Q.Calculate surface area to volume ratio of a spherical particle. See how the ratio increases with the reduction of radius of the particle. Plot the ratio against the radius.

Factors Affecting Adsorption

Imagine a crowded bus. People stand closer together near the doors because that's where the action is — getting on and off. The surface of a solid is like that bus door. Molecules from a gas or a liquid (the adsorbate) naturally want to cling to the surface of a solid (the adsorbent). But how many of them actually stick depends on a few key conditions.

Let's build that intuition first, then make it precise.

1. Surface Area of the Adsorbent

The bigger the surface, the more places there are for molecules to land. A lump of charcoal has a small outer surface. But if you grind it into a fine powder, you expose millions of tiny crevices and pores — the total surface area skyrockets. More area means more adsorption.

This is why activated charcoal (which is full of microscopic pores) is used in gas masks and water filters — it has an enormous surface area per gram.

2. Temperature

Think of gas molecules as hyperactive kids. At low temperature, they move slowly and are easily caught by the surface. At high temperature, they bounce around too fast — they have enough energy to break free from the surface's grip.

For physical adsorption (physisorption), which is the weak, reversible kind, adsorption decreases as temperature rises. This is an exothermic process — heat is released when molecules stick. Le Chatelier's principle tells you: if you add heat, the equilibrium shifts to undo the sticking.

3. Pressure (for Gaseous Adsorbates)

At low pressure, only a few gas molecules hit the surface per second — adsorption is low. As pressure increases, more molecules collide and stick, so the amount adsorbed rises. But there's a limit. Once the surface is completely covered in a single layer (a monolayer), raising pressure further does almost nothing — the surface is full.

This behaviour is captured by the Freundlich adsorption isotherm (for moderate pressures):

Where:

• $x/m$ = mass of adsorbate per unit mass of adsorbent
• $P$ = pressure
• $k$ and $n$ are constants ( $n > 1$ )

At very high pressures, $x/m$ becomes constant — the surface is saturated.

4. Nature of the Adsorbent and Adsorbate

Not all surfaces are equally sticky. Some general rules:

• Polar adsorbents (like silica gel, alumina) attract polar adsorbates (like water, ammonia). "Like attracts like" works here.
• Non-polar adsorbents (like charcoal) attract non-polar adsorbates (like methane, nitrogen). …