Question

Find the rms speed in air at 0.0 degrees celsius and 1.00 atm of the N2 molecules, the O2 molecules and the CO2 molecules

Answer 1

N₂= 697.24 m/s,

O₂= 652.38 m/s

CO₂= 393.35 m/s

Step-by-step explanation:

The rms speed,
`v_(rms)` of a gas is the following:

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

where R: is the ideal gas constant, T: is the temperature and M: is the molar mass.

Knowing that the molar mass of the given gases are:

N₂ = 14.0067 g/mol = 14.0067x10⁻³ kg/mol

O₂ = 15.999 g/mol = 15.999x10⁻³ kg/mol

CO₂ = 44.009 g/mol = 44.009x10⁻³ kg/mol

Also that T is 0 °C = 273 K, and R = 8.314 J/ K.mol = 8.314 kg.m². s⁻². K⁻¹. mol⁻¹. The rms speed of the gases are:

For N₂:

`v_(rms) = \sqrt (3 \cdot 8.314 (kg.m^(2))/(s^(2).K.mol) \cdot 273 K)/(14.0067 \cdot 10^(-3) (kg)/(mol)) = 697.24 m/s`

For O₂:

`v_(rms) = \sqrt (3 \cdot 8.314 (kg.m^(2))/(s^(2).K.mol) \cdot 273 K)/(15.999 \cdot 10^(-3) (kg)/(mol)) = 652.38 m/s`

For CO₂:

`v_(rms) = \sqrt (3 \cdot 8.314 (kg.m^(2))/(s^(2).K.mol) \cdot 273 K)/(44.009 \cdot 10^(-3) (kg)/(mol)) = 393.35 m/s`

Therefore, the rms speed of N₂ is 697.24 m/s, of O₂ is 652.38 m/s and of CO₂ is 393.35 m/s

I hope it helps you!