At what temperature is the root mean square speed of hydrogen molecules equal to the root mean square speed of oxygen molecules at 27^{circ}text{C}?…

The root mean square speed is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$. For $v_{rms}$ of hydrogen to equal that of oxygen, $\frac{T_{H_2}}{M_{H_2}} = \frac{T_{O_2}}{M_{O_2}}$. Given $T_{O_2} = 27^{\circ}\text{C} = 300\text{ K}$, $M_{H_2} = 2$, and $M_{O_2} = 32$. Thus, $T_{H_2} = 300 \times \frac{2}{32} = \frac{300}{16} = 18.75\text{ K}$.