Question

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

Answer 1

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

Further explanation

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)  

$\large {\boxed {\bold {v_ {rms} = \sqrt {\dfrac {3RT} {Mm}}}}$

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 :

$\tt v_{rms}=\sqrt{\dfrac{3\times 8.314\times 300}{2.10^{-3}} }\\\\v_{rms}=1934.22$

V rms of unknown gas =

$\tt \dfrac{1}{3}\times 1934.22=644.74$

$\tt 644.74^2=\dfrac{3\times 8.314\times 300}{M_{gas}}\\\\M_{gas}=18\times 10^{-3}~kg/mol$