The average molar Kinetic Energy of N₂ and H₂ at the same Temperature are same.
Kinetic energy of a certain amount of gas of mass m is = [tex]\frac{1}{2}[/tex] m v² [Here, v = r.m.s velocity of the gas]
We know, the r.m.s velocity = [tex]\sqrt{\frac{3RT}M} }[/tex]
Here, T = Temperature
R = Universal gas constant
M = Molecular weight of the gas
∴ K.E. = [tex]\frac{1}{2}[/tex] × m × [tex]\frac{3RT}{M}[/tex] [By putting the value of v]
⇒ K.E. = [tex]\frac{3}{2}[/tex] n RT [n = number of moles of the gas, n= m/M]
For 1 mole of gas,
K.E. = [tex]\frac{3}{2}[/tex] RT
So,
- The average molar K.E. does not depend on the molecular weight of the gas.
- It depends only upon the Temperature.
As the temperature is same, so, the average molar kinetic energy of N₂ and H₂ will also be same.