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  4. What will be the number of molecules in 1 cm3 of a gas at a pressure of 1.38 atm and temperature 27°C ?

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Q. What will be the number of molecules in $1\,cm^3$ of a gas at a pressure of 1.38 atm and temperature $27^\circ$C ?

Thermodynamics

Solution:

$pV=n\,RT\,\Rightarrow \,n=\frac{pV}{RT}.Here\,nR=nN_A\,k$where $n\,N_A$ is the number of molecules in the sample.$Hence\,N=n N_A=\frac{pV}{kT} =\frac{1.38\,\times\,10^{-5}\,\times10^{-6}}{1.38 \times 10^-{23}\times\,300}=3.3\,\times 10^9$