Question

if He(g) has an average kinetic energy of 4610 J/mol under certain conditions, what is the root mean square speed of N2(g) molecules under the same conditions?

Answer 1

We know

Vrms=RT/M

where

Vrms→RMS velocity of the gas

T→absolute temperature of the gas

M→Molar mass of the gas

R→Universal gas constant

So average molar kinetic energy of the gas

E=1/2 MV²rms =1/2 R T

This equation reveals that molar KE is independent of the nature of the gas .

It only depends on temperature .

So both He(g) and N2(g) will have same average KE=4610J/mol .under the same condition of temperature.

So for N2(g) ------ 1/2MV_RMS² = 4610J/mol

molecular mass of N2 = 28g

therefore V_RMS² = 2x4610J/mol/28g/mol

      => Vrms = 2x4610J/mol/28g/mol

                     = 18.15ms-2