Mean Free Path Calculator

Calculate mean free path of gas molecules using kinetic theory: lambda = kT/(sqrt(2)*pi*d^2*P). Find average distance between collisions from gas diameter, pressure, and temperature.

💨 Gas Theory📐 λ = kT/(√2πd²P)🧪 Chemistry

Temperature T (K)

Pressure P (Pa)

Molecular diameter d (pm)

Please enter valid values.

Formula & Reference

Variable	Symbol	Formula	Units
Mean Free Path Calculator	—	λ = kT/(√2πd²P)	m or nm

Step-by-Step Examples

Example 1

N2 at STP

N2: d=370 pm, T=273 K, P=101325 Pa.

lambda = k*T/(sqrt(2)*pi*d^2*P)
= 1.381x10^-23 x 273/(1.414 x 3.14159 x (370x10^-12)^2 x 101325)
= 3.77x10^-21/(1.414x3.14159x1.369x10^-19x101325)
= 3.77x10^-21/6.16x10^-14 = 61 nm

✓ lambda(N2, STP) ~ 61 nm

Example 2

At Low Pressure

N2 at 1 Pa (high vacuum), T=298 K.

lambda = (lambda at 1 atm) x (101325/1)
~ 61 nm x 101325 = 6.2 m
At this pressure: molecules rarely collide

✓ lambda ~ 6.2 m at 1 Pa (near molecular flow)

Example 3

Comparison to Size

N2 diameter = 370 pm = 0.37 nm. MFP at STP = 61 nm.

Ratio: MFP/diameter = 61/0.37 = 165
Molecules travel ~165 diameters between collisions at STP

✓ MFP is ~165x molecular diameter

Real-World Applications

🧪

Vacuum Technology

MFP determines flow regime: viscous (MFP << tube size), transition, or molecular (MFP >> tube size).

💨

Gas Transport

Diffusion, viscosity, thermal conductivity of gases depend on MFP.

📺

MEMS Devices

Microdevices with features ~MFP: must use Knudsen number to determine flow regime.

⚡

Electrical Discharges

MFP determines where electrons can travel between collisions in gas discharge tubes.

Common Mistakes to Avoid

⚠️

Diameter d is collision diameter

Use kinetic diameter, not covalent radius. N2: 370 pm. O2: 346 pm. H2: 289 pm. CO2: 330 pm. These are effective sizes for collisions.

⚠️

Pressure in Pascals

P must be in Pa (SI). 1 atm = 101,325 Pa. 1 bar = 100,000 Pa. 1 torr = 133.3 Pa.

⚠️

MFP inversely proportional to P

Doubling pressure halves MFP. Very low pressure (high vacuum): MFP meters to kilometers.

Frequently Asked Questions

What is mean free path? ▾

Average distance a gas molecule travels between successive collisions with other molecules. Depends on T, P, and molecular diameter.

What is the Knudsen number? ▾

Kn = lambda / L where L is a characteristic dimension of the device. Kn << 1: continuum flow. Kn >> 1: molecular (Knudsen) flow. Kn ~ 1: transition.

How does MFP relate to viscosity? ▾

Gas viscosity eta ~ (1/3)*rho*v_avg*lambda. Independent of pressure! (lambda ~ 1/P, v_avg independent, rho ~ P: cancels). Explains why gas viscosity barely changes with P.

How does MFP relate to diffusion? ▾

Diffusivity D ~ v_avg*lambda/3. Higher T: faster molecules, longer MFP, faster diffusion. Lower P: longer MFP, faster diffusion.

What is MFP in typical vacuum systems? ▾

Atmospheric (101325 Pa): ~65 nm. Rough vacuum (100 Pa): ~65 um. High vacuum (0.1 Pa): ~65 mm. Ultra-high vacuum (10^-7 Pa): ~65 km!

Related Chemistry Calculators

Formula Explorer connections

Interpretation: This relationship connects pressure, volume, temperature, amount or phase composition for gases and volatile mixtures. Assumption: Use absolute temperature and compatible pressure-volume units. Ideal behavior weakens at high pressure, low temperature, strong intermolecular attraction or near phase change.

Gas Mixture Partial Pressure Calculator →Raoult's Law Calculator →Raoult's Law Mixture Calculator →Chemistry Formula Explorer →