Question

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

• A. $3\times {10}^{11}$
• B. $1.5\times {10}^{11}$
• C. $0.75\times {10}^{11}$
• D. $6\times {10}^{11}$

Answer 1

The correct option is B $1.5\times {10}^{11}$

Given:
$T=300\text{K};P=2\text{atm}$
$KE=2\times {10}^{–9}\text{J};V={10}^{-3}{\text{m}}^3$

Average kinetic energy per molecules is given by,

$KE=\frac{3}{2}kT=\frac{3}{2}\frac{R}{N_A}T$

$\Rightarrow \frac{RT}{N_A}=\frac{2\times KE}{3}=\frac{4\times {10}^{-9}}{3}$

Ideal gas equation is given by,

$PV=\frac{N}{N_A}RT$

Putting the value in the above equation, we get

$2\times 1.01325\times {10}^5\times {10}^{-3}=N\times \frac{4\times {10}^{-9}}{3}$

$\therefore N=1.5\times {10}^{11}\text{molecules}$

Hence, option $\left(\text{C}\right)$ is correct.