The rate of the reaction 2 N_2 O_5 → 4 NO_2+ O_2 can be written in three ways: (-d[ N_2 O_5])/(d t)=k[ N_2 O_5]; (d[ NO_2])/(d t)=k^′[ N_2 O_5]; (d[…

The rate of the reaction $\displaystyle 2 \mathrm{~N}_2 \mathrm{O}_5 \rightarrow 4 \mathrm{NO}_2+\mathrm{O}_2$ can be written in three ways : $$\begin{aligned} & \frac{-d\left[\mathrm{~N}_2 \mathrm{O}_5\right]}{d t}=k\left[\mathrm{~N}_2 \mathrm{O}_5\right] \\ & \frac{d\left[\mathrm{NO}_2\right]}{d t}=k^{\prime}\left[\mathrm{N}_2 \mathrm{O}_5\right] \\ & \frac{d\left[\mathrm{O}_2\right]}{d t}=k^{\prime \prime}\left[\mathrm{N}_2 \mathrm{O}_5\right] \end{aligned} $$ The relationship between k and k' and between k and k" are :