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In the reversible reaction, $2 \mathrm{NO}_2 \underset{\mathrm{k}_2}{\stackrel{\mathrm{k}_1}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_4$ the rate of disappearance of $\mathrm{NO}_2$ is equal to
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$2 k_1\left[\mathrm{NO}_2\right]^2-2 k_2\left[\mathrm{~N}_2 \mathrm{O}_4\right]$
$2 \mathrm{NO}_2 \underset{\mathrm{k}_2}{\stackrel{\mathrm{k}_1}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_4$
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. $\frac{-\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=2 \mathrm{k}_1\left[\mathrm{NO}_2\right]^2-2 \mathrm{k}_2\left[\mathrm{~N}_2 \mathrm{O}_4\right]$
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. $\frac{-\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=2 \mathrm{k}_1\left[\mathrm{NO}_2\right]^2-2 \mathrm{k}_2\left[\mathrm{~N}_2 \mathrm{O}_4\right]$
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