Question

Which from following electrolytes, molar conductivity is determined using Kohlrausch theory?

• A. $\mathrm{KCl}$
• B. $\mathrm{Na_2SO_4}$
• C. $\mathrm{CH_3COOH}$
• D. $\mathrm{HCl}$

Hint:

Whenever a question asks about calculating limiting molar conductivity using Kohlrausch's Law, look through the options for a weak acid (like $\mathrm{CH_3COOH}$) or a weak base (like $\mathrm{NH_4OH}$). Strong mineral salts or acids never require this indirect method because they can be extrapolated directly.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks to identify which of the listed electrolytes relies on Kohlrausch's theory (Kohlrausch's Law of Independent Migration of Ions) to determine its limiting molar conductivity ($\Lambda_m^{\circ}$).

Step 2: Key Formula or Approach:
Strong Electrolytes (like $\mathrm{KCl}$, $\mathrm{HCl}$, and $\mathrm{Na_2SO_4}$) dissociate completely in solution. Their limiting molar conductivity can be determined easily by graphing and extrapolating $\Lambda_m$ versus $\sqrt{c}$ to zero concentration using the Debye-Hückel-Onsager equation. Weak Electrolytes dissociate incompletely. At high dilutions, their graphs curve sharply upward, making direct graphical extrapolation impossible. Kohlrausch's Law solves this by stating that the limiting molar conductivity of any electrolyte is the sum of its individual ionic conductivities: $$\Lambda_m^{\circ} = \nu_+ \lambda_+^{\circ} + \nu_- \lambda_-^{\circ}$$

Step 3: Detailed Explanation:
$\mathrm{KCl}$, $\mathrm{HCl}$, and $\mathrm{Na_2SO_4}$ are strong electrolytes, so we can find their $\Lambda_m^{\circ}$ values via direct extrapolation. Acetic acid ($\mathrm{CH_3COOH}$) is a weak electrolyte. To find its limiting molar conductivity, we must use Kohlrausch's Law to mathematically combine the experimental values of strong electrolytes: $$\Lambda_m^{\circ}(\mathrm{CH_3COOH}) = \Lambda_m^{\circ}(\mathrm{CH_3COONa}) + \Lambda_m^{\circ}(\mathrm{HCl}) - \Lambda_m^{\circ}(\mathrm{NaCl})$$ This indirect approach is the primary practical application of Kohlrausch's theory.

Step 4: Final Answer:
The electrolyte whose molar conductivity is determined using Kohlrausch theory is $\mathrm{CH_3COOH}$, which corresponds to option (C).