Question

The SI unit of the molar conductivity of an electrolyte solution is 

• A. S m⁻¹ mol ⁻¹
• B. S mol ⁻¹
• C. S m mol ⁻¹
• D. S m² mol ⁻¹

Answer 1

The Correct Option is D

The molar conductivity of an electrolyte solution, denoted by the symbol Λ_m, is defined as the conductivity of the solution divided by the molar concentration of the electrolyte. The formula for calculating molar conductivity is:

\[\Lambda_m = \frac{\kappa}{c}\]

• Where \kappa is the conductivity of the solution and has units of Siemens per meter (S m^-1).
• c is the concentration in moles per cubic meter (mol m^-3).

By substituting the units into the formula, the units of molar conductivity are derived as follows:

\[\Lambda_m = \frac{\text{S m}^{-1}}{\text{mol m}^{-3}} = \text{S m}^2 \text{ mol}^{-1}\]

Thus, the SI unit of molar conductivity is S m² mol^-1.

Explanation for each option:

1. S m^-1 mol^-1: This represents an incorrect combination of units as it implies molar conductivity per unit volume, not per unit concentration.
2. S mol^-1: This unit does not account for the spatial factor of conductivity (meter squared) inherent in molar conductivity.
3. S m mol^-1: While closer, this option still misses the ² exponent on the meter which is essential to balance the dimensional analysis for molar conductivity.
4. S m² mol^-1: The correct SI unit as derived from the formula and dimensional analysis.

In conclusion, the SI unit of molar conductivity is S m² mol^-1.