Animated Solution for Chemistry - Surface Chemistry: The qualitative sketches I , II and III given below show the variation of surface tension with molar concentration of three different aqueous solutions of $\text{KCl}$, ${\text{CH}}_3\text{OH}$ and ${\text{CH}}_3({\text{CH}}_2{)}_{11}{\text{OSO}}_3^{-}{\text{Na}}^{+}$ at room temperature. The correct assignment of the sketches is -

Have you ever wondered why water droplets form perfect little spheres? Or why some insects can effortlessly walk on water? The answer lies in a fascinating property called surface tension.

Water molecules are highly social; they love to stick together using strong hydrogen bonds. Molecules deep inside the bulk of the water are pulled equally in all directions by their neighbors. However, the molecules at the surface are missing neighbors above them.

To compensate, they hold onto their side and bottom neighbors even tighter, creating a stretched, elastic "skin" on the surface. This inward pull is what we measure as surface tension, denoted by $\gamma$.

Solutes in Water

What happens when we invite guests into this tightly-knit water community? Adding a solute disrupts the existing harmony, and depending on the nature of the guest, the surface tension can either increase or decrease.

This behavior is beautifully governed by the Gibbs Adsorption Isotherm. If a solute prefers to stay in the bulk of the liquid away from the surface, it undergoes negative adsorption, and the surface tension increases. Conversely, if the solute loves to hang out at the surface, it undergoes positive adsorption, and the surface tension decreases.

Let's analyze our three specific guests to decode the graphs.

The Inorganic Salt ($\text{KCl}$)

Our first guest is $\text{KCl}$, a strong inorganic electrolyte. When dissolved, it completely dissociates into ${\text{K}}^{+}$ and ${\text{Cl}}^{-}$ ions.

Water molecules are highly polar and are intensely attracted to these charged ions, forming ion-dipole interactions. These interactions are actually stronger than the hydrogen bonds between the water molecules themselves!

Because the ions are pulled deep into the bulk water surrounded by their hydration shells, the water molecules are also dragged inward. This is a classic case of negative adsorption. The surface becomes "depleted" of solute, and the inward pull on the surface molecules intensifies, causing the surface tension to increase linearly with concentration.

Looking at our options, Graph II is the only one showing an upward trend. Therefore, Graph II perfectly represents $\text{KCl}$.

The Simple Organic (${\text{CH}}_3\text{OH}$)

Next, we have methanol (${\text{CH}}_3\text{OH}$). This is a simple organic molecule with a dual personality: a hydrophilic (water-loving) $\text{-OH}$ group and a small hydrophobic (water-fearing) ${\text{-CH}}_3$ group.

Because of that tiny hydrophobic methyl group, methanol doesn't perfectly fit into the bulk water's hydrogen-bonded network. It prefers to migrate towards the surface, sticking its methyl group out into the air. This is positive adsorption.

As methanol molecules accumulate at the surface, they replace some of the strongly interacting water molecules. Since the intermolecular forces between methanol and water are weaker than water-water hydrogen bonds, the overall tension of the surface "skin" relaxes. This results in a gradual decrease in surface tension.

Graph I beautifully illustrates this smooth, gradual downward curve, making it the perfect match for ${\text{CH}}_3\text{OH}$.

The Heavyweight Surfactant

Finally, we meet the heavyweight: ${\text{CH}}_3({\text{CH}}_2{)}_{11}{\text{OSO}}_3^{-}{\text{Na}}^{+}$. This is a classic surfactant (surface-active agent), specifically Sodium Dodecyl Sulfate (SDS).

Unlike methanol, this molecule has a massive, 12-carbon-long hydrophobic tail. This tail absolutely despises water. When added to the solution, these molecules aggressively rush to the surface to escape the aqueous environment, packing themselves tightly side-by-side.

This massive accumulation at the surface causes a drastic and sharp drop in surface tension. But there's a catch! Eventually, the surface gets completely full. There is simply no more room for any new surfactant molecules.

At this specific concentration, known as the Critical Micelle Concentration (CMC), any additional surfactant added to the water is forced to stay in the bulk. To hide their hydrophobic tails, they clump together into spherical structures called micelles. Because the surface composition stops changing after the CMC, the surface tension becomes completely constant, forming a flat plateau.

Graph III captures this dramatic story perfectly: a sharp, steep drop followed by a sudden flat line at the CMC. Thus, Graph III represents our long-chain surfactant.

By understanding the physical chemistry of intermolecular forces and adsorption, we've successfully decoded the mystery:

Graph I (Gradual decrease) $\to {\text{CH}}_3\text{OH}$ Graph II (Linear increase) $\to \text{KCl}$ Graph III* (Sharp drop to plateau) $\to {\text{CH}}_3({\text{CH}}_2{)}_{11}{\text{OSO}}_3^{-}{\text{Na}}^{+}$

Matching this sequence with our given choices, we arrive at the correct answer: Option (D).