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 solve the question regarding the reaction \(2N_2O_5 \rightarrow 4NO_2 + O_2\), we need to analyze the rates of formation and disappearance of the reactants and products involved in the reaction.

### Step-by-Step Solution:

1. **Write the Balanced Reaction**:
The balanced chemical equation is:
\[ 2N_2O_5 \rightarrow 4NO_2 + O_2 \]

2. **Identify the Rates of Change**:
The rate of reaction can be expressed in terms of the change in concentration of the reactants and products over time. For the reaction, we can denote:
- Rate of disappearance of \(N_2O_5\) as \(-\frac{1}{2} \frac{d[N_2O_5]}{dt}\)
- Rate of formation of \(NO_2\) as \(\frac{1}{4} \frac{d[NO_2]}{dt}\)
- Rate of formation of \(O_2\) as \(\frac{1}{1} \frac{d[O_2]}{dt}\)

3. **Relate the Rates**:
From the stoichiometry of the reaction:
- The rate of disappearance of \(N_2O_5\) is twice the rate of formation of \(NO_2\) and half the rate of formation of \(O_2\).
- Therefore, we can write:
\[ -\frac{1}{2} \frac{d[N_2O_5]}{dt} = \frac{1}{4} \frac{d[NO_2]}{dt} = \frac{1}{2} \frac{d[O_2]}{dt} \]

4. **Express the Relationships**:
From the above relationships, we can derive:
- The rate of formation of \(O_2\) is \(0.5\) times the rate of disappearance of \(N_2O_5\):
\[ \frac{d[O_2]}{dt} = 0.5 \left(-\frac{d[N_2O_5]}{dt}\right) \]

5. **Conclusion**:
Based on the stoichiometric coefficients and the rates of change, we can conclude that the rate of formation of \(O_2\) is indeed \(0.5\) times the rate of disappearance of \(N_2O_5\). Therefore, any statement claiming otherwise would be incorrect.

### Final Answer:
The correct statement is that the rate of formation of \(O_2\) is \(0.5\) times the rate of disappearance of \(N_2O_5\).

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