RMS speed of gas molecules
Molecular model of gases · Physics
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Study notes
Compute the rms speed of (a) hydrogen molecules (M = 2.0 g/mol) and (b) oxygen molecules (M = 32 g/mol) at 300 K. (c) What is their ratio, and why? Solution: c_rms = sqrt(3RT/M). (a) H2: sqrt(3 x 8.31 x 300 / 0.002) = sqrt(3,739,500) = 1934 m/s. (b) O2: sqrt(3 x 8.31 x 300 / 0.032) = sqrt(233,719) = 483 m/s. (c) Ratio = 1934/483 = 4.0 = sqrt(32/2): at the same temperature all gases share the same mean KE, so lighter molecules must move faster by sqrt(M_heavy/M_light).