[vmelkon]

When you dissolve NH4Cl in water, some of the NH4+ reacts with water, right?
NH4+ + H2O -> NH3 + H3O+

so the solution is acidic a bit.
If we distill it, does the NH3 evaporate as well?
Oh yes, I guess the hydrochloric acid would evaporate as well and you end up with NH4Cl solution again.

[Arkcon]

Many things will happen.  As the water distills of, the solution becomes more concentrated.  As more heat is felt by the ionic solid in solution, some of it will sublime, as a white cloud of very fine ammonium chloride crystals.  And yes, because if the dissociation, some ammonia and HCl will escape, even though those vapors will spontaneously reform ammonium chloride solid.  That last one is a common beginner chem lab experiment, HCl vapor and NH3 vapor travel down a tube to form NH₄Cl solid at the point where the vapors meet.