Question

$50\;ml$ of a mixture of $N{H_3}$ and ${H_2}$ was completely decomposed by sparking into nitrogen and hydrogen. $40$ ml of oxygen was then added and the mixture was sparked again. After cooling to room temperature, the mixture was shaken with alkaline pyrogallol and a contraction of $6\;ml$ was observed. Calculate the % of $N{H_3}$ in the original mixture. (Assuming that nitrogen does not react with oxygen.)

Answer 1

Hint : The volume of Hydrogen can be calculated from the total volume by taking the volume of ammonia as V ml. The Oxygen is added later, and then the volume of Hydrogen can be calculated from the volume of Oxygen added. Finally, the contraction in the mixture is equal to the volume of Oxygen remaining, useful for the calculation of volume of ammonia.

Complete Step By Step Answer:
Let the mixture of ammonia and Hydrogen contain $V$ ml of ammonia.
The total volume of mixture is $50$ ml.
The decomposition of ammonia and hydrogen to nitrogen and hydrogen are given as:
$2N{H_3} + {H_2} \to {N_2} + 3{H_2} + {H_2}$
The total volume of Hydrogen will be $\left( {50 - V + \dfrac{3}{2}V} \right)ml$
It will be equal to $\left( {50 + \dfrac{V}{2}} \right)ml$
Now, $40$ ml of Oxygen is added to the mixture,
$2{H_2} + {O_2} \to 2{H_2}O$
As, the volume of Hydrogen is $\left( {50 + \dfrac{V}{2}} \right)ml$ , the volume of reacted Oxygen will be $\left( {25 + \dfrac{V}{4}} \right)ml$
Thus, the volume of Oxygen remained will be $40 - \left( {25 + \dfrac{V}{4}} \right) = \left( {15 - \dfrac{V}{4}} \right)ml$
Given that, there is a contraction of $6$ ml when the mixture is shaken with alkaline pyrogallol.
Thus, the volume of oxygen remaining in the mixture will be equal to the contraction volume.
$\left( {15 - \dfrac{V}{4}} \right)ml = 6ml$
Thus, the value of $V$ will be $36$ ml.
Thus, the volume of ammonia will be $36$ ml.
Given that, the initial volume of mixture is $50$ ml.
Thus, the percentage of ammonia in the mixture will be
$\dfrac{{36}}{{50}} \times 100 = 72\%$
Thus, the percentage of ammonia is $72\%$ .

Note :
The percentage of ammonia must be calculated by taking the original volume of mixture only. The volume of Hydrogen must be calculated from the decomposition of ammonia and hydrogen into nitrogen and Hydrogen. Finally, the volume of oxygen remaining is equal to the contraction volume of the mixture.