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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol–1 K-1, molecular mass of O2 = 32 u).
Explanation: We have to consider 2 cases here and find the masses of O2 in each case and then by calculating the difference of those masses gives the the mass of oxygen taken out of the cylinder.
Given:
Initially, Case1
V1 = 30 litres = 0.03 m3
P1 = 15 atm = 15 × 1.01 × 105 Pa
T1 = 27+273 = 300 K
If n1 is the moles O2 in the cylinder, then by using
P1V1 = n1RT1 ---( Ideal Gas Law )
⇒ n1 = 
= 
⇒ n1 = 18.276 moles
Molecular weight of O2 (M) = 32 g
Initial mass of cylinder (m1) = n1M
⇒ m1 = n1M
⇒ m1 = (18.276 moles) × ( 32 g)
⇒ m1 = 584.84 g
Now,
Let n2 be the moles of O2 left in the cylinder
V2 = 30 litres = 0.03 m3
P2 = 11 atm = 11 × 1.01 × 105 Pa
T2 = 17+273 = 290 K
Thus n2 = 
= 
⇒ n1 = 13.86 moles
Therefore, m2 be the final mass of O2 in the cylinder
⇒ m2 = n2M
⇒ m2 = (13.86 moles) × ( 32 g)
⇒ m2 = 453.1 g
∴ the mass of oxygen taken out of the cylinder
Δm = m1-m2
⇒ Δm = 584.84 g - 453.1 g
⇒ Δm = 131.74 g
The mass of oxygen taken out of the cylinder is 131.74 g.