The root-mean-square speed of CO at 113 °C is ________ m/s.
To calculate the root-mean-square speed of a gas molecule, we can use the formula:
vrms = √(3kT/m)
where:
- vrms is the root-mean-square speed
- k is the Boltzmann constant (1.38 × 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas molecule
First, we need to convert the temperature from Celsius to Kelvin:
113 °C + 273 = 386 K
The molar mass of CO (carbon monoxide) is:
m = 12.01 g/mol (for carbon) + 16.00 g/mol (for oxygen) = 28.01 g/mol = 0.02801 kg/mol
Now, we can plug the values into the formula:
vrms = √(3 * 1.38 × 10^-23 J/K * 386 K / 0.02801 kg/mol)
vrms = √(1.61 x 10^-20 J / kg)
vrms = 1.27 x 10^(-10/2) m/s
vrms = 1.27 x 10^-5 m/s
Therefore, the root-mean-square speed of CO at 113 °C is approximately 1.27 x 10^-5 m/s.