Can't answer on date or purpose, but it is an image A&G had previously (I assume) used in another photo advertising card (taken from the Gallery and' 'stretched'), but its not the same image they used in the set of 50 - images below.
Each of the 3 cards gives this Washington building a slightly different name. From top to bottom "War and State Department", "War & Navy Department", "War Department".
(i) Old card hobby history, particularly vintage publications - magazines, price lists, books, hobby correspondence.
(ii) And any cards pre-1885, particularly Thos. H. Hall.