Question

At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? 

Answer 1

Given : T₂ = 273 k,  M_o1 (oxygen)= 32 ×10^-3 kg/mole, M_o2 (hydrogen)= 4 ×10^-3 kg/mole

v_rms = \(\sqrt{\frac{3RT}{M_o}}\) 

The rms speed of oxygen molecule v₁ = \(\sqrt{\frac{3RT_1}{M_{o1}}}\) 

The rms speed of helium molecule v₂ = \(\sqrt{\frac{3RT_2}{M_{o2}}}\) 

When v₁ = v₂

 \(\sqrt{\frac{3RT_1}{M_{o1}}}\) = \(\sqrt{\frac{3RT_2}{M_{o2}}}\) 

∴  \(\frac{T_1}{M_{o1}}\) = \(\frac{T_2}{M_{o2}}\) 

∴ Temprature T₁ = \(\frac{M_{o1}}{M_{o2}}.T_2\)

= \(\frac{32×10^{-3}×273}{4×10^{-3}}\) = 2184K

Answer = 2184 K