A contair of volume `0.1m^(3)` is filled with nitrogen at a temperature of `47^(@)` C and a gauge pressure of `4.0xx10^(5)` Pa. After ome time, due to leakage, the gauge pressure drops to `3.0xx10^(5)` Pa and the temperature to `27^(@)` C. The mass of nitrogen that has leaked out is about-

Options

A. 128g
B. 84g
C. 154g
D. 226g

Answer

B

Explanation

`P_(1)=5xx10^(5)`
`V_(1)=0.1m^(3)`
`T_(1)=320K`
`n_(1)=(P_(1)V_(1))/(RT_(1))=(5xx10^(4))/(8.3xx320)`
`n_(2)=(4xx10^(4))/(8.3xx300)`
`Deltan=n_(1)-n_(2)=(10^(4))/(8.3)[(5)/(320)+(4)/(300)]`
`rArr(10^(4))/(8.3)[(1500-1280)/(300xx320)]`
`rArr(220xx10^(24))/(320xx3xx8.3xx10^(2))`
`rArr2.76` mole
Now of `N_(2)` leaked out `=2.763xx28`
`rArr77.28` gm
Most probable answer =84 gm