The following data were obtained the first order thermal decomposition of `"N"_(2)"O"_(5)(g)` at constant volume : `2"N"_(2)"O"_(5)(g)to2"N"_(2)"O"_(4)(g)+"O"_(2)(g)`
`{:("S. No.",,,"Time/s",,,"Total pressure (atm)"),(1,,,0,,,0.5),(2,,,100,,,0.512):}`
Calculate the rate constant.

Explanation

To calculate the rate constant for the first-order thermal decomposition of \( \text{N}_2\text{O}_5(g) \), we will follow these steps:

### Step 1: Write the reaction and understand the initial conditions
The reaction is:
\[ 2 \text{N}_2\text{O}_5(g) \rightarrow 2 \text{N}_2\text{O}_4(g) + \text{O}_2(g) \]

At time \( t = 0 \):
- Total pressure \( P_0 = 0.5 \, \text{atm} \)
...