Find the rms speed of hydrogen molecules (M = 2 g/mol) and of oxygen molecules (M = 32 g/mol) at…

Step 1. Hydrogen. $v_{rms} = \sqrt{\dfrac{3 \times 8.314\ \text{J/(mol K)} \times 300\ \text{K}}{0.002\ \text{kg/mol}}} = 1934$ m/s.

Step 2. Oxygen. $3RT = 3 \times 8.314\ \text{J/(mol K)} \times 300\ \text{K} = 7483\ \text{J/mol}$, so $v_{rms} = \sqrt{\dfrac{7483\ \text{J/mol}}{0.032\ \text{kg/mol}}} = 484$ m/s.

Step 3. Ratio. $\dfrac{1934\ \text{m/s}}{484\ \text{m/s}} = 4$, which is $\sqrt{32/2} = \sqrt{16}$.