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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

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Here, `V= 25.0 m^(3) , T=27+273 = 300 K , K=1.38 xx 10^(-23) JK^(-1)` ,
Now `PV = nRT = n(Nk)T = (nN)kT = N'kT` where `nN=N'` = total no. Of air molecules in the given gas
`:. N' =(PV)/(kT) = ((1.01xx10^(5))xx25)/((1.38 xx 10^(-23))xx300) = 6.10 xx 10^(26)`.
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