A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds (( vrms(helium)/vrms(argon))) is

Question

A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds (( vrms(helium)/vrms(argon))) is (A) 0.32 (B) 0.45 (C) 2.24 (D) 3.16

Tardigrade Admin · Accepted Answer

vrms=√(3RT/M) or vrms propto (1/√ M) ∴ ((vrms)He/(vrms)Ar)=√(MAr/MHe)=√(40/4) =√10=3.16

Q. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds $(\frac{v _{r m s} ( h e l i u m )}{v _{r m s (a r g o n)}})$ is

0.32

0.45

2.24

3.16

$v_{r m s} = \frac{3 RT}{M} or v_{r m s} \propto \frac{1}{M}$
$∴ \frac{( v _{r m s} ) He}{( v _{r m s} ) A r} = \frac{M _{A r}}{M _{He}} = \frac{40}{4}$
$= 10 = 3.16$

Q. A mixture of 2 moles of helium gas (atomic mass = 4 amu) and 1 mole of argon gas (atomic mass = 40 amu) is kept at 300 K in a container. The ratio of the rms speeds (vrms(argon)​vrms​(helium)​) is