Can the solution of $H C l_{(} g)$ in $N H_{3 (I)}$ be considered as an Arrhenius acid-base?

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Solution

Arrhenius acid-base model is restricted to compounds that have $H^{+}$ or $O H^{-}$ ions.
It is restricted to aqueous solutions.
It does not explain acid-base reactions that occur in non-aqueous solvents or in the gas phase where dissociation does not take place.
Hence Arrhenius theory does not consider the reaction of ${N H_{3}}_{(g)} + H C l_{(g)} ⟶ N H_{4} C l_{(s)}$ as an acid-base reaction since there are no $H^{+}$ ions are $O H^{-}$ ions in solution.

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