This relationship is known as Graham's Law of Effusion:
```
Rate₁ / Rate₂ = √(M₂ / M₁)
```
Where:
* Rate₁ is the effusion rate of gas 1
* Rate₂ is the effusion rate of gas 2
* M₁ is the molar mass of gas 1
* M₂ is the molar mass of gas 2
Explanation:
The effusion rate is determined by the average speed of the gas molecules. Lighter molecules move faster than heavier molecules at the same temperature. This is because the kinetic energy of a gas molecule is proportional to its temperature and its mass.
Therefore, lighter molecules have a higher average speed and thus effuse faster through a small opening.
Example:
Consider helium (He) and oxygen (O₂). Helium has a molar mass of 4 g/mol, while oxygen has a molar mass of 32 g/mol.
According to Graham's Law:
```
Rate(He) / Rate(O₂) = √(32 / 4) = √8 ≈ 2.83
```
This means that helium effuses about 2.83 times faster than oxygen.
Applications:
Graham's Law has several applications in chemistry and physics, including:
* Separating gases: Gases with different molar masses can be separated by allowing them to effuse through a porous membrane.
* Determining molar mass: The molar mass of an unknown gas can be determined by comparing its effusion rate to that of a known gas.
* Understanding gas diffusion: The concept of effusion rate is also related to the diffusion of gases, which is the movement of gas molecules from a region of high concentration to a region of low concentration.
