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1 mol O2 at temperature 27^@C at STP (1....

1 mol `O_2` at temperature `27^@C` at STP `(1.01 times 10^5 N/m^2)` is kept in a vessel.Find the number of collisions the molecules experience(in SI) per second per unit area with the wall of the vessel.
[Given Boltzmann constant k=`1.38 times 10^-23 J//K`]

Text Solution

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Number of molecule in 1 mol of
`O_2=6.023 times 10^23`
`therefore` Mass of a molecule `m=32/(6.023times10^23times1000)`
`=5.316times10^-26kg`
Momentum of the molecule , `p=mv=msqrt((3kT)/m)=sqrt(3kTm)`
Change in momentum due to each collision
`Deltap=2P=2sqrt(3kTm)`
`2sqrt(3times1.38times10^-23times300times5.316times10^-26)`
`=5.139 times 10^-23 kg.m.s^-1`
IF the molecules experience .n. number of collisions per second per square metre of the wall,then the pressure of the gas will be
`p=nDeltapor,1.01times10^10=ntimes5.139times10^-23`
or,`n=1.965times10^27`
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