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Mechanical Properties Of Fluids

Question
CBSEENPH11020182
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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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J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 = 32μ).

Solution
Volume of oxygen, V1 = 30 litres = 30 × 10–3 m3 

Gauge pressure, P1 = 15 atm = 15 × 1.013 × 105 Pa 
Temperature, T1 = 27°C = 300 K 
Universal gas constant, R = 8.314 J mole–1 K–1 

Let the initial number of moles of oxygen gas in the cylinder be n1. 
The gas equation is given as, 
P1V1 = n1RT1 

∴ n1 = fraction numerator straight P subscript 1 straight V subscript 1 over denominator RT subscript 1 end fraction
       =fraction numerator 15.195 space cross times space 10 to the power of 5 space cross times space 30 space cross times space 10 to the power of negative 3 end exponent over denominator 8.314 space cross times space 300 end fraction
        =  18.276 
But n1 = m1 / M 

where, 
m1 = Initial mass of oxygen
M = Molecular mass of oxygen = 32 g 
Therefore, 
m1 = n1M = 18.276 × 32 = 584.84 g 
After some oxygen is withdrawn from the cylinder, the pressure and temperature reduces. 
Volume, V2 = 30 litres = 30 × 10–3 m3 

Gauge pressure, P2 = 11 atm
                              = 11 × 1.013 × 105 Pa 
Temperature, T2 = 17°C = 290 K 
Let n2 be the number of moles of oxygen left in the cylinder. 
The gas equation is given as, 
P2V2 = n2RT2 

∴ n2 = P2V2/ RT2 

        =fraction numerator 11.143 space straight x 10 to the power of 5 space straight x space 30 space straight x space 10 to the power of negative 3 end exponent over denominator 8.314 space straight x space 290 end fraction
         =  13.86 
But, 
     n2 = m2 / M 

where, 
m2 is the mass of oxygen remaining in the cylinder 
∴ m2 = n2M = 13.86 × 32 = 453.1 g 
The mass of oxygen taken out of the cylinder is given by the relation, 
Initial mass of oxygen in the cylinder – Final mass of oxygen in the cylinder 
= m1 – m2 

= 584.84 g – 453.1 g 
= 131.74 g 
= 0.131 kg 
Therefore, 0.131 kg of oxygen is taken out of the cylinder.

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