if an unknown gas has one third the root mean squarevspeed of H2 at 300 K, what is the molar mass of the gas?

The molar mass of the gas : 18 x 10⁻³ kg/mol

Given

An unknown gas has one third the root mean square speed of H2 at 300 K

Required

the molar mass of the gas

Solution

Average velocities of gases can be expressed as root-mean-square (V rms)  

T = temperature, Mm = molar mass of the gas particles  , kg/mol

R = gas constant 8,314 J / mol K  

v rms An unknown gas = 1/3 v rms H₂

v rms H₂ :

V rms of unknown gas =