Part of JPC-10 — Surface Chemistry & States of Matter

Molecular Speeds

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Three types of molecular speed: (1) Most probable (umpu_{mp}) = sqrt2RTM\frac{2RT}{M} = speed at peak of Maxwell-Boltzmann distribution. (2) Average (uavgu_{avg}) = sqrt(8RTpiM\frac{RT}{piM}) = arithmetic mean. (3) RMS (urmsu_{rms}) = sqrt3RTM\frac{3RT}{M} = root mean square. Ratio: umpu_{mp} : uavgu_{avg} : urmsu_{rms} = 1 : 1.128 : 1.224 = sqrt(2) : sqrt8pi\frac{8}{pi} : sqrt(3). All speeds proportional to sqrtTM\frac{T}{M}. At higher T: distribution broadens, peak shifts right, all speeds increase. At higher M: all speeds decrease. Graham's law: rate of effusion proportional to 1/sqrt(M) (follows from uavgu_{avg} dependence).

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