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 conductivity of an electrolyte solution divided by its molar concentration. It represents the conducting power of all the ions produced by one mole of an electrolyte in solution. Mathematically, \[ \Lambda_m = \frac{\kappa}{C} \] where:
• \(\Lambda_m\) = molar conductivity
• \(\kappa\) = conductivity of the solution
• \(C\) = molar concentration

Step 1: Identify the unit of conductivity. The unit of conductivity \((\kappa)\) is: \[ S\,cm^{-1} \]

Step 2: Divide conductivity by concentration. Since concentration is expressed as \(mol\,cm^{-3}\), dividing conductivity by concentration gives: \[ \Lambda_m = S\,cm^{-1} \times \frac{cm^{3}}{mol} \] \[ \Lambda_m = S\,cm^{2}\,mol^{-1} \]

Step 3: Final unit of molar conductivity. Thus, the unit of molar conductivity is \[ \boxed{S\,cm^{2}\,mol^{-1}} \]