Answer:
209 m/s
Explanation:
From ideal gas law, the root mean square velocity of the gas particles is:
v = √(3RT / M)
where R is the ideal gas constant,
T is absolute temperature,
and M is molar mass.
The molar mass of water H₂O is 2(1) + 1(16) = 18 g/mol = 0.018 kg/mol.
The molar mass of carbon dioxide CO₂ is 1(12) + 2(16) = 44 g/mol = 0.044 kg/mol.
The average speed of the water molecules is 327 m/s, so the temperature of the gas mixture is:
327 m/s = √(3 × 8.314 J/K/mol × T / (0.018 kg/mol))
T = 77.2 K
The average speed of the carbon dioxide molecules is therefore:
v = √(3 × 8.314 J/K/mol × 77.2 K / (0.044 kg/mol))
v = 209 m/s
