The following data were reported for the decompoistion of `N_(2)O_(5)` in `C Cl_(4)` at `303 K`:
`|{:("Time (min)",120,160,200,240,oo),("Vol of" O_(2) (mL),37.70,45.85,52.67,58.34,84.35):}|`
Show that the reaction is the first order and calculate the rate constant.
Note: This is an example of direct-estimation of Product, i.e., `O_(2)`.

Explanation

To demonstrate that the decomposition of \( N_2O_5 \) in \( CCl_4 \) is a first-order reaction and to calculate the rate constant, we will follow these steps:

### Step 1: Understand the Reaction
The decomposition of \( N_2O_5 \) produces \( O_2 \) and \( NO_2 \). The reaction can be represented as:
\[ N_2O_5 \rightarrow NO_2 + O_2 \]

### Step 2: Gather the Data
We have the following data for the volume of \( O_2 \) produced at different times:
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