Question

The thermal decomposition of $N_2{O}_5$ occurs in the following steps:
Step I $N_2{O}_5\stackrel{slow}{\to }N{O}_2+N{O}_3$
Step II $N_2{O}_5+N{O}_2\stackrel{fast}{\to }3N{O}_2+O_2$
Overall reaction $\overline{2N_2{O}_5\to 4N{O}_2+O_2}$
Suggest the rate expression.

Answer 1

Step $I:$

$N_2{O}_5\stackrel{Slow}{\to }{NO}_2+{NO}_3$

Step$II:$

$N_2{O}_5+{NO}_3\stackrel{fast}{\to }3{NO}_2{+O}_2$

Overall reaction$:2N_2{O}_5⟶4{NO}_2{+O}_2$
Generally, it is a complex reaction, the rate of overall reaction is determined by the $slow-step$ reaction.

$\therefore$ Rate of overall reaction $\left(R\right)$ =Rate of step $I=\frac{-d\left[N_2{O}_5\right]}{dt}=\frac{d\left[N{O}_2\right]}{dt}=\frac{d\left[{NO}_3\right]}{dt}$