A vessel of volume $$33.2$$×$$10$$−$$3m3$$ contains an ideal gas at $$300K$$ and $$200$$ kPa. The gas is allowed to leak until the pressure falls to $$125$$ kPa. Calculate the amount of the gas (in$$ $$moles) leaked assuming that the temperature remains constant.

Question

A vessel of volume $$33.2$$×$$10$$−$$3m3$$ contains an ideal gas at $$300K$$ and $$200$$ kPa. The gas is  allowed to leak until the pressure falls to $$125$$ kPa. Calculate the amount of the gas  (in$$ $$moles) leaked assuming that the temperature remains constant.

Infinity Learn · Accepted Answer

As he gas leaks out, the volume and the temperature of the remaining gas do not change. The number of moles of the gas in the vessel is given by $n = \frac{P V}{R T}$ .
The number of moles in the vessel before the leakage is $n_{1} = \frac{P_{1} V}{R T}$ .
The number of moles in the vessel after the leakage is $n_{2} = \frac{P_{2} V}{R T}$ .
Thus, the number of moles leaked is $n_{1} - n_{2} = \frac{(P_{1} - P_{2}) V}{R T}$
$= \frac{(200 - 125) \times 10^{3} \times (33.2 \times 10^{- 3})}{8.3 (300)} = 1 m o l e$ .

Kinetic theory of ideal gases

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A vessel of volume $33.2 \times 10^{- 3} m^{3}$ contains an ideal gas at 300K and 200 kPa. The gas is allowed to leak until the pressure falls to 125 kPa. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.

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Kinetic theory of ideal gases

Remember concepts with our Masterclasses.

A vessel of volume 33.2×10−3m3 contains an ideal gas at 300K and 200 kPa. The gas is allowed to leak until the pressure falls to 125 kPa. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.

Ready to Test Your Skills?

free study material

A vessel of volume $33.2 \times 10^{- 3} m^{3}$ contains an ideal gas at 300K and 200 kPa. The gas is allowed to leak until the pressure falls to 125 kPa. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.