The equilibrium reaction that is not influenced by volume change at constant temperature is :

Options

A. `H_(2)(g)+I_(2)(g) rarr 2HI(g)`
B. `N_(2)(g) + 3H_(2)(g) rarr 2NH_(3)(g)`
C. `N_(2)O_(4)(g) rarr 2NO_(2)(g)`
D. `2NO(g) + O_(2)(g) rarr 2NO_(2)(g)`

Explanation

To determine the equilibrium reaction that is not influenced by volume change at constant temperature, we need to analyze the given reactions based on the relationship between the number of moles of reactants and products.

### Step-by-Step Solution:

1. **Understanding the Equilibrium Constant (Kc)**:
The equilibrium constant \( K_c \) for a reaction can be expressed as:
\[ K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]
where \( [A], [B], [C], [D] \) are the molar concentrations of the reactants and products, and \( a, b, c, d \) are their respective stoichiometric coefficients.

2. **Effect of Volume Change**:
The concentration of a species is defined as the number of moles divided by the volume. If the volume changes, the concentrations will change, which in turn can affect the equilibrium constant \( K_c \).

3. **Deriving the Relationship**:
If we substitute the expressions for concentration into \( K_c \), we can express it in terms of the number of moles and volume:
\[ K_c = \frac{\left(\frac{n_C}{V}\right)^c \left(\frac{n_D}{V}\right)^d}{\left(\frac{n_A}{V}\right)^a \left(\frac{n_B}{V}\right)^b} \]
This simplifies to:
\[ K_c \propto \frac{n_C^c \cdot n_D^d}{n_A^a \cdot n_B^b} \cdot V^{-(a+b-c-d)} \]

4. **Condition for Independence from Volume Change**:
For \( K_c \) to be independent of volume change, the exponent of \( V \) must equal zero:
\[ a + b - c - d = 0 \quad \Rightarrow \quad a + b = c + d \]
This means that the total number of moles of reactants must equal the total number of moles of products.

5. **Analyzing Given Reactions**:
We need to evaluate the provided reactions to see which one satisfies the condition \( a + b = c + d \).

- **Reaction 1**: \( A + B \rightleftharpoons 2C + 2D \)
- \( a + b = 1 + 1 = 2 \)
- \( c + d = 2 + 2 = 4 \)
- Difference: \( 2 - 4 = -2 \)

- **Reaction 2**: \( A + 3B \rightleftharpoons 2C \)
- \( a + b = 1 + 3 = 4 \)
- \( c + d = 2 + 0 = 2 \)
- Difference: \( 4 - 2 = 2 \)

- **Reaction 3**: \( A \rightleftharpoons 2B \)
- \( a + b = 1 + 0 = 1 \)
- \( c + d = 2 + 0 = 2 \)
- Difference: \( 1 - 2 = -1 \)

- **Reaction 4**: \( 2A + B \rightleftharpoons 2C \)
- \( a + b = 2 + 1 = 3 \)
- \( c + d = 2 + 0 = 2 \)
- Difference: \( 3 - 2 = 1 \)

6. **Conclusion**:
The first reaction is the only one where \( a + b = c + d \) is satisfied. Therefore, the equilibrium reaction that is not influenced by volume change at constant temperature is:
\[ \text{Reaction 1: } A + B \rightleftharpoons 2C + 2D \]