Chemistry

Problem

A rigid, evacuated vessel of negligible mass is simultaneously filled with equal numbers of nitrogen molecules and neon atoms until the internal pressure reaches

1.0\,\text{atm}

300\,\text{K}

. The molar masses are

28\,\text{g\,mol}^{-1}

for

\text{N}_2

and

20.18\,\text{g\,mol}^{-1}

for Ne. Assume ideal‐gas behavior in your analysis. (a) Calculate the ratio of the root‐mean‐square speeds

v_{\text{rms,N}_2}/v_{\text{rms,Ne}}

at this temperature. (b) A small pinhole is opened briefly in the vessel wall. Determine which gas exits the vessel faster and by what factor, explaining your reasoning in terms of molecular motion.

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