`N_(2)O_(4(g))rArr2NO_(2),K_(c)5.7xx10^(-9)` at 298 K At equilibrium :-

Options

A. concentration of `NO_(2)` is higher than that of `N_(2)O_(4)`
B. concentration of `N_(2)O_(4)` is higher than of `NO_(2)`
C. both `N_(2)O_(4) and NO_(2)` have same concentration
D. concentration of `N_(2)O_(4) and NO_(2)` keeps on changing

Answer

To solve the problem regarding the equilibrium of the reaction \( N_2O_4(g) \rightleftharpoons 2NO_2(g) \) with the equilibrium constant \( K_c = 5.7 \times 10^{-9} \) at 298 K, we will analyze the implications of the given equilibrium constant.

### Step-by-Step Solution:

1. **Write the expression for the equilibrium constant \( K_c \)**:
The equilibrium constant for the reaction can be expressed as:
\[ K_c = \frac{[NO_2]^2}{[N_2O_4]} \]
where \([NO_2]\) is the concentration of nitrogen dioxide and \([N_2O_4]\) is the concentration of dinitrogen tetroxide at equilibrium.

2. **Substitute the value of \( K_c \)**:
Given that \( K_c = 5.7 \times 10^{-9} \), we can substitute this value into the equilibrium expression:
\[ 5.7 \times 10^{-9} = \frac{[NO_2]^2}{[N_2O_4]} \]

3. **Analyze the value of \( K_c \)**:
The value of \( K_c \) is very small (much less than 1), which indicates that at equilibrium, the concentration of the reactants (in this case, \( N_2O_4 \)) is much greater than the concentration of the products (\( NO_2 \)). This means that the reaction favors the formation of the reactants.

4. **Conclude the relationship between concentrations**:
Since \( K_c \) is small, we conclude that:
\[ [N_2O_4] > [NO_2] \]
This implies that at equilibrium, the concentration of \( N_2O_4 \) is higher than that of \( NO_2 \).

5. **Evaluate the statements**:
Based on our analysis, we can evaluate the given statements:
- Concentration of \( NO_2 \) is higher: **Incorrect**
- Concentration of \( N_2O_4 \) is higher than \( NO_2 \): **Correct**
- Both have the same concentration: **Incorrect**
- Concentration of \( N_2O_4 \) and \( NO_2 \) keeps on changing: **Incorrect**

Thus, the correct statement is that the concentration of \( N_2O_4 \) is higher than that of \( NO_2 \).