Hydrogen peroxide `H_(2)O_(2)` (aq) decomposes to `H_(2)O`(l) and `O_(2)`(g) in a reaction that is first order in `H_(2)O_(2)` and has a rate constant `k=1.06xx10^(3) min^(-1)`
(i) How long will it takes for 15% of a sample of `H_(2)O_(2)` to decompose?
(ii) How long will it take for 87.5% of the sample to decompose?

Explanation

To solve the problem, we need to use the first-order reaction kinetics formula. The formula for the time taken for a certain percentage of a reactant to decompose in a first-order reaction is given by:

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

where:
- \( t \) = time taken for the reaction to reach a certain point
- \( k \) = rate constant
- \( A_0 \) = initial concentration of the reactant
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