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# What would be the final pressure of $O_2$ in following experiment ? A collapsed polyethylene bag of 30 litre capacity is partially blown up by the addition of 10 litre of $N_2$ at 0.965 atm at 298K . Subsequently enough $O_2$ is pumped into bag so that at 298K and external pressure of 0.990 atm, the bag contains full 30 litre.

$(a)\;6.68 atm\qquad(b)\;0.5 atm\qquad(c)\;0.8 atm\qquad(d)\;0.66 atm$

Given
Pressure of $N_2$ = 0.965 atm
Volume of $N_2$ = 10 litre
Temperature of $N_2$ = 298 K
For $N_2$ when bag is fully expanded ,
Volume of $N_2$ (alone) = 30 litre at 298 K
$\Rightarrow P_1V_1 = P_2V_2$
$\Rightarrow 0.965\times10 = P_2\times30$
$\therefore P_{N_2}$ (alone) in 30 litre bag at 298 K = 0.322 atm
Now
$P_M = P_{O_2} + P_{N_2}$
$\Rightarrow 0.990 = P_{O_2} + 0.322$
$\Rightarrow P_{O_2}$ = 0.668 atm