Question

Calculate the rms speed of an oxygen gas molecule, o2, at 31.0 ∘c . express your answer numerically in meters per second.

Answer 1

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:

`v_(rms)=\sqrt{(3RT)/(M)`

where,

R = Gas constant = 8.314 J/K mol =
`8.314\text{ kg }m^2s^(-2)K^(-1)mol^(-1)`

T = Temperature of the gas = 31°C = (273 + 31)K = 304K

M = Molar mass of the gas =
`32g/mol=0.032kg/mol` (Gas is Oxygen)

Putting values in above equation, we get:

`v_(rms)=\sqrt{\frac{3* 8.314\text{ kg }m^2s^(-2)K^(-1)mol^(-1)* 304K}{0.032kg/mol}`

`v_(rms)=486.77m/s`