For the reaction,
`2N_2O_5rarr4NO_2+O_2`
Select the correct statement

Options

A. Rate of formation of `O_2` is same as rate of formation of `NO_2`
B. Rate of disappearance of `N_2O_5` is two times the rate of formation of `NO_2`
C. Rate of formation of `O_2` is 0.5 time rate disappearance of `N_2O_5`
D. Rate of formation of `NO_2` is equal to rate of disappearance of `N_2O_5`

Answer

To analyze the reaction \( 2N_2O_5 \rightarrow 4NO_2 + O_2 \) and select the correct statement regarding the rates of formation and disappearance of the substances involved, we can follow these steps:

### Step 1: Write the rate expressions for the reaction.
For the reaction \( 2N_2O_5 \rightarrow 4NO_2 + O_2 \), we can express the rates of disappearance of the reactant and the rates of formation of the products as follows:

- The rate of disappearance of \( N_2O_5 \):
\[ -\frac{1}{2} \frac{d[N_2O_5]}{dt} \]

- The rate of formation of \( NO_2 \):
\[ \frac{1}{4} \frac{d[NO_2]}{dt} \]

- The rate of formation of \( O_2 \):
\[ \frac{1}{1} \frac{d[O_2]}{dt} \]

### Step 2: Relate the rates of formation and disappearance.
From the stoichiometry of the reaction, we can relate these rates:

1. The rate of formation of \( NO_2 \) is related to the rate of disappearance of \( N_2O_5 \):
\[ -\frac{1}{2} \frac{d[N_2O_5]}{dt} = \frac{1}{4} \frac{d[NO_2]}{dt} \]

2. The rate of formation of \( O_2 \) is also related to the rate of disappearance of \( N_2O_5 \):
\[ \frac{1}{1} \frac{d[O_2]}{dt} = -\frac{1}{2} \frac{d[N_2O_5]}{dt} \]

### Step 3: Analyze the statements.
Now we can analyze the statements provided:

1. **Statement 1**: The rate of formation of \( O_2 \) is the same as the rate of formation of \( NO_2 \).
- This is incorrect because the rate of formation of \( O_2 \) is \( 0.5 \) times the rate of formation of \( NO_2 \).

2. **Statement 2**: The rate of disappearance of \( N_2O_5 \) is \( 2 \) times the rate of formation of \( NO_2 \).
- This is incorrect because the rate of disappearance of \( N_2O_5 \) is \( 2 \) times the rate of formation of \( O_2 \), not \( NO_2 \).

3. **Statement 3**: The rate of formation of \( O_2 \) is \( 0.5 \) times the rate of disappearance of \( N_2O_5 \).
- This is correct as derived from the rate expressions.

4. **Statement 4**: The rate of formation of \( NO_2 \) is equal to the rate of disappearance of \( N_2O_5 \).
- This is incorrect because the rate of formation of \( NO_2 \) is \( 2 \) times the rate of disappearance of \( N_2O_5 \).

### Conclusion
The correct statement is **Statement 3**: The rate of formation of \( O_2 \) is \( 0.5 \) times the rate of disappearance of \( N_2O_5 \).

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