Question

A 30 litres oxygen cylinder has an initial temperature and gauge pressure of 27 0C and 20 atm respectively. When a certain amount of oxygen escapes from the cylinder the temperature and gauge pressure drops to 17 0C and 22 atm, respectively. Find the mass of oxygen that escaped the cylinder.
[R = 8.31 J mol-1 K -1, molecular mass of O2 = 32 u]​

Answer 1

$\large{\underline{\rm{\pink{\bf{Question:-}}}}}$

A 30 litres oxygen cylinder has an initial temperature and gauge pressure of $\sf 28^{o} \: C$ and 20 atm respectively.  When a certain amount of oxygen escapes from the cylinder the temperature and gauge pressure drops to $\sf 17^{o} \: C$ and 22 atm, respectively. Find the mass of oxygen that escaped the cylinder.

$\sf [R=8.31 \: J \: mol^{-1} \: K^{-1} , \: molecular \: mass \: of \: O_2 =32u]$

$\large{\underline{\rm{\pink{\bf{Given:-}}}}}$

Initial volume of oxygen, $\sf V_1=$ 30 liters = $\sf 30 \times 10^{-3} \: m^{3}$

Gauge pressure, $\sf P_1=$ 30, atm = $\sf 30 \times 1.013 \times 10^{5} \: Pa$

Temperature, $\sf T_1=27^{o} \: C = 300 \: K$

Universal gas constant, R = $\sf 8.314 \: J \: mole^{-1} \: K^{-1}$

$\large{\underline{\rm{\pink{\bf{To \: Find:-}}}}}$

The mass of oxygen that escaped the cylinder.

$\large{\underline{\rm{\pink{\bf{Solution:-}}}}}$

Let the initial number of moles of oxygen in the cylinder be $\sf n_1$

We know that,

$\sf P_1 \: V_1 = n_1RT_1$

$\sf ie. \: n_1=\dfrac{P_1}{RT_1}$

$\sf = \dfrac{30.39 \times 10^{5} \times 30 \times 10^{-3}}{8.314 \times 300}$

$\sf =36.552$

But,

$\sf n_1=\dfrac{m_1}{M}$

Where,

$\sf m_1=$ initial mass of oxygen

M = molecular mass of oxygen = 32 g

$\sf m_1=n_1 \times M=36.552 \times 32 =1169.6 \: g$

After some oxygen escapes,

Volume, $\sf V_2=30 \times 10^{-3} \: m^{3}$

Gauge pressure, $\sf P_2=22; \: atm \: =22 \times 1.013 \times 10^{5} \: Pa$

Temperature, $\sf T_2=17^{o} \: C=290 \: K$

Let the number of moles of oxygen  left in the cylinder be $\sf n_2$

Now,

$\sf P_2 \: V_2=n_2RT_2$

$\sf ie. \: n_2=\dfrac{P_2}{RT_2}$

$\sf = \dfrac{22.286 \times 10^{5} \times 30 \times 10^{-3}}{8.314 \times 290} =27.72$

But,

$\sf n_2=\dfrac{m_2}{M}$

Where, $\sf m_2=$ remaining mass of oxygen

$\sf ie. \: n_2=m_2 \times M =27.72 \times 32=906.2 \: g$

Therefore the mass of  oxygen that escaped the cylinder = $\sf m_1-m_2=1169.6-906.2=263.4 \: g$

Answer 2

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