Graham's Law
The Rates of Effusion and Diffusion of Gases.
Have you ever wondered why a balloon filled with Helium shrinks much faster than a balloon filled with normal air? Or why the smell of perfume spreads across a room? The answer lies in the kinetic motion of gas molecules, governed by Graham's Law.
1. Effusion vs. Diffusion
Before stating the law, we must clarify two closely related processes:
- Diffusion: The natural, spontaneous intermixing of two or more gases to form a homogeneous mixture, driven by the random thermal motion of molecules (e.g., perfume spreading in air).
- Effusion: The process by which a gas under pressure escapes from one compartment of a container to another (usually a vacuum) through a tiny pinhole.
2. Statement & Mathematical Formula
In 1829, Thomas Graham discovered that lighter gases travel faster than heavier gases.
Graham's Law states: Under identical conditions of temperature and pressure, the rate of effusion (or diffusion) of a gas is inversely proportional to the square root of its molar mass (or density).
The Problem-Solving Equation:
When comparing the rates ($r_1$ and $r_2$) of two different gases:
$$\frac{r_{H_2}}{r_{O_2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4$$ This means Hydrogen gas effuses 4 times faster than Oxygen gas!
3. Critical Variations of the Formula
In competitive exams, "Rate" ($r$) can be defined in multiple ways depending on what is being measured.
A. Rate in terms of Volume or Moles
If $r = \frac{Volume}{time} = \frac{V}{t}$ (or $\frac{n}{t}$):
B. Rate in terms of Distance traveled in a tube
If two gases are released at opposite ends of a tube at the same time ($t_1 = t_2$), their meeting point depends on the distance ($x$) traveled:
C. Effect of Different Pressures
If the gases are NOT at the same initial pressure, a higher pressure will physically push the gas out faster. The formula must be modified to include pressure:
4. Real-World Application: Isotope Separation
Graham's Law is not just a theoretical concept; it was historically crucial for nuclear energy.
- Uranium Enrichment: Natural uranium contains mostly U-238 and a tiny amount of the fissile U-235 (needed for reactors and bombs). Because they are chemically identical, they cannot be separated by chemical reactions.
- Scientists convert Uranium into a gas, Uranium Hexafluoride ($UF_6$).
- Because $^{235}UF_6$ is slightly lighter than $^{238}UF_6$, it effuses through a porous membrane just a tiny fraction of a percent faster. By passing the gas through thousands of successive porous barriers in a massive facility, the gas becomes gradually "enriched" with the lighter U-235 isotope.
Knowledge Check
Test your ability to apply Graham's Law
💨 Complete Guide to the Gaseous State
Master critical concepts including Boyle's Law, Charles's Law, Ideal Gas Equation, Dalton's Law, Graham's Law of Effusion, and Kinetic Molecular Theory with exam-focused notes for JEE Main, JEE Advanced, NEET and CBSE.
🚀 Explore the States of Matter Hub
No comments:
Post a Comment