N_2 O_5 decomposes following first order kinetics according to the reaction 2 N_2 O_5( g ) → 4 NO_2( g )+ O_2( g ) N_2 O_5 is introduced in a closed…

$\displaystyle \mathrm{N}_2 \mathrm{O}_5$ decomposes following first order kinetics according to the reaction $$2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow 4 \mathrm{NO}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) $$ $\displaystyle \mathrm{N}_2 \mathrm{O}_5$ is introduced in a closed vessel. After $\displaystyle 46$ minutes, the pressure in the vessel is $\displaystyle 549.43$ mm of Hg . After a very long time, the pressure saturated at $\displaystyle 584.5$ mm of Hg. The rate constant of the reaction in $\displaystyle \mathrm{hr}^{-1}$ is \_\_\_\_. (Nearest integer) [Assume : $\displaystyle \ln 10=2.3$, Assume all gases behave as ideal gases]