1. Key idea: behavior of molar conductivity with concentration

For a strong electrolyte, molar conductivity $\Lambda_m$ generally decreases with increase in concentration because inter-ionic interactions increase.

For sodium stearate, which is a soap and hence a surfactant electrolyte, there is an additional effect:

• Below CMC: sodium stearate exists mostly as normal ions in solution.
• At and above CMC: the stearate ions aggregate to form micelles.

2. Effect of micelle formation on conductivity

Micelles are large aggregates and have much lower mobility than individual ions. Hence, after micelle formation starts, the conducting species change in nature and the variation of $\Lambda_m$ with concentration shows a break/kink at the CMC.

Thus, the correct plot must show:

• a decreasing trend of $\Lambda_m$ with $C$,
• and a distinct change in slope at the CMC.

3. Why does the slope change?

• Before CMC: addition of sodium stearate increases ionic concentration in the usual way for a strong electrolyte, so $\Lambda_m$ decreases relatively normally with $\sqrt{C}$ or with $C$.
• After CMC: added surfactant mostly goes into micelles; the mobility of these aggregates is much smaller, so the conductivity behavior changes abruptly.

Therefore, the graph is not smooth throughout; it must have a break point at the CMC.

4. Choosing the correct option

Among the given choices, the correct graph is the one showing a decrease in molar conductivity with concentration and a clear kink/break at CMC due to micellization.

That corresponds to Option C.

5. Comparison with stored answer

Stored correct answer = C.

My derived answer = C.

Hence, they agree.