For $2{\mathrm{H}}_2{\mathrm{O}}_2\to 2{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2$
if, the rates are given as, $\frac{-\mathrm{d}}{\mathrm{dt}}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]={\mathrm{K}}_1\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]$;
$\frac{+\mathrm{d}\left[{\mathrm{H}}_2\mathrm{O}\right]}{\mathrm{dt}}={\mathrm{K}}_2\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]\text{ and }\frac{+\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}={\mathrm{K}}_3\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]$

The given reaction is:

$2{\mathrm{H}}_2{\mathrm{O}}_2\to 2{\mathrm{H}}_2\mathrm{O}+{\mathrm{O}}_2$

The rate of the reaction will be written as:

$\frac{1}{2}\frac{-\mathrm{d}\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]}{\mathrm{dt}}=\frac{1}{2}\frac{+\mathrm{d}\left[{\mathrm{H}}_2\mathrm{O}\right]}{\mathrm{dt}}=\frac{+\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}$

This can be written as:

$$\begin{gathered} \frac{1}{2}{\mathrm{K}}_1\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]=\frac{1}{2}{\mathrm{K}}_2\left[{\mathrm{H}}_2{\mathrm{O}}_2\right]={\mathrm{K}}_3\left[{\mathrm{H}}_2{\mathrm{O}}_2\right] \\ \frac{1}{2}{\mathrm{K}}_1=\frac{1}{2}{\mathrm{K}}_2={\mathrm{K}}_3 \\ {\mathrm{K}}_1={\mathrm{K}}_2=2{\mathrm{K}}_3 \end{gathered}$$