The root mean square (rms) velocity of hydrogen () gas is measured to be exactly times the rms veloc — States of Matter and Gaseous State Chemistry Question
Question
The root mean square (rms) velocity of hydrogen ($H_2$) gas is measured to be exactly $\sqrt{7}$ times the rms velocity of nitrogen ($N_2$) gas. If $T(N_2)$ and $T(H_2)$ are their respective absolute temperatures, which of the following is true?
Answer: C
💡 Solution & Explanation
$U_{rms}(H_2) = \sqrt{7} U_{rms}(N_2) \implies \sqrt{3RT_{H2}/2} = \sqrt{7} \sqrt{3RT_{N2}/28}$. Squaring both sides: $3RT_{H2}/2 = 7 \times (3RT_{N2}/28)$. Simplifying gives $T_{H2}/2 = T_{N2}/4$, or $T_{H2} = T_{N2}/2$. Thus, $T(H_2) < T(N_2)$.
💬Ask on WhatsApp →
Still have doubts about this question?
Send it to our AI chemistry tutor on WhatsApp — gets answered in minutes