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Estimate the total number of air molecul...

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour and other constituents) in a room of capacity `25.0 m^(3)` at a temperature of `27^(@) C` and 1 atm pressure. (Boltzmann constant `= 1.38 xx 10^(-23) JK^(-1))`.

Text Solution

Verified by Experts

The correct Answer is:
6.12
As Boltzmann.s constant,
`k_B=R/N therefore R=k_B N`
Now PV=nRT=`nk_B NT`
`therefore` The number of molecules in the room
`=nN=(PV)/(Tk_B)`
`=(1.013 xx 10^5 xx 25.0)/(300 xx 1.38 xx 10^(-23))=6.117 xx 10^(26)`
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