Question

What is the correct official unit measurement scale used to represent Molar Conductivity (\( \Lambda_m \)) profiles within electrolytic systems?

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

Hint:

When using concentration values in moles per liter (\(\text{mol L}^{-1}\)), apply a scaling factor of 1000 to keep your units consistent: \( \Lambda_m = \frac{\kappa \times 1000}{\text{Molarity}} \), which yields the final value directly in \( \text{S cm}^2 \text{ mol}^{-1} \).

Answer 1

The Correct Option is D

Concept: Molar conductivity (\( \Lambda_m \)) measures the electrolytic conductance capacity of a solution containing exactly one mole of dissolved electrolyte. It is mathematically related to specific conductivity (\( \kappa \)) and concentration (\( C \)) by the equation: \[ \Lambda_m = \frac{\kappa}{C} \]

Step 1: Analyze the base units of the individual variables.
Derive the units systematically through dimensional analysis:

• Specific Conductivity (\(\kappa\)): Measured in Siemens per centimeter (\( \text{S cm}^{-1} \)), where Siemens (\(\text{S}\)) represents reciprocal ohms (\(\Omega^{-1}\)).
• Concentration (\(C\)): Expressed in terms of solution volume as moles per cubic centimeter (\( \text{mol cm}^{-3} \)).

Step 2: Combine the units within the equation.
Substitute these units into our molar conductivity expression: \[ \text{Units of } \Lambda_m = \frac{\text{S cm}^{-1}}{\text{mol cm}^{-3}} = \text{S} \cdot \text{cm}^{-1} \cdot \text{cm}^3 \cdot \text{mol}^{-1} \] Simplify the overlapping centimeter exponents: \[ \text{Units of } \Lambda_m = \text{S cm}^2 \text{ mol}^{-1} \]