One litre of oxygen at a pressure of 1 atm and two litres of nitrogen at a pressure of 0.5 atm are introduced into a vessel of volume 1 litre. If there is no change in temperature, the final pressure of the mixture of gas (in atm) is

Options

A. 1.5
B. 2.5
C. 2
D. 4

Answer

C

Explanation

Ideal gas equation is given by
`pV=nRT` " "..(i)
For oxygen ,`P =1atm,V=1L,n=n_(0)`
Therefore,Eq (i) becomes
`therefore` " "` 1xx1=nO_(2)RT rArr n_(O_(2))=1/RT`
and `0.5xx2=n_(N_(2))RT rArr n_(N_(2))=1/RT`
For mixture of gas,
`P_(mix)V_(mix)=n_(mix)RT`
Here, `n_(mix)=n_(O_(2))+n_(N_(2))`
`therefore` " "`(P_(mix)V_(mix))/(RT)=1/RT+1/RT`
`rArr P_(mix)V_(mix)=2`