Kinetic Theory

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Question : 4
Total: 14
An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27°C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17°C. Estimate the mass of oxygen taken out of the cylinder (R=8.31Jmol1K1, molecular mass of O2=32u).
Solution:  
Here, initially in the oxygen cylinder
Volume V1=30litres=30×103m3
Pressure P1=15atm
=15×1.013×105Pa
Temperature T1=27+273=300K
If the cylinder contains n1 moles of the oxygen gas then P1V1=n1RT,
n1=
P1V1
RT1

=
15×1.013×105×30×103
8.31×300

=18.253
Initial mass of oxygen in the cylinder
m1=n1× molecular weight of O2
=18.253×32=584.1g
Finally in the oxygen cylinder, let n2 moles of oxygen be left Final volume V2=30×103m3
Final pressure P2=11atm
=11×1.013×105Pa
Final temperature T2=17+273=290K
n2=?
Now,P2V2=n2RT2
n2=
P2V2
RT2

=
(11×1.013×105)×(30×103)
8.31×290
Therefore, final mass of the oxygen gas in the cylinder
m2=n2× molecular weight of O2=13.847×32=443.1g
Mass of oxygen gas taken out =m1m2
=(584.1443.1)=141g
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