Key idea: how solutes affect surface tension of water

We compare the three solutes:

• $KCl$ : an electrolyte
• $CH_3OH$ : a small alcohol
• $\mathrm{CH_3(CH_2)_{11}OSO_3^-\ Na^+}$ : a surfactant (sodium lauryl sulfate type)

General trends

(i) $KCl$

Electrolytes like $KCl$ generally increase the surface tension of water slightly.

Reason: ions are not preferred at the air-water interface and tend to remain in bulk water, so the surface becomes relatively depleted of solute, making surface tension increase.

So the graph for $KCl$ should show:

• surface tension increasing with concentration.

(ii) $CH_3OH$

Methanol is an alcohol and is surface-active compared to ions. It tends to accumulate somewhat at the surface and hence decreases the surface tension of water.

So the graph for $CH_3OH$ should show:

• surface tension decreasing gradually with concentration.

(iii) $\mathrm{CH_3(CH_2)_{11}OSO_3^-\ Na^+}$

This is a surfactant. Surfactants strongly lower surface tension because they adsorb strongly at the surface.

As concentration increases:

• initially, surface tension drops sharply,
• after the critical micelle concentration (CMC), the surface becomes saturated and the curve becomes nearly constant.

So the graph for this substance should be:

• sharp decrease followed by a plateau.

Matching with sketches

Therefore the three qualitative sketches must correspond to:

• Increasing curve $\to KCl$
• Gradually decreasing curve $\to CH_3OH$
• Sharp decrease then plateau $\to \mathrm{CH_3(CH_2)_{11}OSO_3^-\ Na^+}$

Check options

• A: I = $KCl$, II = $CH_3OH$, III = surfactant
• B: I = surfactant, II = $CH_3OH$, III = $KCl$
• C: I = $KCl$, II = surfactant, III = $CH_3OH$
• D: I = $CH_3OH$, II = $KCl$, III = surfactant

From the standard qualitative behavior, the correct mapping is:

• I : $CH_3OH$
• II : $KCl$
• III : $\mathrm{CH_3(CH_2)_{11}OSO_3^-\ Na^+}$

Hence, Option D is correct.

Final answer

$\boxed{D}$