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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27°C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17°C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J m o l – 1 K – 1 , molecular mass of O 2 = 32 u ).
Solution:
Here, initially in the oxygen cylinder
VolumeV 1 = 30 litres = 30 × 10 – 3 m 3
PressureP 1 = 15 atm
= 15 × 1.013 × 10 5 P a
TemperatureT 1 = 27 + 273 = 300 K
If the cylinder containsn 1 moles of the oxygen gas then P 1 V 1 = n 1 R T ,
n 1 =
=
= 18.253
Initial mass of oxygen in the cylinder
m 1 = n 1 × molecular weight of O 2
= 18.253 × 32 = 584.1 g
Finally in the oxygen cylinder, letn 2 moles of oxygen be left Final volume V 2 = 30 × 10 − 3 m 3
Final pressureP 2 = 11 atm
= 11 × 1.013 × 10 5 P a
Final temperatureT 2 = 17 + 273 = 290 K
n 2 = ?
N o w , P 2 V 2 = n 2 R T 2
n 2 =
=
Therefore, final mass of the oxygen gas in the cylinder
m 2 = n 2 × molecular weight of O 2 = 13.847 × 32 = 443.1 g
∴ Mass of oxygen gas taken out = m 1 − m 2
= ( 584.1 − 443.1 ) = 141 g
Volume
Pressure
Temperature
If the cylinder contains
Initial mass of oxygen in the cylinder
Finally in the oxygen cylinder, let
Final pressure
Final temperature
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