Answer: The rms speed of an oxygen gas molecule is 486.77 m/s.
Explanation: The expression for the rms speed of the molecule is given by:
[tex]v_{rms}=\sqrt{\frac{3RT}{M}[/tex]
where,
R = Gas constant = 8.314 J/K mol = [tex]8.314\text{ kg }m^2s^{-2}K^{-1}mol^{-1}[/tex]
T = Temperature of the gas = 31°C = (273 + 31)K = 304K
M = Molar mass of the gas = [tex]32g/mol=0.032kg/mol[/tex] (Gas is Oxygen)
Putting values in above equation, we get:
[tex]v_{rms}=\sqrt{\frac{3\times 8.314\text{ kg }m^2s^{-2}K^{-1}mol^{-1}\times 304K}{0.032kg/mol}[/tex]
[tex]v_{rms}=486.77m/s[/tex]
