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. 106.25m m Hg
B. 116.25m m Hg
C. 125m m Hg
D. 150m m Hg

Answer

A

Explanation

`2N_(2)O_(5) rarr 4NO_(2)+O_(2)`
`P_(o) " "-" "-`
`P_(o)-2p" "4p" "p`
`P_(T) =p_(o) -2p +4p +p =po+3p`
`p=(P_(T) -p_(o))/(3)" ….(1)"`
`p^(o) =p_(o)-2p=p_(o)-2 ((P_(T)-P_(o))/(3))`
`p^(o) =(3P_(o) -2P_(T) +2P_(o))/(3) =(5P_(o) -2P_(T))/(3) rArr K=(2.303)/(t) log""(P_(o))/(P^(o))=(2.303)/(t)" log "((3P_(o))/(5P_(o)-2P_(T)))`
at t=30 m in
`k=(2.303)/(30)" log "((3xx50)/(5xx50-2xx87.5))`
`k=0.023" at "t=60`
`k=(2.303)/(60)" log "((3xx50)/(5xx50-2P_(T)))`
`0.023 =(2.303)/(60)" log "(150)/(250-2P_(T)) rArr 4 = (150)/(250-2P_(T)) rArr 1000 -8P_(T) =150 rArr P_(T) =106.25`