The decomposition reaction `2N_(2)O_(5) (g) rarr 2N_(2) O_(4) (g) +O_(2) (g)` is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After `Yxx10^(3)` s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is `5xx10^(-4) s^(-1)`, assuming ideal gas behavior, the value of Y is

Explanation

To solve the problem, we need to analyze the decomposition reaction of dinitrogen pentoxide (N2O5) and calculate the time (Y) at which the pressure inside the cylinder reaches 1.45 atm. We will use the information given about the reaction, the initial and final pressures, and the rate constant.

### Step-by-Step Solution:

1. **Write the Reaction and Initial Conditions**:
The decomposition reaction is:
\[
2N_{2}O_{5} (g) \rightarrow 2N_{2}O_{4} (g) + O_{2} (g)
...