2. The decomposition reaction of N$_2$O$_5$ as shown below:
2N$_2$O$_5$ $\longrightarrow$ 4NO$_2$ + O$_2$
Given that $\frac{d[O_2]}{dt}$ = k[N$_2$O$_5$]. At 45°C, the rate constant k has a value of 1.5 x 10$^{-4}$ s$^{-1}$.
(a) Determine the half-life of N$_2$O$_5$ at 45 °C.
(b) Given the initial N$_2$O$_5$ concentration is 2.50 mol L$^{-1}$, determine the percentage of N$_2$O$_5$
decomposed after 50 min.