A rigid, evacuated vessel of negligible mass is simultaneously filled with equal…

CHEMISTRY · Multi-part · A Level · Chemistry · Amount of substance · Amount of substance

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 atm1.0\,\text{atm} at 300 K300\,\text{K}. The molar masses are 28 g mol−128\,\text{g\,mol}^{-1} for N2\text{N}_2 and 20.18 g mol−120.18\,\text{g\,mol}^{-1} for Ne. Assume ideal‐gas behavior in your analysis. (a) Calculate the ratio of the root‐mean‐square speeds vrms,N2/vrms,Nev_{\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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