(a) The reaction $\mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\frac{1}{2} \mathrm{O}_{2}(g)$ is first order. Near room temperature, the rate constant equals $7.0 \times 10^{-4} \mathrm{~s}^{-1} .$ Calculate the half-life at this temperature.
(b) At $415^{\circ} \mathrm{C},\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}$ decomposes in the gas phase, $\left(\mathrm{CH}_{2}\right)_{2} \mathrm{O}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{CO}(g) .$ If the reaction is first
order with a half-life of 56.3 min at this temperature, calculate the rate constant in $\mathrm{s}^{-1}$.