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 50 seconds at 400 K, the pressure of `Cl_2O_7` falls from 0.062 to 0.044 atm. Calculate the rate constant.

Explanation

To calculate the rate constant \( k \) for the decomposition of \( Cl_2O_7 \) at \( 400 \, K \), we will use the first-order reaction formula:

\[ k = \frac{2.303}{t} \log \left( \frac{P_0}{P_t} \right) \]

Where:
- \( P_0 \) is the initial pressure of \( Cl_2O_7 \)
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