Graham's Law
Understanding Graham's Law
Graham's Law, named after the Scottish chemist Thomas Graham, is a principle in chemistry that describes the rate of effusion or diffusion of a gas. Effusion refers to the process by which gas molecules escape through a tiny hole into a vacuum, while diffusion is the spreading of gas molecules throughout a space until they are evenly distributed.
Graham's Law of Effusion
The law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, Graham's Law of Effusion can be expressed as:
[ \text{Rate of Effusion} \propto \frac{1}{\sqrt{\text{Molar Mass}}} ]
Or, when comparing two different gases (1 and 2):
[ \frac{\text{Rate of Effusion of Gas 1}}{\text{Rate of Effusion of Gas 2}} = \sqrt{\frac{\text{Molar Mass of Gas 2}}{\text{Molar Mass of Gas 1}}} ]
Graham's Law of Diffusion
Similarly, Graham's Law of Diffusion states that the rate of diffusion of a gas is also inversely proportional to the square root of its molar mass. The formula is the same as for effusion.
Table of Differences and Important Points
| Property | Effusion | Diffusion |
|---|---|---|
| Definition | Escape of gas molecules through a tiny hole into a vacuum | Spreading of gas molecules throughout a space |
| Dependence on Molar Mass | Inversely proportional to the square root of molar mass | Inversely proportional to the square root of molar mass |
| Formula | $\text{Rate} \propto \frac{1}{\sqrt{\text{Molar Mass}}}$ | $\text{Rate} \propto \frac{1}{\sqrt{\text{Molar Mass}}}$ |
| Comparison Formula | $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{\text{Molar Mass}_2}{\text{Molar Mass}_1}}$ | $\frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{\text{Molar Mass}_2}{\text{Molar Mass}_1}}$ |
Examples to Explain Important Points
Example 1: Effusion Rates of Hydrogen and Oxygen
Let's calculate the relative rates of effusion for hydrogen (H₂) and oxygen (O₂) gases.
- Molar mass of H₂ = 2 g/mol
- Molar mass of O₂ = 32 g/mol
Using Graham's Law of Effusion:
[ \frac{\text{Rate of Effusion of H}_2}{\text{Rate of Effusion of O}_2} = \sqrt{\frac{\text{Molar Mass of O}_2}{\text{Molar Mass of H}_2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 ]
This means that hydrogen gas effuses four times faster than oxygen gas.
Example 2: Diffusion Rates in a Room
Imagine a scenario where ammonia (NH₃) and chlorine (Cl₂) gases are released in a room at the same time. Which gas will reach the other side of the room first?
- Molar mass of NH₃ = 17 g/mol
- Molar mass of Cl₂ = 70.9 g/mol
Using Graham's Law of Diffusion:
[ \frac{\text{Rate of Diffusion of NH}_3}{\text{Rate of Diffusion of Cl}_2} = \sqrt{\frac{\text{Molar Mass of Cl}_2}{\text{Molar Mass of NH}_3}} = \sqrt{\frac{70.9}{17}} \approx \sqrt{4.17} \approx 2.04 ]
Ammonia will diffuse approximately two times faster than chlorine gas.
Conclusion
Graham's Law provides a simple way to predict the relative rates of effusion and diffusion for different gases based on their molar masses. It is important to note that this law assumes ideal gas behavior and may not hold perfectly for real gases under all conditions. However, it is a useful approximation for many practical purposes in chemistry and physics.