compare the root mean square velocities of he at 30 c and co2 at 300 c

Question

compare the root mean square velocities of he at 30 c and co2 at 300 c

Answer 1

How you calculate v_rms depends on the degrees of freedom of the particles of the gas.  Since He is a monoatomic gas, He atoms have 3 degrees of freedom.  However, CO₂ is polyatomic, and therefore can have more than 3 degrees of freedom.  I will show you how to calculate v_rms for He atoms, but you need to know the number of degrees of freedom to do the same calculation for CO₂ molecules.  That information is not in the problem statement.  (Perhaps it is given somewhere in your textbook?)

 

n = number of degrees of freedom of the gas particles = 3 (for a monoatomic gas like He)

m = mass of a gas particle = mass of a He atom (look it up in your book)

k = the Boltzmann constant (look it up in your book)

T = absolute temperature of the gas = (30 + 273) Kelvin (for the He gas at 30°C)

 

v_rms satsifies:

 

mv_rms²/2 = nkT/2

 

v_rms = √(3kT/m)

 

Plug in the numbers for He, and do the same calculation for CO₂.  Convert the temperature of the CO₂ to Kelvins, find the mass of a CO₂ molecule, and find out the number of degrees of freedom of a CO₂ molecule.  Then plug in the numbers and compare v_rms values for the He and CO₂ gases at their respective temperatures.