Rate of disappearance of HI

                              $= \frac{-\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}$

Rate of appearance of ${\mathrm{I}}_2 = \frac{\mathrm{d}\left[{\mathrm{I}}_2\right]}{\mathrm{dt}}.$

From the chemical equation,
Rate of production ${\mathrm{I}}_2$

                $= \frac{1}{2}\times \mathrm{Rate} \mathrm{of} \mathrm{disappearance} \mathrm{of} \mathrm{HI}$

Therefore, $\frac{\mathrm{d}\left[{\mathrm{I}}_2\right]}{\mathrm{dt}} = \frac{1}{2} \frac{\mathrm{d}\left[\mathrm{HI}\right]}{\mathrm{dt}}.$

Rate of production of water

                      $= \frac{1}{2}\times \frac{\mathrm{d}\left[{\mathrm{H}}_2\mathrm{O}\right]}{\mathrm{dt}}$
Rate of disappearance of oxygen

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

The rate of the reaction is proportional to the
first power of the concentration of the reactant R. For example,

R → P