The following first order reaction takes places at `410 K`:
`2CO(g) rarr CO_(2)(g)+C(s)`
The total pressure at the end of `401 s` after starting with pure `CO(g)` is found to be `0.313 atm`. At the time the reaction is `100%` complete, the total pressure is found to be `0.1645 atm`. Find
The rate constant of the reaction.

Explanation

To find the rate constant of the given first-order reaction, we will follow these steps:

### Step 1: Understand the Reaction
The reaction is:
\[ 2 \text{CO}(g) \rightarrow \text{CO}_2(g) + \text{C}(s) \]

### Step 2: Define Initial and Final Conditions
- Let the initial pressure of CO be \( P \).
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