If, at a particular temperature, the average speed of CH4 molecules is 1000 mine/hr, what would be the average speed of CO2 molecules at the same temperature?
what is mine/hr ?
mass* 108.23.118.127averagespeed^2 is proportional to temp
mass CH4=16
mass CO2=44
avgspeedCO2=1000mine/hr * sqrt (16/44)
Sorry I meant mi/hr
To determine the average speed of CO2 molecules at the same temperature, we can use the concept of the root mean square (rms) velocity. The rms velocity is given by the equation:
v(rms) = √(3RT / M)
where:
v(rms) represents the rms velocity,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature in Kelvin (K), and
M is the molar mass of the gas.
First, let's find the molar mass of methane (CH4) and carbon dioxide (CO2):
- The molar mass of methane (CH4):
- Carbon (C) molar mass: 12.01 g/mol
- Hydrogen (H) molar mass: 1.008 g/mol
- Molar mass of methane (CH4) = (4 × H) + C = (4 × 1.008) + 12.01 ≈ 16.04 g/mol.
- The molar mass of carbon dioxide (CO2):
- Carbon (C) molar mass: 12.01 g/mol
- Oxygen (O) molar mass: 16.00 g/mol
- Molar mass of carbon dioxide (CO2) = (2 × O) + C = (2 × 16.00) + 12.01 ≈ 44.01 g/mol.
Now, let's substitute the values into the rms velocity equation:
v(CH4) = √(3RT / M(CH4))
v(CO2) = √(3RT / M(CO2))
Since the temperature is the same for both gases and the gas constant is constant, we can compare the average speeds by taking the ratio:
v(CO2) / v(CH4) = √(M(CH4) / M(CO2))
Substituting the values:
v(CO2) / v(CH4) = √(16.04 / 44.01) ≈ 0.634
Therefore, the average speed of CO2 molecules at the same temperature would be approximately 0.634 times the average speed of CH4 molecules.