For a large number of molecules of a given gas at a specific temperature, the ratio of the most prob — States of Matter and Gaseous State Chemistry Question
Question
For a large number of molecules of a given gas at a specific temperature, the ratio of the most probable speed ($\alpha_{mp}$), average speed ($v_{av}$), and root mean square speed ($u_{rms}$) is exactly:
Answer: A
💡 Solution & Explanation
The formulas are $\alpha_{mp} = \sqrt{2RT/M}$, $v_{av} = \sqrt{8RT/\pi M}$, and $u_{rms} = \sqrt{3RT/M}$. Taking the ratio $\sqrt{2} : \sqrt{8/\pi} : \sqrt{3} \approx 1.414 : 1.595 : 1.732$, which simplifies to exactly $1 : 1.128 : 1.224$.
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