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

NO₂ is consumed in forward reaction and is formed in backward reaction

rate of disappearance of NO₂ in forward reaction :

$-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}={\mathrm{K}}_1{\left[{\mathrm{NO}}_2\right]}^2$

rate of formation of NO2 in backward reaction 

$\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}={\mathrm{K}}_2\left[{\mathrm{N}}_2{\mathrm{O}}_4\right]$

net rate of disappearance of NO₂ 

$-\frac{\mathrm{d}\left[{\mathrm{NO}}_2\right]}{\mathrm{dt}}=2{\mathrm{K}}_1{\left[{\mathrm{NO}}_2\right]}^2-{\mathrm{K}}_2\left[{\mathrm{N}}_2{\mathrm{O}}_4\right]$