At what temperature does the rms speed of O2 molecules equal 475 m/s?

Answer 1

Recall that the formula for root mean square speed is given by
v,rms = (3RT/M)^(1/2)
where
R = universal gas constant = 8.314 J/mol-K
T = temperature in K
M = molar mass in kg/mol

We know that the molar mass of O2 is 32 g/mol or 0.032 kg/mol, and the v,rms is equal to 475. Substituting,
475 = (3 * 8.314 * T / 0.032)^(1/2)
475^2 = 779.4375 * T
T = 225625 / 779.4375
T = 289.47 K
In degree Celsius, T = 289.47 - 273 = 16.5 C

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