A vessel contains an ideal gas at 27^@ C...

A vessel contains an ideal gas at `27^@ C` and pressure 200 kPa. The volume of the gas is 8.0 L. The molecules of the gas collide with the walls of the vessel and exert a pressure. The gas is allowed to leak till the pressure falls to 150 kPa and the temperature remains the same. The diameter of the ideal gas molecule is 300 pm. The average distance traveled by the molecule between collisions is termed as the mean free path. The mean free path of a gas molecule varies directly proportional to the temperature and inversely proportional to the pressure. Take, R = 8.3 J/mol K and `N_A = 6.02 xx 10^(23)`/mol.
The number of moles of the gas in the vessel before the gas was leaked is

0.64

0.48

0.16

0.8

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The correct Answer is:

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A vessel contains an ideal gas at 27^@ C and pressure 200 kPa. The volume of the gas is 8.0 L. The molecules of the gas collide with the walls of the vessel and exert a pressure. The gas is allowed to leak till the pressure falls to 150 kPa and the temperature remains the same. The diameter of the ideal gas molecule is 300 pm. The average distance traveled by the molecule between collisions is termed as the mean free path. The mean free path of a gas molecule varies directly proportional to the temperature and inversely proportional to the pressure. Take, R = 8.3 J/mol K and N_A = 6.02 xx 10^(23) /mol. The amount of gas leaked is

0.64 mol

`0.48 mol`

`0.16 mol`

`0.8 mol`

`2.07 xx 10^(-19 ) J`

`2.07 xx 10 ^(-20) J`

`2.07 xx 10^(-21)` J

`2.07 xx 10^(-22) J`

`V/(RT)(P+P')`

`V/(2RT)(P+P')`

`V/(RT)(P-P')`

`V/(2RT)(P-P')`