Question

In the Haber process $30$ litres of dihydrogen and $30$ litres of dinitrogen were taken for reaction which yielded only $50\% $ of the expected product. What will be the composition of gaseous mixture under these conditions in the end.

Answer 1

Hint: Haber process: It is the reaction of hydrogen and nitrogen to form ammonia. Reaction is as ${N_2} + 3{H_2} \to 2N{H_3}$. By using this reaction if composition of reactant is given and by applying the mole concept we can find the composition of products and reactants after the reaction.
Complete step by step answer:
Haber process: It is the method to produce ammonia. When hydrogen reacts with nitrogen then ammonia is formed. This reaction is very exothermic (which generates heat during the reaction) in nature. The reaction is as: ${N_2} + 3{H_2} \to 2N{H_3}$.
From the reaction, we can see that one mole of nitrogen reacts with three moles of hydrogen to generate two moles ammonia.
Now, in the question it is given that initially the amount of hydrogen and nitrogen was taken as $30$ litres. And the amount of ammonia will be $0$ initially. Now let’s suppose $x$ litres is converted to product i.e. ammonia.
Initially,
 $
  {N_2} + 3{H_2} \to 2N{H_3} \\
  30{\text{ 30 0}} \\
 $
The total litres is $60$.
After reaction,
$
  {N_2}{\text{ + }}3{H_2} \to 2N{H_3} \\
  30 - x{\text{ 30 - 3x 2x}} \\
 $.
We know that before and after the reaction, the total amount of reactants and products remains the same.
Hence,
 $
  30 - x + 30 - 3x = 2x \\
  60 = 6x \\
  x = 10 \\
 $
So the amount of ammonia formed will be $2x$ i.e. $20$litres.
But in the question it is given that only the $50\% $ product is given by the reaction. So, the value of $x$ will be $5$.
So the amount of dihydrogen left will be $30 - 3 \times 5 = 15$litres
The amount of dinitrogen left will be $30 - 5 = 25$litres
And the amount of ammonia formed will be $2 \times 5 = 10$litres.

Note:
By the reaction we will calculate the amount of reactant and product. If the reaction has coefficient then to determine the amount of reactant left we have to subtract the assumed amount multiplied by the coefficient of that reactant from the given amount of the reactant.