`N_(2)(g)` and `H_(2)(g)` are allowed to react in a closed vessel at given temp. and pressure for the formation of `NH_(3)(g),[N_(2)(g)+3H_(2)(g)hArr2NH_(3)(g)+22.4kcal]` If He (g) is added at equilibrium at constant pressure than which is/are correct ?

Options

A. Concentration of `N_(2)(g),H_(2)(g)` and `NH_(3)(g)` decrease.
B. Moles of `NH_(3)(g)` decreases.
C. The extent of cooling depends on amount of he (g) added.
D. Concentration of `N_(2)` and `H_(2)` increases and concentration of `NH_(3)` decreases.

Answer

To solve the problem, we need to analyze the reaction and the effects of adding helium gas at equilibrium. The reaction is:

\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) + 22.4 \text{ kcal} \]

### Step-by-Step Solution:

1. **Identify the Reaction and Moles of Gases:**
- The balanced equation shows that 1 mole of nitrogen gas (N₂) reacts with 3 moles of hydrogen gas (H₂) to produce 2 moles of ammonia (NH₃).
- Total moles of reactants = 1 (N₂) + 3 (H₂) = 4 moles.
- Total moles of products = 2 (NH₃) = 2 moles.

2. **Understand the Effect of Adding Helium Gas:**
- Helium is an inert gas and does not react with the components of the equilibrium system.
- When helium is added at constant pressure, the volume of the system increases.

3. **Le Chatelier's Principle:**
- According to Le Chatelier's principle, if a system at equilibrium is subjected to a change in conditions (such as volume), the equilibrium will shift to counteract that change.
- Since the volume increases, the equilibrium will shift towards the side with more moles of gas.

4. **Determine the Direction of the Shift:**
- The reactants side has 4 moles of gas, while the products side has only 2 moles.
- Therefore, the equilibrium will shift to the left (towards the reactants) to increase the number of moles of gas.

5. **Concentration Changes:**
- As the equilibrium shifts to the left, the concentration of nitrogen (N₂) and hydrogen (H₂) will increase.
- Conversely, the concentration of ammonia (NH₃) will decrease.

6. **Evaluate the Statements:**
- **Statement 1:** Concentration of nitrogen, hydrogen, and ammonia gas decreases. (Incorrect)
- **Statement 2:** Moles of ammonia decrease. (Cannot be definitively stated without volume information; Incorrect)
- **Statement 3:** The extent of cooling depends on the amount of helium gas added. (Incorrect)
- **Statement 4:** Concentration of nitrogen and hydrogen increases and the concentration of ammonia decreases. (Correct)

### Final Conclusion:
The correct statement is that the concentration of nitrogen and hydrogen increases while the concentration of ammonia decreases.