When we buy a bottle of concentrated ammonia (the stuff that brings tears to your eyes if you smell it), this is approx. #15*mol*L^-1# with respect to #NH_3#. Ammonia is mostly present in aqueous solution as #NH_3*H_2O#. Ammonia (as a pure solvent not a solution) is very water like in its properties, is supplied in gas bottles. It has similar acid base chemistry, and this property can be attributed to the capacity of ammonia to hydrogen bond.
As a weak base, ammonia undergoes hydrolysis in water:
#NH_3(aq) + H_2O(l) rarr NH_4^+ + HO^-#.
You can find the extent of hydrolysis by using #K_b#. The extent of this hydrolysis is fairly small. The ammonia fountain is a common experiment that illustrates the solubility of gaseous ammonia in water. To represent the chemistry we use the equation:
#NH_3(g) + H_2O rarr NH_3(aq)#,
where #NH_3(aq) -=NH_3*(H_2O)_n#.
I suppose you could say that #NH_3*OH_2-=NH_4OH#, but the reagent sold as ammonium hydroxide is aqueous ammonia.