Question

An oxygen cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of $27^{\circ} C$. After some oxygen is withdrawn from the cylinder, the pressure drops to 11 atm and its temperature drops to $17^{\circ} C$. Estimate the mass of oxygen taken out of the cylinder $\left(R=8.3 \,J \,mole ^{-1} K ^{-1}\right.$ molecular mass of $\left. O _{2}=32\right)$

• A. 131 g
• B. 141 g
• C. 153 g
• D. 164 g

Answer 1

Answer: (B)

$n_{1}=\frac{P_{1} V_{1}}{R T_{1}}=\frac{(15 \,atm )(30 \,L )}{ R (27+273) K }$
$n_{1}=\frac{\left(15 \times 1.01 \times 10^{5}\right)\left(30 \times 10^{-3}\right)}{(8.3)(300)}$
$=18.253$
Initial mass of $O _{2}$ in cylinder $\left(m_{1}\right)=n_{1} M$
$=18.253 \times 32$ $=584.1 \,g$
Similarly,
$n_{2}=\frac{P_{2} V_{2}}{R T_{2}}$
$=\frac{\left(11 \times 1.01 \times 10^{5}\right)\left(30 \times 10^{-3}\right)}{(8.3)(290)}=13.847$
$m_{2}=n_{2} M=13.847 \times 32=443.1 g$
Mass of oxygen taken out $=m_{1}-m_{2}$
$=584.1 \,g -443.1 \,g =141 \,g$