At a pressure of 3 atm air (treated an ideal gas) is pumped into the tubes of a cycle rickshaw. The volume of each tube at a given pressure is $0.004 m^{3}$ . One of the tubes gets punched and the volume of the tube reduces to $0.0008 m^{3}$ . Find the number of moles of air that have leaked out?
[Assume that the temperature remains constant at 300K. $R = 25 / 3 J {m o l}^{- 1} K^{- 1}$ ]

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Solution

$P_{1} = 3 a t m P_{2} = ?$
$V_{1} = 0.004 m^{3} = 4 L, V_{2} = 0.0008 m^{3} = 0.8 L$
$T = 300 K$

No. of moles before the leakage of the air,

$n_{1} = \frac{P V}{R T} = \frac{3 \times 4}{0.082 \times 300}$

$n_{1} = 0.488 m o l e$

No. of moles after the leakage of the air,

Assuming the pressure becomes equal to atmospheric pressure.
$P_{2} V_{2} = n_{2} R T$

$n_{2} = \frac{P V}{R T} = \frac{1 a t m \times 0.8 L}{0.082 L - a t m - m o l^{- 1} K^{- 1} \times 300 K} = 0.0325 m o l$

$∴$ leaked mole of gas = $0.488 - 0.0325 = 0.455 m o l$

No. of moles of air leaked out $= 0.455 m o l$

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