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

Molecular Speeds

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Three types of molecular speed: (1) Most probable (u_mp) = sqrt(2RT/M) = speed at peak of Maxwell-Boltzmann distribution. (2) Average (u_avg) = sqrt(8RT/(piM)) = arithmetic mean. (3) RMS (u_rms) = sqrt(3RT/M) = root mean square. Ratio: u_mp : u_avg : u_rms = 1 : 1.128 : 1.224 = sqrt(2) : sqrt(8/pi) : sqrt(3). All speeds proportional to sqrt(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 u_avg dependence).

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