1. What Is Collision Frequency?
Collision frequency is the number of collisions made by a single gas molecule per unit time. It tells how often a molecule bumps into other molecules while moving randomly.
1.1. Symbol and Meaning
Collision frequency is usually represented by Z. A higher value of Z means the molecule is colliding more frequently.
2. What Is Collision Number?
Collision number is the total number of molecular collisions occurring in the entire volume of gas per second.
It gives a broader picture of how active all the molecules in the gas are collectively.
2.1. Difference from Collision Frequency
Collision frequency → collisions by one molecule per second.
Collision number → total collisions by all molecules per second.
3. Expressions for Collision Frequency
For a molecule moving with average speed \( \bar{c} \), the collision frequency is approximately:
Z = \sqrt{2} \pi d^2 n \bar{c}
where:
- \( d \) = molecular diameter
- \( n \) = number of molecules per unit volume
- \( \bar{c} \) = average molecular speed
3.1. Meaning of Each Factor
Higher density (n) → more molecules → more collisions.
Bigger molecules (d) → easier to collide → higher Z.
Higher speed (\(\bar{c}\)) → more distance travelled → more collisions.
4. Expression for Collision Number
The total number of collisions happening per unit volume per second is:
Z_{total} = \dfrac{1}{2} n Z
The factor \(\dfrac{1}{2}\) avoids counting the same collision twice.
4.1. Why Divide by 2?
Because when molecule A collides with molecule B, we should not count the same event once as A’s collision and again as B’s collision.
5. Factors Affecting Collision Frequency
Several factors influence how often collisions occur.
5.1. 1. Molecular Speed
Faster molecules collide more frequently.
Speed increases with temperature, so collision frequency increases when temperature rises.
5.2. 2. Number Density
More molecules in a given volume means more collisions.
Thus collision frequency increases when pressure increases.
5.3. 3. Molecular Size
Larger molecules present a bigger "target area", leading to more collisions.
6. Typical Values
In ordinary air at room temperature and atmospheric pressure:
- Each molecule collides around 109 times per second.
- The gas contains an enormous number of molecules, so the total collisions per second are unimaginable.
7. Why Collision Frequency Matters
Collision frequency is important because many gas properties depend on how often collisions happen. These include:
- viscosity
- diffusion
- thermal conductivity
- reaction rates in gases
7.1. Simple Example
A fragrance spreads faster in a room on a hot day because molecules move faster at higher temperature, increasing collision frequency and diffusion rate.