Question

Which of the following expression correctly represents molar conductivity?

• A. $\Lambda_m = \frac{K}{C}$
• B. $\Lambda_m = \frac{KA}{1}$
• C. $\Lambda_m = KV$
• D. all of these

Hint:

Key Exam Tip:
Molar conductivity ($\Lambda_m$) is the conductivity of one mole of electrolyte. It is calculated by dividing the specific conductivity ($K$) by the molar concentration ($C$). Ensure you use consistent units for $K$ and $C$ to obtain the correct units for $\Lambda_m$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Molar conductivity (\( \Lambda_m \)) is the conductance of a volume of solution containing one mole of electrolyte placed between two electrodes with unit distance between them and large enough area to accommodate the whole volume.
Step 2: Key Formula or Approach:
The basic definition is:
\[ \Lambda_m = \frac{\kappa}{C} \]
where \( \kappa \) (kappa, represented as \( K \) here) is electrolytic conductivity and \( C \) is molar concentration.
Step 3: Detailed Explanation:
1. Expression (a): This is the direct formula where \( K \) is specific conductance and \( C \) is concentration.
2. Expression (c): If \( V \) is the volume of solution in \( cm^3 \) containing 1 mole of electrolyte, then \( V = 1/C \). Substituting this gives \( \Lambda_m = K \cdot V \).
3. Expression (b): Molar conductivity can also be derived from the general conductance formula \( G = \kappa \cdot \frac{A}{l} \). When the cell is designed such that it contains exactly one mole of solute, the conductance \( G \) becomes the molar conductivity. In many memory-based papers, this generic form is accepted as a foundational representation.
Step 4: Final Answer:
Since both (a) and (c) are standard definitions and (b) represents the structural basis of conductance, "all of these" is the correct choice.