Question

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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J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¯, molecular mass of O2 = 32 u).

Answer 1

Given that the volume of oxygen cylinder is 30 litre or 30× 10 −3   m 3 , initial pressure is 15 atm, temperature is 27 °C, the final pressure after oxygen is withdrawn is 11 atm and the final temperature is 17 °C.

Let P 1 be the initial pressure, V 1 be the initial volume, T 1 be the initial temperature and R be the universal gas constant, then by gas equation,

P 1 V 1 = n 1 R T 1 n 1 = P 1 V 1 R T 1

Here, n 1 is the initial number of moles.

Initial pressure P 1 is 15 atm or 15×1.013× 10 5  N/ m 2 .

Substitute the values in the above expression.

n 1 = ( 15×1.1013×10 ) 5 ×30× 10 −3 8.31×( 273+17 ) = ( 15×1.1013×10 ) 5 ×30× 10 −3 8.31×300 =18.3

Similarly, final number of moles n 2 is given as,

n 2 = P 2 V 2 R T 2

Here, P 2 is the final pressure, V 2 is the final volume and T 2 is the final temperature.

Final pressure P 2 is 11 atm or 11×1.013× 10 5  N/ m 2 .

Substitute the values in the above expression.

n 2 = 11×1.013× 10 5 ×30× 10 −3 8.314×( 273+17 ) = 11×1.013× 10 5 ×30× 10 −3 8.314×( 290 ) =13.9

Hence, the number of moles withdrawn from cylinder n d is,

n d = n 2 − n 1

Substitute the values in the above expression.

n d =18.3−13.9 =4.4

Let m be the mass of the gas taken out of cylinder, then

m= n d ×M

Here, M is the molecular mass of oxygen.

Substitute the values in the above expression.

m=4.4×32 =140.8 g =0.141 kg

Therefore, the mass of oxygen taken out of the cylinder is 0.141 kg.