Consider the following equilibrium
`N_(2)O_(4)(g)hArr2NO_(2)(g)`
Then the select the correct graph , which shows the variation in concentratins of `N_(2)O_(4)` Against concentrations of `N_(2)`O_(4)`:

Options

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B.
C.
D.

Answer

To solve the problem, we need to analyze the equilibrium reaction given:

\[ N_2O_4(g) \rightleftharpoons 2NO_2(g) \]

We are tasked with determining the correct graph that shows the variation in concentrations of \( N_2O_4 \) against the concentrations of \( NO_2 \).

### Step-by-Step Solution:

1. **Understanding the Reaction**:
- The reaction shows that one mole of \( N_2O_4 \) dissociates to form two moles of \( NO_2 \).
- This implies that as the concentration of \( N_2O_4 \) decreases, the concentration of \( NO_2 \) increases.

2. **Setting Up the Equilibrium Expression**:
- The equilibrium constant \( K_c \) for the reaction can be expressed as:
\[ K_c = \frac{[NO_2]^2}{[N_2O_4]} \]
- Rearranging this gives:
\[ [NO_2]^2 = K_c \cdot [N_2O_4] \]

3. **Graphing the Relationship**:
- In the equation \( [NO_2]^2 = K_c \cdot [N_2O_4] \), we can see that if we let \( y = [NO_2] \) and \( x = [N_2O_4] \), we can rewrite it as:
\[ y^2 = K_c \cdot x \]
- This is a quadratic equation in terms of \( y \), which indicates that the graph will be a parabola.

4. **Determining the Orientation of the Parabola**:
- The equation \( y^2 = K_c \cdot x \) suggests that as \( x \) (the concentration of \( N_2O_4 \)) increases, \( y^2 \) (the square of the concentration of \( NO_2 \)) also increases.
- Therefore, the graph opens upwards, indicating that \( y \) increases as \( x \) increases.

5. **Identifying the Correct Graph**:
- Since we are looking for a graph that represents a parabolic relationship where \( y^2 \) is proportional to \( x \), and it opens upwards, we can eliminate options that show a downward-opening parabola.
- The correct graph will show a curve that starts at the origin and rises as \( [N_2O_4] \) increases.

### Conclusion:
The correct graph is the one that represents a parabolic curve opening upwards, indicating that as the concentration of \( N_2O_4 \) increases, the concentration of \( NO_2 \) also increases.