Following data were obtained during the thermal decompoistion of sulphuryl chloride at constant volume and `285^(@)C`.
`SO_(2)Cl_(2)(g) rarr SO_(2) + Cl_(2)(g)`
`|{:("Time (s)",0,240,600),("Pressure (torr)",180,244,302):}|`
Show that it is first order reaction.

Explanation

To show that the thermal decomposition of sulfuryl chloride (SO₂Cl₂) is a first-order reaction, we will analyze the provided data and calculate the rate constant (k) for two different time intervals.

### Step-by-Step Solution:

1. **Write the Reaction:**
The thermal decomposition of sulfuryl chloride can be represented as:
\[
\text{SO}_2\text{Cl}_2(g) \rightarrow \text{SO}_2(g) + \text{Cl}_2(g)
...