Question

The relation between molar conductivity \( \Lambda_m \), conductivity \( \kappa \), and concentration \( C \) of an electrolyte solution is:

• A. \( \Lambda_m = \dfrac{\kappa}{1000C} \)
• B. \( \Lambda_m = \dfrac{C}{\kappa \times 1000} \)
• C. \( \Lambda_m = \dfrac{\kappa \times 1000}{C} \)
• D. \( \Lambda_m = \kappa C \)

Hint:

Remember the key electrochemistry relation: \[ \Lambda_m = \frac{\kappa \times 1000}{C} \] On dilution, concentration \(C\) decreases and therefore molar conductivity \( \Lambda_m \) increases.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks for the correct mathematical formula that connects three key properties of an electrolyte solution: molar conductivity (\( \Lambda_m \)), conductivity (\( \kappa \), also called specific conductance), and molar concentration (\( C \)).
Step 2: Key Formula or Approach:
Molar conductivity (\( \Lambda_m \)) is defined as the conductivity of a volume of solution containing exactly one mole of the electrolyte. It is given by the product of conductivity (\(\kappa\)) and the volume (\(V\)) of the solution containing one mole of the electrolyte.
\[ \Lambda_m = \kappa \times V \] Step 3: Detailed Explanation:
1. We start with the definition: \( \Lambda_m = \kappa \times V \).
2. The concentration \( C \) is given in moles per litre (mol L\(^{-1}\)). This means that \( C \) moles are present in 1 Litre (or 1000 cm\(^3\)) of solution.
3. We need the volume \( V \) that contains exactly one mole. From the definition of concentration:
Volume for 1 mole (\(V\)) = \( \frac{1}{C} \) Litres.
4. The standard unit for conductivity \( \kappa \) is Siemens per centimetre (S cm\(^{-1}\)). To maintain unit consistency, we must express the volume \( V \) in cubic centimetres (cm\(^3\)).
Since 1 Litre = 1000 cm\(^3\), the volume is:
\[ V = \frac{1}{C} \text{ L} = \frac{1000}{C} \text{ cm}^3 \] 5. Now, substitute this expression for \( V \) back into the original formula for molar conductivity:
\[ \Lambda_m = \kappa \times \frac{1000}{C} \] Step 4: Final Answer:
The correct relationship is \( \Lambda_m = \frac{\kappa \times 1000}{C} \), which matches option (C).