1. What Is Mean Free Path?
The mean free path is the average distance a gas molecule travels between two successive collisions. Because molecules are constantly moving and colliding, they do not travel in straight lines for long.
The mean free path gives an idea of how often collisions happen inside a gas.
2. Why Collisions Happen
Gas molecules move randomly in all directions. Since there are millions of molecules in a small space, they frequently collide with one another.
2.1. Effect on Motion
Molecules move in a zig-zag path: straight-line motion until a collision → sudden change in direction → another straight path → next collision.
3. Formula for Mean Free Path
The mean free path depends on how many molecules are present and how large they are. The expression for mean free path is:
\( \lambda = \dfrac{1}{\sqrt{2} \pi d^2 n} \)
where:
- \( d \) = diameter of a molecule
- \( n \) = number of molecules per unit volume
3.1. Meaning of the Formula
Smaller molecules (small d) → longer mean free path.
Lower density (small n) → fewer collisions → longer mean free path.
4. Factors Affecting Mean Free Path
Several factors influence how long a molecule can travel before colliding.
4.1. 1. Pressure
Higher pressure means more molecules packed into the same space, so collisions are more frequent. Therefore:
\( \lambda \propto \dfrac{1}{P} \)
4.2. 2. Temperature
Increasing temperature makes molecules move faster, spreading them out slightly. This increases the mean free path.
4.3. 3. Molecular Size
Larger molecules collide more easily, so they have a shorter mean free path.
5. Typical Values
In air at room temperature and normal pressure, the mean free path is extremely small—about:
\( 10^{-7} \text{ m} \)
This is around 100 nanometers, which is tiny, but still much larger than the size of a molecule.
6. Why Mean Free Path Matters
Mean free path helps understand gas properties like viscosity, diffusion, and thermal conductivity. All these depend on how far molecules travel before colliding.
6.1. Simple Example
A fragrance spreads faster in low-pressure environments because molecules can travel longer distances before colliding, giving a longer mean free path.