We are given an equation that shows the differential rate change of the reaction and it is given as
![-(1)/(2)(d)/(dt)\lbrack N_2O_5\rbrack=(1)/(4)(d)/(dt)\lbrack NO_2\rbrack=(d)/(dt)\lbrack O_2\rbrack](https://img.qammunity.org/2023/formulas/chemistry/college/3pryi2lnxy0rgcvzzir8ne3z0ielphngyv.png)
This depicts the decomposition reaction of N₂O₅. The forward reaction (product) carries a positive sign while the backward reaction or (reactant) carries a negative sign.
We can as well integrate this, but for the sake of simplicity, the equation of reaction is given as
![2N_2O_5\rightleftarrows4NO_2+O_2](https://img.qammunity.org/2023/formulas/chemistry/college/e8c40cziclyjmv1o38ofd331181r2kqbfy.png)