In the course of the reaction
`CH_(3) COOCH_(3) (g) to C_(2)H_(4)(g)+H_(2)(g) +CO(g)`
the initial pressure was found to be `0.42` atm while after `6.5` minutes , it was `0.54` atm . If the reaction follows first order kinetics find the rate constant.

Explanation

To solve the problem step by step, we will use the first-order kinetics equation. The reaction given is:

\[ \text{CH}_3 \text{COOCH}_3 (g) \rightarrow \text{C}_2 \text{H}_4 (g) + \text{H}_2 (g) + \text{CO} (g) \]

### Step 1: Understand the Initial and Final Pressures
- The initial pressure (\(P_0\)) is given as \(0.42 \, \text{atm}\).
- The pressure after \(6.5\) minutes (\(P\)) is \(0.54 \, \text{atm}\).

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