Question

Which from following is the correct relationship between molar conductivity (\(\Lambda\)), conductivity (\(\text{k}\)) and molarity (\(\text{M}\)) of solution for electrolyte?

• A. \(\text{k} = \frac{\Lambda \times \text{C}}{1000}\)
• B. \(\Lambda = \frac{100 \times \text{k}}{\text{C}}\)
• C. \(\Lambda = \frac{\text{k} \times \text{C}}{1000}\)
• D. \(\text{k} = \frac{1000 \times \text{C}}{\Lambda}\)

Hint:

Always remember: \(\Lambda = \frac{1000k}{C}\). Rearranging gives all required relations.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Molar conductivity (\(\Lambda_m\) or simply \(\Lambda\)) is defined as the conducting power of all the ions produced by dissolving one mole of an electrolyte in solution. It is related to specific conductivity (\(\kappa\), here denoted as \(\text{k}\)) and concentration (\(C\)).
Step 2: Key Formula or Approach:
The standard textbook relationship between molar conductivity (\(\Lambda\)), specific conductivity (\(\kappa\) in \(\text{S cm}^{-1}\)), and molar concentration (\(C\) in \(\text{mol L}^{-1}\) or \(\text{mol dm}^{-3}\)) is given by: \[ \Lambda = \frac{\kappa \times 1000}{C} \] where the factor of $1000$ is used to convert the volume from \(\text{L}\) (\(\text{dm}^3\)) to \(\text{cm}^3\).
Step 3: Detailed Explanation:
Let's rearrange the standard formula to see which option it matches: \[ \Lambda = \frac{\text{k} \times 1000}{C} \] Cross-multiplying yields: \[ \Lambda \times C = \text{k} \times 1000 \] Solving for \(\text{k}\) gives: \[ \text{k} = \frac{\Lambda \times C}{1000} \] Comparing this rearranged equation with the given options, we see that it perfectly matches option (A).
Step 4: Final Answer:
The correct relationship is given in option (A).