For the reaction ${\text{2N}}_{\text{2}}{\text{O}}_{\text{5(g)}}\to 4{\text{NO}}_{\text{2(g)}}+{\text{O}}_{\text{2(g)}}$ , the rate of reaction in terms of ${\text{O}}_{\text{2}}\text{ is }+\frac{\text{d}}{\text{dt}}\left[{\text{O}}_{\text{2}}\right]$  in terms of ${\text{N}}_2{\text{O}}_5$  it will be

      ${\text{2N}}_{\text{2}}{\text{O}}_{\text{5}}{}_{\left(\text{g}\right)}\to 4{\text{NO}}_{\text{2}}{}_{\left(\text{g}\right)}+{\text{O}}_{\text{2}}{}_{\left(\text{g}\right)}$

The rate is

$-\frac{1}{2}\frac{\text{d}\left[{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}\right]}{\text{dt}}=+\frac{1}{4}\frac{\text{d}\left[{\text{NO}}_{\text{2}}\right]}{\text{dt}}=+\frac{{\text{d[O}}_{\text{2}}]}{\text{dt}}$

The rate in terms of ${\text{N}}_{\text{2}}{\text{O}}_{\text{5}}$ $=-\frac{1}{2}\frac{\text{d}\left[{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}\right]}{\text{dt}}$