The molar conductance of an infinitely dilute solution of ammonium chloride was found to be 185 S cm² mol⁻¹ and the ionic conductance of hydroxyl and chloride ions are 170 and 70 S cm² mol⁻¹, respectively. If molar conductance of 0.02 M solution of ammonium hydroxide is 85.5 S cm² mol⁻¹, its degree of dissociation is given by x × 10⁻¹. The value of x is __________ . (Nearest integer)

Solution

Chemistry ma’am · 3 steps

You cannot measure NH₄OH at infinite dilution, so build its Λ° from the ions.

1. Find the ammonium ion. Kohlrausch's law says Λ° of a salt is the sum of its ions' limiting conductances. So λ°(NH₄⁺) = Λ°(NH₄Cl) - λ°(Cl⁻) = 185 - 70 = 115 S cm² mol⁻¹.
2. Build ammonium hydroxide. Add the hydroxide ion to it: Λ°(NH₄OH) = 115 + 170 = 285 S cm² mol⁻¹.

   α = Λₘ/Λ°ₘ = 85.5/285 = 0.3

3. So. α = 0.3 = 3 × 10⁻¹, so x = 3.

The common slip: 2. Adding λ°(OH⁻) to Λ°(NH₄Cl) without removing Cl⁻ gives Λ° = 355, so α ≈ 0.24 and x = 2, not 3.

The idea to keep. For a weak electrolyte, get Λ° by adding and subtracting strong-electrolyte values until only its own ions remain. Then α = Λₘ / Λ°ₘ.

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