`N_(2)O_(5)` decomposes to `NO_(2)` and`O_(2)` and follows first order kinetics. After `50` minutes the pressure inside the vessel increases from 50 mm Hg to `87.5 mmHg`. The pressure of the gaseous mixture afte 100 minute at constant temperature will be :

Options

A. 136,25 mm Hg
B. 106.25 mm Hg
C. 175.0 mm Hg
D. 116.25 mm Hg

Answer

B

Explanation

Total pressure at 50 minutes
`=50-p_(1)+2p_(1)+(p_(1))/(2)=87.5`
`50+(3p_(1))/(2)=87.5` If `(3p_(1))/(2)=37.5`
`:. p_(1)=(37.5 xx 2)/(3)=25`
At t=100 min `50-p_(2)" "2p_(2)" "(p_(2))/(2)`
50 minutes is half life period
For 100 minutes i.e. for 2 half lives `50-p_(2)=12.5`
`:. p_(2)=37.5` mm of Hg
Total pressure at 100 minutes
`=50-p_(2)+2p_(2)+(p_(2))/(2)`
`=50+(3p_(2))/(2)=50+(3)/(2) xx 37.5`
= 50 + 56.25, = 106.25 mm of Hg