The decomposition of `Cl_2O_7" at "` 400 K in the gas phase to `Cl_2 and O_2` is a first order reaction. After 55 seconds at 400K, the pressure of `Cl_2` falls from 0.062 atm to 0.044 atm. Calculate the rate constant.
Also calculate the pressure of `Cl_2O_7` after 100 sec of decomposition at this temperature.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Reaction and Given Data
The decomposition of \( Cl_2O_7 \) at \( 400 \, K \) is a first-order reaction. We are given:
- Initial pressure of \( Cl_2 \) (\( P_i \)) = 0.062 atm
- Pressure of \( Cl_2 \) after 55 seconds (\( P_t \)) = 0.044 atm
- Time (\( t \)) = 55 seconds

...