In the reversible reaction, 2 NO_2 k_2 k_1 leftharpoons N_2 O_4 the...

2 \mathrm{NO}_2 \underset{\mathrm{k}_2}{\stackrel{\mathrm{k}_1}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_4$Rate of reaction$=-\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}} =\mathrm{k}_1\left[\mathrm{NO}_2\right]^2-\mathrm{k}_2\left[\mathrm{~N}_2 \mathrm{O}_4\right] \therefore$Rate of disappearance of$\mathrm{NO}_2$i.e.$\frac{-\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=2 \mathrm{k}_1\left[\mathrm{NO}_2\right]^2-2 \mathrm{k}_2\left[\mathrm{~N}_2 \mathrm{O}_4\right]