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Question : 4 of 14
Marks: +1, -0
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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27°C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17°C. Estimate the mass of oxygen taken out of the cylinder (R=8.31Jmol1K1R = 8.31\,\mathrm{J}\,\mathrm{mol}^{-1}\,\mathrm{K}^{-1}, molecular mass of O2=32u\mathrm{O}_2 = 32\,\mathrm{u}).
Solution:  
Here, initially in the oxygen cylinder
Volume V1=30litres=30×103m3V_1 = 30\,\mathrm{litres} = 30 \times 10^{-3}\,\mathrm{m}^3
Pressure P1=15atmP_1 = 15\,\mathrm{atm}
=15×1.013×105Pa= 15 \times 1.013 \times 10^{5}\,\mathrm{Pa}
Temperature T1=27+273=300KT_1 = 27 + 273 = 300\,\mathrm{K}
If the cylinder contains n1n_1 moles of the oxygen gas then P1V1=n1RT,P_1V_1 = n_1RT,
n1=P1V1RT1n_{1}= \frac{P_{1} V_{1}}{R T_{1}}
=15×1.013×105×30×1038.31×300= \frac{15 \times 1.013 \times 10^{5} \times 30 \times 10^{-3}}{8.31 \times 300}
=18.253=18.253
Initial mass of oxygen in the cylinder
m1=n1×m_{1}=n_{1} \times molecular weight of O2\mathrm{O}_{2}
=18.253×32=584.1g=18.253 \times 32 = 584.1\,\mathrm{g}
Finally in the oxygen cylinder, let n2n_2 moles of oxygen be left Final volume V2=30×103m3V_2 = 30 \times 10^{-3}\,\mathrm{m}^3
Final pressure P2=11atmP_2 = 11\,\mathrm{atm}
=11×1.013×105Pa= 11 \times 1.013 \times 10^{5}\,\mathrm{Pa}
Final temperature T2=17+273=290KT_2 = 17 + 273 = 290\,\mathrm{K}
n2=?n_2 = ?
Now,P2V2=n2RT2\text{Now}, P_2 V_2 = n_2 R T_2
n2=P2V2RT2n_2 = \frac{P_2 V_2}{R T_2}
=(11×1.013×105)×(30×103)8.31×290= \frac{(11 \times 1.013 \times 10^{5}) \times (30 \times 10^{-3})}{8.31 \times 290}
Therefore, final mass of the oxygen gas in the cylinder
m2=n2×m_2 = n_2 \times molecular weight of O2=13.847×32=443.1g\mathrm{O}_2 = 13.847 \times 32 = 443.1\,\mathrm{g}
\therefore Mass of oxygen gas taken out =m1m2= m_1 - m_2
=(584.1443.1)=141g= (584.1 - 443.1) = 141\,\mathrm{g}
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