Can acid-base reactions occur in a non-aqueous medium?
If you dissolve $\ce{NH4Cl}$ in water, your solution contains $\ce{NH4+}$ and $\ce{Cl-}$ ions. If you dissolve $\ce{NaOH}$ in water, your solution contains $\ce{Na+}$ and $\ce{OH-}$ ions.
Now if you mix those two solutions, nearly all $\ce{NH4+}$ and $\ce{OH-}$ will react and produce $\ce{NH3}$ and $\ce{H2O}.$ This shows that $\ce{NH4OH}$ cannot exist. It is decomposed into a solution of $\ce{NH3}$ in water, with only a few percent of $\ce{NH4+}$ and $\ce{OH-}$ ions. 

You will certainly object and say that $\ce{NH4OH}$ is a commercial substance, that you can buy anywhere in the market. You are right. But you may not know that the reason of this mistake is commercial and goes back to the 19th century. In the 19th century, the ions were unknown. All substances had a chemical formula, whatever pure or in solution. $\ce{NaOH}$ in solution was made of $\ce{NaOH}$ and that's all. Charged ions like $\ce{H3O+}$ and $\ce{OH-}$ did not exist. 

At this time, chemists were often studying the neutralisation reaction 

$$\ce{Acid + Base -&gt; Salt + Water}$$

They succeeded in carrying out this reaction with mineral or organic acids, and with many hydroxides (hydroxide was synonymous to base). When a new organic acid was discovered, they tried to make salts with all available hydroxides. Each new salt deserved a publication. And this was fine!

Unfortunately, ammonia was a problem: $\ce{NH3}$ reacts with any acid, but it does not produce any water. $\ce{NH3 + HCl}$ makes $\ce{NH4Cl}$ and that's all: no water! This was difficult to admit. So the chemists decided that, when dissolved in water, $\ce{NH3}$ is transformed into $\ce{NH4OH}.$ This makes sense, because $\ce{NH3}$ was very soluble in water, as if a chemical reaction happens. It was fine. When neutralizing a solution of ammonia by reaction with any acid, the equation of the reaction was:

$$\ce{NH4OH + HCl -&gt; NH4Cl + H2O}$$

$\ce{NH3}$ was only existing in a gaseous state. It was considered as a sort of "dehydrated ammonium hydroxyde". A little bit like other hydroxides, which can easily lose water. At high temperature, $\ce{Cu(OH)2}$ becomes $\ce{CuO}$ and $\ce{Al(OH)3}$ becomes $\ce{Al2O3}.$

So the merchants started to sell ammonia solution with the label $\ce{NH4OH}.$ It was soon discovered that this solution is helpful unblocking blocked up pipes. Everything was OK!

Unfortunately at the end of the century, Arrhenius discovered the ions, and showed that $\ce{NH4+}$ and $\ce{OH-}$ ions cannot exist simultaneously in solution. Disaster! The so called "ammonium hydroxyde" was mainly containing $\ce{NH3}$ and $\ce{H2O},$ with only a few percent of remaining ions $\ce{NH4+}$ and $\ce{OH-}.$ So the merchants changed their labels and started to sell "concentrated ammonia solution". It was OK for the chemists.

But this change was not accepted by the caretakers, managers and contractors. They protested to the manufacturers against this new "ammonia solution" which was useless to unblock blocked pipes. They said they have tried the new and the old solutions. They demanded to get the old ammonium hydroxide, which was "much better" than this stupid ammonia solution. 

Well! The merchants are not stupid. They want to sell and get money. So they renounced to modernize their labels, and continued to sell $\ce{NH4OH}$ solutions. This was accepted by chemists and non-chemists. 

That is why $\ce{NH4OH}$ is still on sale today. I am an old man, 82. This story was reported to me by my father, who was a chemist who remembered this old time.