For the first order reaction 2 ~N_2 O_5(~g) 4 NO_2(g)+O_2(g)

(a) For a first order reaction, the concentration of reactant remaining after time $t$ is given by $[A]=[A]_0 e^{-k t}$ Therefore, concentration of reactant decreases exponentially with time. (b) Rise in temperature increases rate constant $(k)$ and therefore decreases half-life \left(t_{1/2}\right)$as t_{1/2}=$\frac{\operatorname{In} 2}{k}$\\ (d) For a first order reaction, if 100 moles of reactant is taken initially, after$n$half-lives, reactant remaining is given by$$\begin{aligned}& \text{ Percentage }A=100\left(\frac{1}{2}\right)^n=100\left(\frac{1}{2}\right)^8=0.3906 \\ & \Rightarrow \text{ A reacted }=100-0.3906=99.6 \% \end{aligned}$$(c) Half-life of first order reaction is independent of initial concentration.