Question
Hydrogen peroxide, which decomposes in a first-order reaction, has a half-life of 10 hours in air. How long will it take for hydrogen peroxide to decompose to $10 \%$ of its original concentration?
Step 1
The formula for the half-life of a first-order reaction is given by: \[ t_{1/2} = \frac{\ln(2)}{k} \] Given that the half-life (t_{1/2}) is 10 hours, we can rearrange the formula to solve for k: \[ k = \frac{\ln(2)}{t_{1/2}} \] Show more…
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Hydrogen peroxide, $\mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}),$ decomposes to $\mathrm{H}_{2} \mathrm{O}(\ell)$ and $\mathrm{O}_{2}(\mathrm{g})$ in a reaction that is first order in $\mathrm{H}_{2} \mathrm{O}_{2}$ and has a rate constant $k=1.06 \times 10^{-3} \mathrm{min}^{-1}$ (a) How long will it take for $15 \%$ of a sample of $\mathrm{H}_{2} \mathrm{O}_{2}$ to decompose? (b) How long will it take for $85 \%$ of the sample to decompose?
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