Question

Compare the rms speed of hydrogen molecules at 127 ºC with rms speed of oxygen molecules at 27 ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively. 

Answer 1

M_o1 (hydrogen) = 2 g/mole

M_o2 (oxygen) = 32 g/mole

T₁ (hydrogen) = 273+127=400 K

T₂ (oxygen) = 273+27=300 K

The rms speed v_rms = $\sqrt{\frac{3RT}{M_o}}$ 

$\frac{v_{rms1}(hydrogen)}{v_{rms2}(oxygen)}$ = $\sqrt{\frac{M_{o2}{T}_1}{M_{o1}{T}_2}}$

= $\sqrt{\frac{32\times 400}{2\times 300}}$ = $\frac{8}{\sqrt{3}}$