In Haber process 30 litre 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 the aforesaid condition in the end ?

Options

A. 20 litres ammonia, 25 litres nitrogen, 15 litres hydrogen
B. 20 litres ammonia, 20 litres nitrogen, 15 litres hydrogen
C. 10 litres ammonia, 25 litres nitrogen, 15 litrers hydrogen
D. 20 litres ammoina, 10 litres nitrogen, 30 litres hydrogen

Explanation

To solve the problem, we need to analyze the Haber process and the stoichiometry involved in the reaction between dihydrogen (H₂) and dinitrogen (N₂) to form ammonia (NH₃). The balanced equation for the Haber process is:

\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]

### Step-by-Step Solution:

1. **Identify Initial Volumes**:
- We have 30 liters of dihydrogen (H₂) and 30 liters of dinitrogen (N₂).

2. **Determine the Stoichiometric Ratios**:
- According to the balanced equation, 1 volume of N₂ reacts with 3 volumes of H₂ to produce 2 volumes of NH₃.
- Therefore, for 30 liters of N₂, we would need \( 3 \times 30 = 90 \) liters of H₂ to fully react.

3. **Identify the Limiting Reagent**:
- Since we only have 30 liters of H₂, H₂ is the limiting reagent.
- The maximum amount of NH₃ that can be produced from 30 liters of H₂ is calculated as follows:
- From the stoichiometry, 3 liters of H₂ produce 2 liters of NH₃.
- Thus, \( 30 \text{ liters H₂} \) will produce \( \frac{2}{3} \times 30 = 20 \) liters of NH₃.

4. **Calculate the Expected Yield**:
- We are told that the yield is only 50% of the expected product.
- Therefore, the actual yield of NH₃ is \( 50\% \times 20 \text{ liters} = 10 \text{ liters} \).

5. **Calculate Remaining Volumes**:
- Let \( X \) be the volume of N₂ that reacted. From the stoichiometry, \( 3X \) liters of H₂ will also react.
- Since we produced 10 liters of NH₃, we can set up the equation:
\[ 2X = 10 \]
\[ X = 5 \text{ liters of N₂ reacted} \]

6. **Calculate Remaining Gases**:
- Remaining N₂: \( 30 - X = 30 - 5 = 25 \text{ liters} \)
- Remaining H₂: \( 30 - 3X = 30 - 15 = 15 \text{ liters} \)

7. **Final Composition of the Gaseous Mixture**:
- Ammonia (NH₃): 10 liters
- Dinitrogen (N₂): 25 liters
- Dihydrogen (H₂): 15 liters

### Final Answer:
The composition of the gaseous mixture at the end is:
- 10 liters of NH₃
- 25 liters of N₂
- 15 liters of H₂