Question

A $2.00mL$ volume container contains $50mg$ of gas at a pressure of $100kPa$. The mass of each gas particle is $8.0\times {10}^{-26}kg$. Find the average translational kinetic energy of each particle.

Answer 1

Mass of one mole of gas will be

$M=\left(8X{10}^{-23}\right)\left(6.022X{10}^{23}\right)g=48.18g$

Thus number of moles will be

$n=\frac{m}{M}=\frac{0.05}{48.18}=1.04X{10}^{-3}$

Thus temperature is $T=\frac{PV}{nR}=\frac{{10}^5\left(2X{10}^{-6}\right)}{\left(1.04X{10}^{-3}\right)\left(8.314\right)}=23.13K$

Translational energy per particle is

$e=\frac{3}{2}kT=\frac{3}{2}\left(1.38X{10}^{-23}\right)\left(23.13\right)=4.88X{10}^{-22}J$

Answer is $4.88X{10}^{-22}J$