The reaction `SO_(2)Cl_(2) overset(k_(1))rarr SO_(2)+Cl_(2)` is a first order reaction with `k_(1) = 2.2 xx 10^(-5) s^(-1)` at `575 K`. What percentage of `SO_(2)Cl_(2)` will get decomposed in `90 min` when the reaction is carried out at `575 K`.

Explanation

To solve the problem, we will use the first-order reaction kinetics formula. The formula for a first-order reaction is given by:

\[ k = \frac{2.303}{t} \log \left( \frac{[A_0]}{[A]} \right) \]

Where:
- \( k \) is the rate constant,
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