One mole of `N_(2)O_(4)` gas at 300 K is kept in a closed container at 1 atm. It is heated to 600 K when `20%` of `N_(2)O_(4)` decomposes to `NO_(2)(g).` The resultant pressure in the container would be

Options

A. 1.2 atm
B. 2.4 atm
C. 2.0 atm
D. 1.0 atm

Answer

B

Explanation

Initially, `p_(1)=1` atm, `T_(1)=300K, n_(1)="1 mol"`
`"Finally, "p=?," "T_(2)=600K`
When `20%` of `N_(2)O_(4)` decomposes to `NO_(2)`, then
`{:(,N_(2)O_(4)(g),hArr,2NO_(2)(g)),("Initial conc.","1 mol",,0),("Final conc.",=1(1-0.2),,2(0.2)),(,="0.8 mol",,"0.4 mol"):}`
Total number of moles after decomposition
`=0.8+0.4`
`="1.2 mol"`
From ideal gas equation,
`(p_(1)V)/(p_(2)V)=(n_(1)RT_(1))/(n_(2)RT_(2))`
`(1xxV)/(p_(2)xxV)=(1xxRxx300)/(1.2xxRxx600)`
`p_(2)=(1.2xx600)/(300)="2.4 atm"`