Question

An oxygen cylinder of volume $30$ litre has an initial gauge pressure of $15\, atm$ and a temperature of $27^{\circ}C$ After some oxygen is withdrawn from the cylinder, the gauge pressure drops to $11\, atm$ and its temperature drop to $17^{\circ}C$ Estimate the mass (in kg) of oxygen taken out of the cylinder, $R=8.3\,J\, mol^{-1}\,K^{-1}$, molecule weight of oxygen $=32$

Answer 1

Given, $P_{1} = 15+1$
= 16 atm (absolute)
$V_{1} = 30 \times 10^{-3}\,m^{3}$,
$T_{1} = 273 +27$
$=300\,K$
$P_{2} = 12\,atm$,
$T_{2} = 273 +17$
$=290\,K$
We have $PV=\frac{m}{M} RT$
$\therefore m=\frac{P_{1}VM}{RT_{1}}$
$=\left[\frac{\left(16\times1.013\times10^{5}\right)\times\left(30\times10^{-3}\right)\times\left(32\times10^{-3}\right)}{8.31\times300}\right]$
$=0.624\,kg$
Finally $m'=\frac{P_{2}VM}{RT_{2}}$
$=\left[\frac{\left(12\times1.013\times10^{5}\right)\times\left(30\times10^{-3}\right)\times\left(32\times10^{-3}\right)}{8.31\times290}\right]$
$=0.484\,kg$
The mass of the oxygen taken out $= m — m' $
$=0.624-0.484$
$= 0.141\,kg$