Question

Which of the following expressions correctly represents molar conductivity?

• A. \( \Lambda_m = \frac{K}{C} \)
• B. \( \Lambda_m = \frac{KA}{l} \)
• C. \( \Lambda_m = K V \)
• D. \( \text{All of these} \)

Hint:

Molar conductivity decreases with increasing concentration due to ion-pair formation but increases with dilution as ions move more freely in the solution.

Answer 1

The Correct Option is D

The molar conductivity (\( \Lambda_m \)) of an electrolyte solution can be understood through its dependence on various factors such as conductivity (\( K \)), concentration (\( C \)), and the geometry of the solution. Here's a step-by-step explanation using different reasoning: 

1. Relationship with Conductivity and Concentration: Using the basic definition of molar conductivity: \[ \Lambda_m = \frac{K}{C}, \] where \( K \) is the conductivity and \( C \) is the molar concentration. This relationship shows that molar conductivity is inversely proportional to concentration at a fixed conductivity. 

 

2. Derivation from Geometry and Conductance: Consider the relationship between conductivity (\( K \)), the geometry of the system, and conductance (\( G \)): \[ G = \frac{K \cdot A}{l}, \] where \( A \) is the cross-sectional area, and \( l \) is the distance between electrodes. Substituting \( G \) into the expression for molar conductivity, we get: \[ \Lambda_m = \frac{KA}{l}. \] This formula emphasizes the role of the geometry of the electrolytic cell in determining molar conductivity. 

3. Dependence on Volume: For a solution containing 1 mole of electrolyte, the molar conductivity can also be expressed in terms of the solution's volume (\( V \)): \[ \Lambda_m = K V. \] Here, \( V \) represents the volume that contains 1 mole of solute, highlighting the dependency of molar conductivity on the extent of dilution. 

Analysis of the Three Expressions: All three expressions—\( \Lambda_m = \frac{K}{C} \), \( \Lambda_m = \frac{KA}{l} \), and \( \Lambda_m = K V \)—are valid representations of molar conductivity, derived from different aspects of the electrolyte solution's behavior. 

Final Answer: \[ \boxed{\text{All of these}} \]