Mean free path

Definition

Mean free path is the average distance a gas molecule travels between collisions with other molecules. It is influenced by factors such as temperature, pressure, and particle size.

5 Must Know Facts For Your Next Test

1. Mean free path decreases with increasing pressure because more molecules are present, leading to more frequent collisions.
2. An increase in temperature generally increases the mean free path because molecules move faster and collide more energetically.
3. Mean free path is inversely proportional to the density of the gas; higher density results in a shorter mean free path.
4. The formula for mean free path $\lambda$ is given by $\lambda = \frac{k_B T}{\sqrt{2} \pi d^2 P}$ where $k_B$ is Boltzmann's constant, $T$ is temperature, $d$ is the diameter of the molecules, and $P$ is pressure.
5. Mean free path plays a crucial role in understanding diffusion and effusion processes in gases.

Review Questions

• How does an increase in pressure affect the mean free path of gas molecules?
• What happens to the mean free path when the temperature of a gas increases?
• Write down the formula for calculating mean free path and explain each variable.

Related terms

Effusion:

The process by which gas particles pass through a tiny opening from one compartment to another.

Diffusion:

The spreading of gas molecules throughout a container until evenly distributed due to random molecular motion.

Boltzmann's Constant: $k_B$, a fundamental physical constant that relates energy at the individual particle level with temperature. Its value is approximately $1.38 \times 10^{-23} \text{J/K}$.