The root mean square (rms) speed of hydrogen () gas is exactly times the rms speed of nitrogen () ga — States of Matter and Gaseous State Chemistry Question
Question
The root mean square (rms) speed of hydrogen ($H_2$) gas is exactly $\sqrt{7}$ times the rms speed of nitrogen ($N_2$) gas. If the absolute temperature of the $N_2$ gas is $300\text{ K}$, what is the exact absolute temperature of the $H_2$ gas (in $\text{K}$)?
Answer: 150
💡 Solution & Explanation
Given $U_{rms}(H_2) = \sqrt{7} \times U_{rms}(N_2)$. $\sqrt{3RT_{H_2}/2} = \sqrt{7} \times \sqrt{3R(300)/28}$. Squaring both sides gives $3RT_{H_2}/2 = 7 \times 3R(300)/28$. Simplifying: $T_{H_2}/2 = 7 \times 300 / 28 = 300 / 4 = 75$. Therefore, $T_{H_2} = 75 \times 2 = 150\text{ K}$.
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