Consider the following two equilibria simultaneously established in a rigid vessel at a particular temperature
`NH_(2)COOMH_(4)(s)hArr2NH_(3)+CO_(2)(g)`
`CaCO_(3)(s)hArrCaO(s)+CO_(2)(g)`
Now, on adding some amout of `NH_(3)` to the reaction vessel, the orignal equilibrium is disturbed and a new equilibrium state is obtained. On comparing the following at the initial & final equilibrium states, select the INCORRECT statement `(s)`:

Options

A. Nothing can be said about the number of moles of `CO_(2)` gas in reaction vessel.
B. Nothing can be said about the number of moles of `NH_(3)` gas in reaction vessel.
C. Number of moles of `NH_(3)` gas would have definitely increased.
D. Number of moles of `CaCO_(3)` solid gas would have definitely decreased.

Explanation

To solve the problem, we need to analyze the two equilibria given and the effect of adding NH₃ on the system.

### Step 1: Identify the Equilibria
We have two equilibria:
1. \( \text{NH}_2\text{COOMH}_4(s) \rightleftharpoons 2\text{NH}_3(g) + \text{CO}_2(g) \)
2. \( \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \)

### Step 2: Understand the Effect of Adding NH₃
When we add NH₃ to the reaction vessel, we disturb the first equilibrium. According to Le Chatelier's principle, the system will respond to counteract the change. In this case, the addition of NH₃ will cause the first equilibrium to shift to the left to reduce the concentration of NH₃.

### Step 3: Analyze the Changes in Equilibrium
- **For the first equilibrium**:
- The addition of NH₃ will cause the reaction to shift left, which means that the amount of NH₂COOMH₄ will increase, and the amount of CO₂ will decrease.

- **For the second equilibrium**:
- The decrease in CO₂ from the first equilibrium will cause the second equilibrium to shift to the right to produce more CO₂. This means that the amount of CaCO₃ will increase.

### Step 4: Evaluate the Statements
Now we need to evaluate the statements provided to identify the incorrect one:

1. **Nothing can be said about the number of moles of CO₂ gas in the reaction vessel.**
- This statement is incorrect because we can say that the number of moles of CO₂ will initially decrease due to the left shift of the first equilibrium, but may later increase due to the right shift of the second equilibrium.

2. **Nothing can be said about the number of moles of NH₃ gas in the reaction vessel.**
- This statement is also incorrect because we know that the addition of NH₃ will increase its initial concentration, but at equilibrium, it will adjust based on the shifts.

3. **The number of moles of NH₃ gas would have definitely increased.**
- This statement is incorrect because while we added NH₃, the equilibrium shift may cause its concentration to decrease after reaching a new equilibrium.

4. **The number of moles of CaCO₃ would have definitely decreased.**
- This statement is correct because the second equilibrium shifts to the right, leading to an increase in CaCO₃.

### Conclusion
The incorrect statements are:
1. Nothing can be said about the number of moles of CO₂ gas in the reaction vessel.
2. Nothing can be said about the number of moles of NH₃ gas in the reaction vessel.
3. The number of moles of NH₃ gas would have definitely increased.

### Final Answer
The incorrect statement is: **The number of moles of NH₃ gas would have definitely increased.**