Decomposition of H₂O₂ follows a first order reaction. In 50 min, the concentration of H₂O₂ decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of H₂O₂ reaches 0.05M, the rate of formation of O₂ will be

In fifty minutes, the concentration of H₂O₂ decreases from 0.5 to 0.125 M or in one half-time, concentration of H₂O₂  decreases from 0.5 to 0.25 M. In two half-lives, concentration of H₂O₂  decreases from 0.5 to 0.125 M or 2t_1/2 = 50 min, t_½  = 25 min

$\therefore \mathrm{k}=\left(\frac{0.693}{25}\right){\min }^{-1}$

$$\begin{gathered} \text{ Or }\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}=-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{\mathrm{dt}}=\frac{\mathrm{k}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{2} \\ =\frac{0.693\times 5\times {10}^{-2}}{2\times 25} \\ =6.93\times {10}^{-4}{\mathrm{Mmin}}^{-1} \end{gathered}$$