An oxygen cylinder of volume $$30$$ liter has an initial gauge pressure of $$15$$ atm and a temperature of $$27$$∘C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to $$11$$ atm and its temperature drop to $$170C$$. Estimate the mass (in$$ kg $$) of oxygen taken out of the cylinder, $$R=8.3Jmol$$−$$1K$$−$$1$$, molecule weight of oxygen $$=32$$

Question

An oxygen cylinder of volume $$30$$ liter has an initial gauge pressure of $$15$$ atm and a temperature of $$27$$∘C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to $$11$$ atm and its temperature drop to $$170C$$. Estimate the mass (in$$ kg $$) of oxygen taken out of the cylinder, $$R=8.3Jmol$$−$$1K$$−$$1$$, molecule weight of oxygen $$=32$$

Infinity Learn · Accepted Answer

Given   $$P1=15+1$$​  $$=16$$ atm (absolute) ​$$V1=30$$×$$10$$−$$3m3$$​$$T1=273+27$$​$$=300K$$ $$P2=12atm$$​$$T2=273+17$$​$$=290K$$  ​ We have  $$PV=mMRT$$​∴ $$m=P1VMRT1$$​$$=$$[(16$$×$$1.013$$×$$105)×(30$$×$$10$$−$$3)×(32$$×$$10$$−$$3)8.31$$×$$300$$]​$$=0.624kg$$ Finally, m'$$=P2VMRT2$$​$$=$$[$$(12$$×$$1.013$$×$$105)×(30$$×$$10$$−$$3)×$$(32$$×$$10$$−$$3)8.31$$×$$290$$]​$$=0.484kg$$​ The mass of the oxygen taken out $$=m$$−m'​$$=0.624$$−$$0.484$$​$$=0.14kg$$ .

Kinetic theory of ideal gases

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