Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for a weak electrolyte, if the symbols carry their usual meaning :

Solution

Chemistry ma’am · 4 steps

For a weak electrolyte, put α = Λₘ/Λₘ° into Ostwald's dilution law and rearrange.

1. Degree of dissociation. A weak electrolyte is only partly ionised. By Kohlrausch's idea, its degree of dissociation is α = Λₘ/Λₘ°.
2. Ostwald's dilution law. For HA ⇌ H⁺ + A⁻ at concentration C, Kₐ = Cα²/(1-α). Substitute α and multiply top and bottom by Λₘ^(° 2).

   Kₐ = CΛₘ²/Λₘ°(Λₘ° - Λₘ)

3. Cross-multiply. KₐΛₘ^(° 2) - KₐΛₘΛₘ° = CΛₘ². Moving everything to one side gives Λₘ² C - KₐΛₘ^(° 2) + KₐΛₘΛₘ° = 0.
4. So. This matches option (d). The √C equations in (a) and (c) describe strong electrolytes, not weak ones.

The idea to keep. Weak electrolyte: combine α = Λₘ/Λₘ° with Kₐ = Cα²/(1-α). The Λₘ = Λₘ° - A√C law is only for strong electrolytes.

Answer from the NTA final answer key. Solution by PrepWiser.