In a reversible reaction, $2{\mathrm{NO}}_2\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_4$the rate of disappearance of NO₂ is equal to

$2{\mathrm{NO}}_2\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_4$

$2\mathrm{N}{\mathrm{O}}_2\underset{{\mathrm{K}}_2}{\stackrel{{\mathrm{k}}_1}{\iff }}{\mathrm{N}}_2{\mathrm{O}}_4$.
For forward reaction, Rate$=-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}=\frac{{\mathrm{dN}}_2{\mathrm{O}}_4}{\mathrm{dt}}= {\mathrm{k}}_1{\left[{\mathrm{NO}}_2\right]}^2$
For backward reaction,                                               

$\text{Rate}=-\frac{\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_4\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}={\mathrm{k}}_2\left[{\mathrm{N}}_2{\mathrm{O}}_4\right]$.
Rate of disappearance of NO₂ = (Rate of disappearance of NO₂- Rate of                                                                                          appearance of NO₂)
                                $=2{\mathrm{k}}_1{\left[{\mathrm{NO}}_2\right]}^2-2{\mathrm{k}}_2\left[{\mathrm{N}}_2{\mathrm{O}}_4\right]$.