13.4 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cylinder of volume 30 litres has an initial gauge pressure of 15 atm and a temperature of 27 °C. After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 17 °C. Estimate the mass of oxygen taken out of the cylinder (R = 8.31 J mol^–1 K^–1, molecular mass of O₂ = 32 u).

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Payal Gupta | Contributor-Level 10

9 months ago

13.4 Volume of oxygen, $V_{1}$ = 30 litres = 30 $* 10^{- 3} m^{3}$

Gauge pressure, $P_{1}$ = 15 atm = 15 $* 1.013 * 10^{5}$ Pa

Temperature, $T_{1}$ = 27 $?$ = 300 K

Universal gas constant, R = 8.314 J/mole/K

Let the initial number of moles of oxygen gas cylinder be $n_{1}$

From the gas equation, we get $P_{1} V_{1} = n_{1} R T_{1}$

$n_{1} = \frac{P_{1} V_{1}}{R T_{1}}$ = $\frac{15 * 1.013 * 10^{5} * 30 * 10^{- 3}}{8.314 * 300}$ = 18.276

But $n_{1}$ = $\frac{m_{1}}{M}$ , where $m_{1}$ = initial mass of oxygen

M = Molecular m

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