At -50°C, autoprotolysis of NH₃ gives $[{NH}_{4}^{+}] = 1 \times 10^{- 15} M$ , hence autoprotolysis constant of NH₃ is

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$1 \times 10^{- 30}$

$2 \times 10^{- 15}$

$\sqrt{1 \times 10^{- 15}}$

$1 \times 10^{- 15}$

answer is B.

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Detailed Solution

${NH}_{3} + {NH}_{3} ⇌ {NH}_{2}^{-} + {NH}_{4}^{+} [{NH}_{2}^{-}] = [{NH}_{4}^{+}] = 1 \times 10^{- 15} M ∴ K = [{NH}_{2}^{-}] [{NH}_{4}^{+}] = 1 \times 10^{- 30}$

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