Dry ammonia has no action on litmus paper, but a solution of ammonia in water turns red litmus paper blue. Why?

Hint: The change in colour of Red litmus to blue is due to the basic nature of solutions, and blue Litmus changes to red colour in presence of acidic solution.
Presence of ions is very important for this change of colour. The acidic and basic nature is shown due to the ions present in the solution.

Complete step by step answer:

The nitrogen has its basic nature by the lone pair on it.
Litmus test is possible only in the presence of ions. In acidic solution, there is presence of hydronium ion, ${H^ + }$ ion and due to this presence turns blue litmus red. In basic solution, we have hydroxyl ion, \[O{H^ - }\] ion and due to this presence turns red litmus blue.
Now in dry ammonia, there are no ions present, so hence we don’t have any positive litmus test. But when Ammonia is present in solution, then we get hydroxyl ions from water, and thus red litmus turns blue. The reaction can be written as under:
 \[N{H_3} + {H_2}O \to N{H_4}OH\]
 \[N{H_4}OH \to N{H_4}^ + + O{H^ - }\]
Thus, this presence of hydroxide ions will turn the red litmus into blue.

Additional information: The pH value for acids is from 0 to below 7 and for bases is above 7 to 14. For a neutral solution the value is exactly 7 and no action of litmus test on the neutral solution. The Litmus test is one of the easiest and best ways of detecting the nature of a solution to be acidic or basic.


Note:
There is one shortcut to remember the colour of litmus paper. For Bases, the first alphabet is ‘B’, and any colour of litmus will remain Blue, ‘B’ is the first letter.
Some medium is required to show the acidic or basic nature of solutions. Generally water is used as medium. As the property of acidic and basic nature is depending on ions presence, especially ${H^ + }$ ion, and \[O{H^ - }\] ions.