The rate constant of the first order, decomposition of `N_(2)O_(5)` at `25^(@)` is `3.00 xx 10^(-3) min^(-1)`. If the initial concentration of `N_(2)O_(2)` is `2.00 xx 10^(-3)` mol `L^(-1)`, How long will it take for the concentration to drop to `5.00 xx 10^(-4)` mol `L^(-1)`?

Explanation

To solve the problem, we need to use the first-order kinetics equation. The equation for the time taken for a first-order reaction to reach a certain concentration is given by:

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

Where:
- \( t \) = time taken
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