The number of molecules in one litre of an ideal gas at 300 K and 2 atmospheric pressure

Question:

The number of molecules in one litre of an ideal gas at $300 \mathrm{~K}$ and 2 atmospheric pressure with mean kinetic energy $2 \times 10^{-9} \mathrm{~J}$ per molecules is :

  1. $0.75 \times 10^{11}$

  2. $3 \times 10^{11}$

  3. $1.5 \times 10^{11}$

  4. $6 \times 10^{11}$


Correct Option: , 3

Solution:

$\mathrm{KE}=\frac{3}{2} \mathrm{kT}$

$\mathrm{PV}=\frac{\mathrm{N}}{\mathrm{N}_{\mathrm{A}}} \mathrm{RT}$

$\mathrm{N}=\frac{\mathrm{PV}}{\mathrm{kT}}$

$=\mathrm{N}=1.5 \times 10^{11}$

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