Why isn't NH3 an Arrhenius base? And why isn't HCl (g) an Arrhenius acid?

According to Arrhenius theory an acid : is a compound that produces (H+) when in water.

And it is said that one of the things against Arrhenius's theory is :-
e.g:- in 
HCl (g) + NH3 ----> NH4Cl
(HCl) is not an Arrhenius acid , because there are no ions.
What I don't understand is : Did Arrhenius say that the acid must be in the shape of ions while it is reacting, or did he just say that if we take it (not necessarily while it's reacting) and put it in water it is going to produce (H+) ?
The same thing goes with (NH3) , if we put it in water it is going to : first change into (NH4OH) and then (NH4+) and (OH-)  ,,, so eventually it produces (OH-) , right? So why isn't it an Arrhenius Base ?
Or did he mean that it must be able to produce the ions directly without changing into another compound first?

HCl (g) + NH3 ----> NH4Cl

See in this reaction there is no solution . According to the arrhenius concept when dissolved in an aqueous solution, certain ions were released into the solution. As defined by Arrhenius acids dissociates in aqueous solution to form hydrogen ions (H+) and bases, which form hydroxide (OH) ions.

But in this reaction the reaction above between HCl and NH3 there are not any hydrogen ions or hydroxide ions in solution - because there isn't any solution.

So, according to "Arrhenius theory" we wouldn't count this as an acid-base reaction, despite the fact that it is producing the same product as when the two substances were in solution.

This is a short  coming ot the arrhenius theory and so it is easy to get confused but thats the reason we have other theories that came up after the arrehnius one which sought to better explain the behavior of acids and bases in a new manner.

I hope this helps !

 

Thank you so much for your answer. I finally understood Arrhenius theory !!