Question

40ml of ammonia gas was taken in a eudiometer tube and subjected to sparks till the volume did not further change. The volume was found to increase by $ 40{\text{ ml}} $ . $ 40{\text{ ml}} $ of oxygen gas then mixed and the mixture was further exploded. The gases remaining were $ 30{\text{ ml}} $ . Deduce the formula of ammonia. (Ammonia contains $ {\text{N}} $ and $ {\text{H}} $ only)

Answer 1

Hint: To answer this question, you must first determine the reactions occurring in the eudiometer tube in the above given conditions. Using the amounts of reactants taken and the products formed, we can find the amount of nitrogen and oxygen reacted and thus, the formula of ammonia gas.

Complete step by step solution
We know that ammonia gas is formed by the combination of nitrogen and hydrogen. So, we assume the formula of ammonia to be $ {{\text{N}}_{\text{x}}}{{\text{H}}_{\text{y}}} $ .
Then we are given that the gas in the eudiometer tube was subjected to electric sparks. As a result, it will dissociate into its elemental gases dinitrogen and dihydrogen. We can write the balanced chemical equation for this decomposition reaction of ammonia as:
 $ {{\text{N}}_{\text{x}}}{{\text{H}}_{\text{y}}} \to \dfrac{{\text{x}}}{{\text{2}}}{{\text{N}}_{\text{2}}} + \dfrac{{\text{y}}}{{\text{2}}}{{\text{H}}_{\text{2}}} $
We are given the initial volume of the gas in the mixture as $ 40{\text{ ml}} $ . After the sparking, an increase by $ 40{\text{ ml}} $ was detected in the tube. This means that the volume occupied by nitrogen and hydrogen gases would be equal to $ 40{\text{ ml}} + 40{\text{ ml}} = 80{\text{ ml}} $
Also from the reaction, we can say that we get $ 20{\text{x ml}} $ of nitrogen gas and $ 20{\text{y ml}} $ of hydrogen gas. So we can write, $ 20x + 20y = 80 $
 $ \Rightarrow x + y = 4 $
Now this mixture of nitrogen and hydrogen is exploded further with oxygen gas. Hydrogen gas would react with oxygen to form water. The reaction is given as:
 $ {\text{2}}{{\text{H}}_{\text{2}}} + {{\text{O}}_2} \to {{\text{H}}_{\text{2}}}{\text{O}} $
We can thus say that the gases remaining in the tube are nitrogen gas and excess oxygen gas.
The final volume of the mixture is given to be $ 30{\text{ ml}} $ . We can thus write,
 $ 40 - 10y + 20x = 30 $
 $ \Rightarrow 2x - y = 1 $
Solving the two relations obtained, we get, $ x = 1 $ and $ y = 3 $
So, the formula of ammonia is $ {\text{N}}{{\text{H}}_{\text{3}}} $

Note
Nitrogen is an inert gas by nature and does not react with oxygen unless subjected to extremely harsh conditions otherwise not possible in an eudiometer tube.