The following data were obtained during the first order thermal decomposition of `N_(2)O_(5)` (g) at constant volume:
`2N_(2)O_(5)(g) to 2N_(2)O_(4)(g) + O_(2)(g)`
`{:("S.no","Time", "Total Pressure / atm"),(1,0,0,5),(2,100,0.512):}`
Calculate the rate constant.

Explanation

To calculate the rate constant \( k \) for the first-order thermal decomposition of \( N_2O_5 \), we will follow these steps:

### Step 1: Understand the Reaction
The reaction is given as:
\[ 2N_2O_5(g) \rightarrow 2N_2O_4(g) + O_2(g) \]

### Step 2: Set Up the Initial Conditions
At time \( t = 0 \):
...