Question

The ratio of rms velocity of oxygen molecules at $ 327{}^\circ C $ to the rms velocity of hydrogen molecules at $ 27{}^\circ C $ . Given that molecular weights of hydrogen and oxygen are 2 and 32 respectively, is:

• A. $ 1 :\sqrt{8} $
• B. $ \sqrt{8}:1 $
• C. 8 : 1
• D. 1 : 8

Answer 1

Answer: (A)

Using the relation $ \frac{{{c}_{1}}}{{{c}_{2}}}=\frac{\text{rms}\,\text{velocity}\,\text{of}\,{{\text{O}}_{\text{2}}}}{\text{rms}\,\text{velocity}\,\text{of}\,{{\text{H}}_{\text{2}}}} $ $ =\sqrt{\frac{{{M}_{2}}}{{{M}_{1}}}\times \frac{{{T}_{1}}}{{{T}_{2}}}}=\sqrt{\frac{2\times 600}{32\times 300}}=1:\sqrt{8} $