The reaction `2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)` follows first order kinetics. The pressure of a vessel containing only `N_(2)O_(5)` was found to increase from 50 mm Hg to `87.5` mm Hg in 30 mim. The pressure exerted by the gases after 60 min. will be (Assume temperature remains constant):

Options

A. 106.25 mm Hg
B. 150 mm Hg
C. 125 mm Hg
D. 116.25 mm Hg

Answer

A

Explanation

Rate law for first order reaction `=k[N_(2)O_(5)]`
`:.` P = 12.5 mm Hg
`:. P_(0)=50&P(t = 30 min)`
`=25 "for" N_(2)O_(5)` reactant
`:. k=(2.303)/(30 min) xx log((50)/(25))=(2.303)/(60 min) xx log((50)/(x))`
On solving x = 12.5 mm Hg = 50-2p
`:.` P=18.75 mm Hg
`:.` Total pressure = 50 + 3P=106.25 mm Hg