Question

Which of the following expression correctly represents molar conductivity?

• A. $\Lambda_m = \frac{K}{C}$
• B. $\Lambda_m = \frac{KA}{1}$
• C. $\Lambda_m = KV$
• D. all of these

Hint:

Key Exam Tip:
Molar conductivity ($\Lambda_m$) is the conductivity of one mole of electrolyte. It is calculated by dividing the specific conductivity ($K$) by the molar concentration ($C$). Ensure you use consistent units for $K$ and $C$ to obtain the correct units for $\Lambda_m$.

Answer 1

The Correct Option is A

Molar conductivity ($\Lambda_m$) is a measure of the efficiency of ion conduction in a solution. It is defined as the conductivity of a solution divided by the molar concentration of the electrolyte. The relationship between molar conductivity ($\Lambda_m$), specific conductivity (or conductivity, $K$), and molar concentration ($C$) is given by the formula: $\Lambda_m = \frac{K}{C}$ Where:
• $\Lambda_m$ is the molar conductivity (units: S m$^2$ mol$^{-1}$ or S cm$^2$ mol$^{-1}$).
• $K$ (kappa) is the specific conductivity (or conductivity) of the solution (units: S m$^{-1}$ or S cm$^{-1}$).
• $C$ is the molar concentration of the electrolyte (units: mol m$^{-3}$ or mol cm$^{-3}$, often mol L$^{-1}$). Let's examine the given options:
• $\Lambda_m = \frac{K}{C}$: This is the correct definition of molar conductivity.
• $\Lambda_m = \frac{KA}{1}$: This expression is dimensionally incorrect. 'A' is not defined in this context, and the units would not match molar conductivity. If 'A' were meant to be volume, it would be $\Lambda_m = \frac{K}{C} = \frac{K}{n/V} = \frac{KV}{n}$.
• $\Lambda_m = KV$: This expression is also dimensionally incorrect and does not represent molar conductivity. If 'V' represents the volume of solution containing one mole of electrolyte (i.e., V = 1/C), then $\Lambda_m = K \times \frac{1}{C} = \frac{K}{C}$, which brings us back to option 1. However, as stated, it's incorrect.
• all of these: Since options 2 and 3 are incorrect, this option is also incorrect. Thus, the only correct expression for molar conductivity is $\Lambda_m = \frac{K}{C}$. Final Answer: \(\boxed{1}\)