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Q.

A container of fixed volume has a mixture of three moles of hydrogen and two moles of helium in equilibrium at temperature T. Assuming the gases are ideal, the correct statement is

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a

The average energy per mole of the gas mixture is 2120RT

b

The average energy per molecule of the gas mixture is 2110kBT

c

The ratio of the rms speed of helium atoms to that of hydrogen molecules is 12

d

The ratio of the rms speed of helium atoms to that of hydrogen molecules is 21

answer is B.

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Detailed Solution

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Total energy of three moles of hydrogen is 523RT

Total energy of two moles of helium is 322RT

Total energy of mixture is 15+62RT=212RT

Average energy per mole of the mixture is 212RT2+3=2110RT

Average kinetic energy per molecule of the mixture is 15+62NRT=2110kBT

vrms=3RTMW,vHevH=24=12

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