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 will follow these steps:

### Step 1: Understand the Reaction and Initial Conditions
The decomposition reaction is given as:
\[ 2N_{2}O_{5} (g) \rightarrow 2N_{2}O_{4} (g) + O_{2} (g) \]
We start with an initial pressure \( P_i = 1 \, \text{atm} \).

### Step 2: Determine the Final Pressure
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