Calculate the root-mean-square velocity of CO at 270 K .
Express the velocity in meters per second to three significant figures.
The root-mean-square velocity of a gas molecule can be calculated using the formula:
vrms = sqrt(3 * k * T / m)
Where:
vrms = root-mean-square velocity
k = Boltzmann constant (1.38 x 10^-23 J/K)
T = temperature in Kelvin (270 K)
m = molar mass of CO (28.01 g/mol)
First, we need to convert the molar mass of CO to kg/mol:
m = 28.01 g/mol * (1 kg / 1000 g) = 0.02801 kg/mol
Now we can plug in the values:
vrms = sqrt(3 * 1.38 x 10^-23 J/K * 270 K / 0.02801 kg/mol)
vrms = sqrt(3 * 1.38 x 10^-23 * 270 / 0.02801)
vrms = sqrt(1.6524 x 10^-20)
vrms = 1.2848 x 10^-10 m/s
Therefore, the root-mean-square velocity of CO at 270 K is approximately 1.28 x 10^3 m/s.