velocity
v_mp = √(2RT/M)
Peak of velocity distribution
Physics Tips
RMS velocity is always the highest of the three velocities
Higher temperature means higher molecular velocities
Lighter molecules move faster than heavier ones
Temperature must be in Kelvin for calculations
Velocities are independent of pressure and volume
Understanding Gas Molecule Velocities
Kinetic Theory of Gases
The kinetic theory of gases describes gas molecules as tiny particles in constant random motion. The theory relates macroscopic properties like temperature and pressure to microscopic molecular motion.
Key Assumptions
- •Gas molecules are point particles with negligible volume
- •No intermolecular forces except during collisions
- •Collisions are perfectly elastic
- •Average kinetic energy is proportional to temperature
Velocity Types Explained
Root Mean Square (RMS) Velocity
The square root of the average of squared velocities. Related to kinetic energy and temperature.
Average Velocity
The arithmetic mean of all molecular velocities. Used in diffusion and effusion calculations.
Most Probable Velocity
The velocity at the peak of the Maxwell-Boltzmann distribution. The most common velocity.
Note: All three velocities increase with temperature and decrease with molecular mass.
Maxwell-Boltzmann Velocity Distribution
The Maxwell-Boltzmann distribution describes the probability distribution of speeds for particles in a gas. It shows that most molecules have intermediate speeds, with fewer having very low or very high speeds.
Distribution Characteristics:
- • Asymmetric curve with a long tail at high velocities
- • Peak occurs at the most probable velocity
- • Average velocity is to the right of the peak
- • RMS velocity is further to the right
- • Higher temperature broadens and shifts the curve
Temperature Effects
Higher Temperature:
• Curve shifts to higher velocities
• Curve becomes broader and flatter
• Peak height decreases
Lower Temperature:
• Curve shifts to lower velocities
• Curve becomes narrower and taller
• Peak height increases
Applications of Gas Velocity Calculations
Diffusion and Effusion
Calculate rates of gas mixing and escape through small openings. Graham's law relates effusion rates to molecular masses.
Chemical Kinetics
Understand reaction rates and collision theory. Molecular velocities determine collision frequencies and energies.
Atmospheric Science
Study atmospheric escape, gas separation, and weather phenomena. Explains why hydrogen escapes Earth's atmosphere.