Question

The kinetic energy of $1 \,g$ molecule of a gas, at normal temperature and pressure is: $( R =8.321 \,J / mol - K )$

• A. $ 1.2\times 10^{2}J $
• B. $ 3.4\times 10^{3}J $
• C. $ 1.66\times 10^{4}J $
• D. $ 2.97\times 10^{4}J $

Answer 1

Answer: (B)

Average kinetic energy per molecule is equal to product of mass. of $1 \,g$ molecule and square of mean square velocity.
The kinetic energy of $1\, g - mol$ is
$E=\frac{1}{2} M \bar{v}^{2}=\frac{1}{2} M\left(\frac{3 R T}{M}\right)$
$\left[\because \bar{v}=\sqrt{\frac{3 R T}{M}}\right]$
$E=\frac{3}{2} R T$ where $R$ is gas constant.
Putting the numerical values, we have
$E=\frac{3}{2} \times 8.31 \times 273=3.4 \times 10^{3} J$