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WORKED EXAMPLE \( 12.5 \) The decomposition of hydrogen peroxide in dilute sodium hydroxide solution is described by the equation \[ 2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \text { at } \mathrm{O}_{2}(g) \] The reaction is first order in \( \mathrm{H}_{2} \mathrm{O}_{2} \), the rate constant for consumption of \( \mathrm{H}_{2} \mathrm{O}_{2} \) at \( 20^{\circ} \mathrm{C} \) is \( 1.8 \times 10^{-5} \mathrm{~s}^{-1} \), and the initial concentration of \( \mathrm{H}_{2} \mathrm{O}_{2} \) is \( 0.30 \mathrm{M} \). (a) What is the concentration of \( \mathrm{H}_{2} \mathrm{O}_{2} \) after \( 4.00 \mathrm{~h} \) ? (b) How long will it take for the \( \mathrm{H}_{2} \mathrm{O}_{2} \) concentration to drop to \( 0.12 \mathrm{M} \) ? (c) How long will it take for \( 90 \% \) of the \( \mathrm{H}_{2} \mathrm{O}_{2} \) to decompose? 45

          WORKED EXAMPLE \( 12.5 \)
The decomposition of hydrogen peroxide in dilute sodium hydroxide solution is described by the equation
\[
2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(l) \text { at } \mathrm{O}_{2}(g)
\]
The reaction is first order in \( \mathrm{H}_{2} \mathrm{O}_{2} \), the rate constant for consumption of \( \mathrm{H}_{2} \mathrm{O}_{2} \) at \( 20^{\circ} \mathrm{C} \) is \( 1.8 \times 10^{-5} \mathrm{~s}^{-1} \), and the initial concentration of \( \mathrm{H}_{2} \mathrm{O}_{2} \) is \( 0.30 \mathrm{M} \).
(a) What is the concentration of \( \mathrm{H}_{2} \mathrm{O}_{2} \) after \( 4.00 \mathrm{~h} \) ?
(b) How long will it take for the \( \mathrm{H}_{2} \mathrm{O}_{2} \) concentration to drop to \( 0.12 \mathrm{M} \) ?
(c) How long will it take for \( 90 \% \) of the \( \mathrm{H}_{2} \mathrm{O}_{2} \) to decompose?
45

WORKED EXAMPLE 12.5
The decomposition of hydrogen peroxide in dilute sodium hydroxide solution is described by the equation

2 H2O2(a q) ⟶ 2 H2O(l) at O2(g)

The reaction is first order in H2O2, the rate constant for consumption of H2O2 at 20^∘C is 1.8 × 10^-5 s^-1, and the initial concentration of H2O2 is 0.30 M.
(a) What is the concentration of H2O2 after 4.00 h ?
(b) How long will it take for the H2O2 concentration to drop to 0.12 M ?
(c) How long will it take for 90 % of the H2O2 to decompose?
45

Added by Nguy?N K.

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