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 = \(\sqrt{\frac{3RT}{M_o}}\) 

\(\frac{v_{rms1}(hydrogen)}{v_{rms2}(oxygen)}\) = \(\sqrt{\frac{M_{o2}T_1}{M_{o1}T_2}}\)

= \(\sqrt{\frac{32×400}{2×300}}\) = \(\frac{8}{\sqrt 3}\)