Consider two equilibrium `2Cl_2(g)+2H_2O(g)hArr4HCl(g)+O_2(g)` and
`N_2(g)+O_2(g)hArr2NO(g)` simultaneously established in a closed vessel.When some amount of HCl is added at equilibrium, which of the following statements is/are correct :

Options

A. Amount of `N_2` gas will increase
B. Amount of `O_2` gas will increase
C. Amount of `O_2` gas will decrease
D. Nothing can be said with certainty about amount of `O_2`gas.

Explanation

To solve the problem, we need to analyze the two equilibrium reactions and the effect of adding HCl on these equilibria.

### Step-by-Step Solution:

1. **Identify the Reactions**:
We have two reactions:
- Reaction 1: \( 2Cl_2(g) + 2H_2O(g) \rightleftharpoons 4HCl(g) + O_2(g) \)
- Reaction 2: \( N_2(g) + O_2(g) \rightleftharpoons 2NO(g) \)

2. **Understand the Effect of Adding HCl**:
When HCl is added to the system, we are increasing the concentration of a product in Reaction 1. According to Le Chatelier's principle, the system will try to counteract this change.

3. **Shift in Reaction 1**:
- Since HCl is a product of Reaction 1, adding HCl will shift the equilibrium of Reaction 1 to the left (backward direction) to reduce the concentration of HCl.
- This shift will result in a decrease in the concentration of \( O_2 \) as it is produced in the forward direction of Reaction 1.

4. **Effect on Reaction 2**:
- Reaction 2 requires \( O_2 \) as a reactant. Since the concentration of \( O_2 \) is decreasing due to the backward shift of Reaction 1, the forward reaction of Reaction 2 will also be affected.
- The decrease in \( O_2 \) will lead to a decrease in the formation of \( NO \) from Reaction 2, which means the concentration of \( N_2 \) will increase as it shifts to the left to compensate for the decrease in \( O_2 \).

5. **Conclusion**:
- The amount of nitrogen gas \( (N_2) \) will increase due to the shift in Reaction 2.
- The amount of oxygen gas \( (O_2) \) will decrease due to the shift in Reaction 1.
- Therefore, we can conclude:
- Statement 1: Amount of nitrogen gas will increase - **True**
- Statement 2: Amount of oxygen gas will increase - **False**
- Statement 3: Amount of oxygen gas decreases - **True**
- Statement 4: Nothing can be said with certainty about the amount of oxygen gas - **False**

### Final Answer:
The correct statements are:
- Amount of nitrogen gas will increase (True)
- Amount of oxygen gas decreases (True)