Model molecular travel between collisions with flexible inputs. Choose pressure or number density. Get clear steps, conversions, and exportable results for labs fast online.
| Scenario | T (K) | p (Pa) | d (nm) | Expected λ (approx) |
|---|---|---|---|---|
| Air near sea level | 288.15 | 101325 | 0.365 | ~70 nm |
| Room air | 300 | 101325 | 0.365 | ~68 nm |
| Rough vacuum | 300 | 1 | 0.365 | ~7 mm |
| High vacuum | 300 | 0.0001 | 0.365 | ~70 m |
Values are illustrative; real gases vary by composition and conditions.
Mean free path (λ) for an ideal gas using a hard-sphere diameter:
If particle number density (n) is known:
For ideal gases, n ≈ p/(kB·T), so both forms are consistent.
Mean free path (λ) is the average distance a molecule travels between collisions. It links microscopic physics to practical design decisions in vacuum systems, gas discharge devices, aerosol transport, and microfluidics where surfaces compete with intermolecular impacts.
For dilute gases modeled as hard spheres, collisions are governed by the cross‑section σ = πd². The √2 factor appears because collisions depend on relative molecular speeds, not single‑particle speed. This calculator applies the standard kinetic‑theory expressions.
At fixed temperature, λ scales inversely with pressure: halving pressure doubles λ. At fixed pressure, λ scales linearly with absolute temperature. These trends explain why high‑vacuum chambers quickly enter collision‑poor regimes, while hot gases at the same pressure show longer paths.
Near 1 atm and 300 K, air has λ on the order of 60–70 nm when d ≈ 0.36 nm. At 1 Pa, λ rises to millimeters. At 10⁻⁴ Pa, λ can reach tens of meters, so molecules are more likely to hit walls than each other.
The diameter d is an effective hard‑sphere size, often estimated from viscosity or collision data. For many common gases, d lies around 0.3–0.4 nm. Because λ depends on d², a 10% change in d shifts λ by about 20%.
Combine λ with a characteristic length L to form the Knudsen number Kn = λ/L. Roughly, Kn < 0.01 indicates continuum flow, 0.01–0.1 slip flow, 0.1–10 transitional flow, and Kn > 10 free‑molecular flow. This guides modeling choices.
If you measure particle density directly (plasmas, beams, or rarefied gas diagnostics), use the number‑density method. For ideal gases, n ≈ p/(kB·T), so both methods agree when p and T are consistent. Exports help document assumptions.
When λ exceeds chamber dimensions, pumping speed and conductance become geometry‑limited, and surface cleanliness dominates. In microchannels, increasing pressure shortens λ and reduces slip. Always report units, temperature, pressure range, and chosen d to keep results reproducible.
No. Spacing is set mainly by number density, while λ depends on both density and collision cross‑section. Two gases with similar density can have different λ if their effective diameters differ.
For ideal gases, pressure tracks number density. Higher pressure means more particles per volume, increasing collision frequency. Because λ is distance between collisions, it decreases as pressure rises.
A common effective value is about 0.36–0.37 nm. If you need higher accuracy, use a diameter derived from viscosity or collision‑integral data for your specific composition and temperature range.
Not reliably. The hard‑sphere dilute‑gas assumption breaks down when interactions become strong. In liquids and dense gases, collision concepts require more advanced models and empirical transport data.
If λ is larger than your chamber or channel size, molecules rarely collide in the bulk. Wall interactions dominate, and free‑molecular or transitional flow models are usually more appropriate than continuum equations.
Yes. Mixtures change effective diameter and collision rates. For rough estimates, use a representative diameter and note the assumption. For precision, compute mixture‑averaged collision parameters or evaluate components separately.
Exports preserve inputs, units, and results for lab notes, design reviews, and traceability. They also reduce transcription errors when comparing multiple operating points across experiments or simulations.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.