Calculate the root-mean-square velocity of SO3 at 306 K

Answer 1

To calculate the root-mean-square velocity of a gas molecule, we use the formula:

vrms = sqrt(3kT/m)

Where:
- vrms is the root-mean-square velocity
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the molecule in kg/mol

The molar mass of SO3 (sulfur trioxide) is calculated as follows:
- Molar mass of S = 32.06 g/mol
- Molar mass of O = 16.00 g/mol
- Total molar mass of SO3 = (3*16.00) + 32.06 = 80.06 g/mol

Converting the molar mass of SO3 from g/mol to kg/mol:
80.06 g/mol x (1 kg / 1000 g) = 0.08006 kg/mol

Now, we can plug in the values into the formula:
vrms = sqrt(3(1.38 x 10^-23)(306)/(0.08006))

vrms = sqrt(1.005 x 10^-20 x 306 / 0.08006)

vrms = sqrt(3.843 x 10^-18 / 0.08006)

vrms = sqrt(4.801 x 10^-16)

vrms ≈ 6.93 x 10^(-8) m/s

Therefore, the root-mean-square velocity of SO3 at 306 K is approximately 6.93 x 10^(-8) m/s.