At what temperature do oxygen () molecules have exactly the same root mean square () speed as helium — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

$U_{rms} = \sqrt{3RT/M}$. For speeds to be equal: $\sqrt{3RT_{O_2}/M_{O_2}} = \sqrt{3RT_{He}/M_{He}}$. Squaring both sides and substituting molar masses ($M_{O_2} = 32$, $M_{He} = 4$): $T_{O_2} / 32 = 300 / 4 \implies T_{O_2} = 75 \times 32 = 2400\text{ K}$.