We are given an equation that shows the differential rate change of the reaction and it is given as
[tex]-\frac{1}{2}\frac{d}{dt}\lbrack N_2O_5\rbrack=\frac{1}{4}\frac{d}{dt}\lbrack NO_2\rbrack=\frac{d}{dt}\lbrack O_2\rbrack[/tex]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
[tex]2N_2O_5\rightleftarrows4NO_2+O_2[/tex]