Each question given below contains STATEMENT -1 (Assertion) and STATEMENT -2 (Reason). It has four choice (a), (b), ( c ) and (d) out of which ONLY ONE is correct . Choose the correct option as under :
Statement -1 Adding inert gas to dissociation equilibrium of `N_(2)O_(4)` at constant pressure and temperature increases the dissociation .
Statement -2. Molar concentrations of the reactants and products decrease .

Options

A. (a) Statement -1 is True , Statement -2 is true , Statement -2 is the correct explanation of Statement -1
B. (b) Statement -1 is True , Statement -2 is not a correct expanation of Statement -1 .
C. (c ) Statement -1 is True, Statement -2 is False .
D. (d) Statement -1 is False , Statement -2 is True .

Explanation

To solve the question, we need to analyze both statements provided in the assertion and reason format.

### Step-by-Step Solution:

**Step 1: Understand the Assertion (Statement 1)**
The assertion states that adding an inert gas to the dissociation equilibrium of \(N_2O_4\) at constant pressure and temperature increases the dissociation.
- **Explanation**: When an inert gas is added to a system at constant pressure, the volume of the system increases. This increase in volume leads to a decrease in the partial pressures (or concentrations) of the reactants and products in the equilibrium system.

**Step 2: Analyze the Reaction**
The dissociation of \(N_2O_4\) can be represented as:
\[ N_2O_4 (g) \rightleftharpoons 2 NO_2 (g) \]
- **Explanation**: This reaction shows that one mole of \(N_2O_4\) dissociates into two moles of \(NO_2\).

**Step 3: Effect of Adding Inert Gas**
When an inert gas is added, the total pressure remains constant, but the volume increases. According to Le Chatelier's principle, if the concentration of reactants decreases (due to increased volume), the equilibrium will shift towards the side with more moles of gas to counteract this change.
- **Conclusion**: Since there are 2 moles of \(NO_2\) produced from 1 mole of \(N_2O_4\), the equilibrium will shift to the right, increasing the dissociation of \(N_2O_4\).

**Step 4: Understand the Reason (Statement 2)**
The reason states that the molar concentrations of the reactants and products decrease.
- **Explanation**: As established, adding an inert gas increases the volume, which in turn decreases the molar concentrations of all gaseous species involved in the equilibrium.

**Step 5: Evaluate the Truth of Both Statements**
- **Statement 1**: True (adding an inert gas increases the dissociation of \(N_2O_4\)).
- **Statement 2**: True (the molar concentrations of the reactants and products decrease).

**Step 6: Determine the Relationship Between the Statements**
Since both statements are true and the second statement provides a correct explanation for the first statement, we conclude that the correct option is that both statements are true and the second is the correct explanation for the first.

### Final Answer:
The correct option is (a): Both Statement 1 and Statement 2 are true, and Statement 2 is the correct explanation for Statement 1.

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