Question

If He(g) has an average kinetic energy of 6750 J/mol under certain conditions, what is the root mean square speed of O2(g) molecules under the same conditions?

Answer 1

He:

KE_ave = ½ M( Vrms)²

Vrms = [2 KE_ave / M]^1/2

M = molar mass of He = 4 x 10^-3 kg/mol

Given that  average kinetic energy KE_ave = 6750 J/mol

Hence,

Vrms = [2 KE_ave / M]^1/2

= [2 x 6750 J/mol / 4 x 10^-3 kg/mol]^1/2

   = 1837.1 m/s

Vrms = 1837.1 m/s

Therefore,

root mean square speed of He = 1837.1 m/s

O2:

Vrms =  [3 RT / M]^1/2

Vrms (O2) /Vrms (He) =  [M_He/ M_O2]^1/2

   Vrms (O2) = Vrms (He) x   [M_He/ M_O2]^1/2

      =   (1837.1 m/s) x [4 x 10^-3 / 32 x 10^-3]^1/2

= 649.5 m/s

  Vrms (O2) =    649.5 m/s

Therefore, root mean square speed of O2(g) molecules =  649.5 m/s