Question

What is the SI unit of molar conductivity?

• A. \(S\,cm^{-1}\)
• B. \(S\,cm^{2}\,mol^{-1}\)
• C. \(S\,mol^{-1}\)
• D. \(S\,cm\)

Hint:

Remember the common conductivity-related units:
• Conductivity \((\kappa)\): \(S\,cm^{-1}\)
• Molar conductivity \((\Lambda_m)\): \(S\,cm^{2}\,mol^{-1}\) Molar conductivity increases with dilution because ions move more freely in dilute solutions.

Answer 1

The Correct Option is B

Concept:
Molar conductivity \((\Lambda_m)\) is defined as the conducting power of all the ions produced by dissolving one mole of an electrolyte in a solution.
Step 1: Understanding the Question:
The task is to identify the correct unit for molar conductivity based on its physical definition.
Step 2: Key Formula or Approach:
The formula for Molar Conductivity is:
\[ \Lambda_m = \frac{\kappa}{C} \]
Where:
- \(\kappa\) = Conductivity (Specific conductance)
- \(C\) = Molar concentration (Molarity)
Step 3: Detailed Solution:
1. The unit of conductivity \(\kappa\) is \(S\,cm^{-1}\) (Siemens per centimeter).
2. The unit of concentration \(C\) is \(mol\,L^{-1}\). To convert to distance units, we use \(mol/cm^{3}\).
3. Substituting the units into the formula:
\[ \Lambda_m = \frac{S \cdot cm^{-1}}{mol \cdot cm^{-3}} \]
\[ \Lambda_m = S \cdot cm^{-1} \cdot cm^{3} \cdot mol^{-1} \]
\[ \Lambda_m = S\,cm^{2}\,mol^{-1} \]
Step 4: Final Answer:
The SI unit (commonly used in chemistry) of molar conductivity is \(S\,cm^{2}\,mol^{-1}\).