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:

Important conductivity units:
• Conductivity \((\kappa)\): \(S\,cm^{-1}\)
• Molar conductivity \((\Lambda_m)\): \(S\,cm^{2}\,mol^{-1}\) Molar conductivity increases as dilution increases.

Answer 1

The Correct Option is B

Concept: Molar conductivity \((\Lambda_m)\) is defined as the conductance of a solution containing one mole of electrolyte placed between two electrodes one centimetre apart. Mathematically, \[ \Lambda_m = \frac{\kappa}{C} \] where
• \(\Lambda_m\) = molar conductivity
• \(\kappa\) = conductivity of the solution
• \(C\) = concentration of the solution

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

Step 2: Include concentration in the formula. Since concentration has the unit \(mol\,cm^{-3}\), \[ \Lambda_m = S\,cm^{-1} \times \frac{cm^{3}}{mol} \]

Step 3: Simplify the units. \[ \Lambda_m = S\,cm^{2}\,mol^{-1} \] Therefore, \[ \boxed{S\,cm^{2}\,mol^{-1}} \]