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 After some oxygen is withdrawn from the cylinder, the pressure drops to 11 atm and its temperature drops to $17^{\circ }C$.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 $(R=8.3Jmol{e}^{-1}{K}^{-1}$ molecular mass of $O_2=32)$

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

Answer 1

Answer: (B)

$n_1=\frac{P_1{V}_1}{R{T}_1}=\frac{(15atm)(30L)}{R(27+273)K}$
$n_1=\frac{\left(15\times 1.01\times 10^5\right)\left(30\times 10^{-3}\right)}{(8.3)(300)}$
$=18.253$
Initial mass of $O_2$ in cylinder $\left(m_1\right)=n_{1}M$
$=18.253\times 32$ $=584.1g$
Similarly,
$n_2=\frac{P_2{V}_2}{R{T}_2}$
$=\frac{\left(11\times 1.01\times 10^5\right)\left(30\times 10^{-3}\right)}{(8.3)(290)}=13.847$
$m_2=n_{2}M=13.847\times 32=443.1g$
Mass of oxygen taken out $=m_1-m_2$
$=584.1g-443.1g=141g$