$2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\to 4{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)$. What is the ratio of the rate of decomposition of ${\mathrm{N}}_2{\mathrm{O}}_5$ to the rate of formation of O₂ ?

$$\begin{gathered} 2{\mathrm{N}}_2{\mathrm{O}}_5\left(\mathrm{g}\right)\to 4{\mathrm{NO}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right) \\ \mathrm{Rate}=-\frac{1}{2}\frac{\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{dt}}=+\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}} \\ -\frac{\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{dt}}:\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{dt}}=2:1 \end{gathered}$$

Here, negative sign represents rate of decomposition and positive sign represents rate of formation.