The root mean square (rms) velocity of hydrogen () gas is times the rms velocity of nitrogen () gas. — States of Matter and Gaseous State Chemistry Question
Question
The root mean square (rms) velocity of hydrogen ($H_2$) gas is $\sqrt{7}$ times the rms velocity of nitrogen ($N_2$) gas. If the temperature of the nitrogen gas is $300\text{ K}$, what is the exact temperature of the hydrogen gas (in $\text{K}$)?
Answer: 150
💡 Solution & Explanation
Given $U_{rms}(H_2) = \sqrt{7} \times U_{rms}(N_2)$. $\sqrt{3RT_H / M_H} = \sqrt{7} \times \sqrt{3RT_N / M_N}$. Squaring both sides: $T_H / 2 = 7 \times (300 / 28)$. $T_H / 2 = 7 \times (300 / 28) = 300 / 4 = 75$. Thus, $T_H = 75 \times 2 = 150\text{ K}$.
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