$($c$)$ In an experiment, it was found that the concentration of $N_2{O}_5$ in liquid bromine varied with time as follows:

$\backslash$table$[[$Time $($s$),0,200,400,600,1000],[[N_2{O}_5](mo{l}^{-}d{m}^{-3}),0\mathrm{.}110,0\mathrm{.}073,0\mathrm{.}048,0\mathrm{.}032,0\mathrm{.}014]]$

Determine graphically whether the reaction is first order or second order.

$(6)$

$($d$)$ A second$-$order reaction of the type $N+2MP$ was carried out in a solution that was initially $0\mathrm{.}075mold{m}^{-3}$ in $N$ and $0\mathrm{.}080mold{m}^{-3}$ in $M.$ After $1\mathrm{.}0h$ the concentration of $N$ had fallen to $0\mathrm{.}045mold{m}^{-3}.$ Calculate the rate constant and consequently the half$-$life of the reactants.